We construct Seiberg-Witten curves for 5d N = 1 gauge theories whose Type IIB 5-brane configurati... more We construct Seiberg-Witten curves for 5d N = 1 gauge theories whose Type IIB 5-brane configuration involves an O7-plane and discuss an intriguing relation between theories with an O7 +-plane and those with an O7 −-plane and 8 D7-branes. We claim that 5-brane configurations with an O7 +-plane can be effectively understood as 5-brane configurations with a set of an O7 −-plane and eight D7-branes with some special tuning of their masses such that the D7-branes are frozen at the O7 −-plane. We check this equivalence between SU(N) gauge theory with a symmetric hypermultiplet and SU(N) gauge theory with an antisymmetric with 8 fundamentals, and also between SO(2N) gauge theory and Sp(N) gauge theory with eight fundamentals. We also compute the Seiberg-Witten curves for non-Lagrangian theories with a symmetric hypermultiplet, which includes the local P 2 theory with an adjoint.
Progress of theoretical and experimental physics, Aug 1, 2015
We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume... more We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local 1 2 K3 surface.
In this article we explore the duality between the low energy effective theory of fivedimensional... more In this article we explore the duality between the low energy effective theory of fivedimensional N = 1 SU (N) M −1 and SU (M) N −1 linear quiver gauge theories compactified on S 1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.
We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiple... more We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to propose (naively) inequivalent magnetic quivers, which will turn out to have the same moduli spaces of vacua, at least locally around their most singular loci. We encounter several interesting new phenomena occurring in the magnetic quivers, such as hypermultiplets between neighbouring symplectic gauge nodes and matter in two-index representations of unitary nodes. We also give a prescription for ...
For any 5d N=1 superconformal field theory, we propose a "complete" prepotential which ... more For any 5d N=1 superconformal field theory, we propose a "complete" prepotential which reduces to the perturbative prepotential for any of its possible gauge theory realizations, manifests its global symmetry when written in terms of the invariant Coulomb branch parameters, and is valid for the whole parameter region. As concrete examples, we consider SU(2) gauge theories with up to 7 flavors, Sp(2) gauge theories with up to 9 flavors, and Sp(2) gauge theories with 1 antisymmetric tensor and up to 7 flavors, as well as their dual gauge theories.
We study the Coulomb branch of class $\mathcal{S}_k$ $\mathcal{N} = 1$ SCFTs by constructing and ... more We study the Coulomb branch of class $\mathcal{S}_k$ $\mathcal{N} = 1$ SCFTs by constructing and analyzing their spectral curves.
In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors ... more In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-...
We show how to map Grothendieck’s dessins d’enfants to algebraic curves as Seiberg-Witten curves,... more We show how to map Grothendieck’s dessins d’enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d$$ \mathcal{N} $$N= 2 supersymmetric instanton partition functions and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent dessins with 4 punctures on the sphere. We find that the parametrizations obtained from a dessin should be related by certain duality for gauge theories. Then we will discuss that some dessins could correspond to conformal blocks satisfying certain rules in different minimal models.
We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, ortho... more We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $$ \mathcal{N} $$ N = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expa...
We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifo... more We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in [1], by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and ℤ2 gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.
We discuss Type IIB 5-brane configurations for 5d $$ \mathcal{N}=1 $$ N = 1 gauge theories with h... more We discuss Type IIB 5-brane configurations for 5d $$ \mathcal{N}=1 $$ N = 1 gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow from a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these SU(6) gauge theories.
We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are class... more We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are classified recently by geometry in [1]. We propose all the 5-brane web diagrams for these rank 2 theories and show dualities between some of different gauge theories with explicit duality map of mass parameters and Coulomb branch moduli. In particular, we explicitly construct 5-brane configurations for G 2 gauge theory with six flavors and its dual Sp(2) and SU(3) gauge theories. We also present 5-brane webs for SU(3) theories of Chern-Simons level greater than 5.
We consider 5d $$ \mathcal{N} $$ N = 1 Sp(1) gauge theory based on a brane configuration with an ... more We consider 5d $$ \mathcal{N} $$ N = 1 Sp(1) gauge theory based on a brane configuration with an O5-plane. At the UV fixed point, the theory with no matter enjoys enhanced global symmetry SU(2) or U(1) depending on the discrete theta angle θ = 0, π (mod 2π). A naive brane configuration with an O5-plane, however, does not distinguish two different theories, as it describes the weak coupling region. We devise a technique for computing 5d Seiberg-Witten curve of the two theories from the brane web with an O5-plane. Their Seiberg-Witten curves show that their M5 configurations under the presence of OM5-planes are different. The decompactification limit of each Seiberg-Witten curve also shows distinct phase structures in their Coulomb branch leading to significantly different (p, q) 5-brane configurations with an O5-plane in the strong coupling region.
We study the Coulomb branch of class S k N = 1 SCFTs by constructing and analyzing their spectral... more We study the Coulomb branch of class S k N = 1 SCFTs by constructing and analyzing their spectral curves.
We propose new five-dimensional gauge theory descriptions of six-dimensional N = (1, 0) superconf... more We propose new five-dimensional gauge theory descriptions of six-dimensional N = (1, 0) superconformal field theories arising from type IIA brane configurations including an ON 0-plane. The new five-dimensional gauge theories may have SO, Sp, and SU gauge groups and further broaden the landscape of ultraviolet complete five-dimensional N = 1 supersymmetric gauge theories. When we include an O8 −-plane in addition to an ON 0-plane, T-duality yields two O7 −-planes at the intersections of an ON 0-plane and two O5 0-planes. We propose a novel resolution of the O7 −-plane with four D7-branes in such a configuration, which enables us to obtain three different types of five-dimensional gauge theories, depending on whether we resolve either none or one or two O7 −-planes. Such different possibilities yield a new five-dimensional duality between a D-type SU quiver and an SO − Sp quiver theories. We also claim that a twisted circle compactification of a six-dimensional superconformal field theory may lead to a five-dimensional gauge theory different from those obtained through a simple circle compactification.
We calculate the fluctuations from the classical multiple M5-brane solution of ABJM action which ... more We calculate the fluctuations from the classical multiple M5-brane solution of ABJM action which we found in the previous paper. We obtain D4-brane-like action but the gauge coupling constant depends on the spacetime coordinate. This is consistent with the expected properties of M5-brane action, although we will need to take into account the monopole operators in order to fully understand M5-branes. We also see that the Nambu-Poisson bracket is hidden in the solution.
Progress of Theoretical and Experimental Physics, 2015
We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume... more We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local 1 2 K3 surface.
We study four-dimensional N = 1 Spin(10) gauge theory with a single spinor and N Q vectors at the... more We study four-dimensional N = 1 Spin(10) gauge theory with a single spinor and N Q vectors at the superconformal fixed point via the electric-magnetic duality and amaximization. When gauge invariant chiral primary operators hit the unitarity bounds, we find that the theory with no superpotential is identical to the one with some superpotential at the infrared fixed point. The auxiliary field method in the electric theory offers a satisfying description of the infrared fixed point, which is consistent with the better picture in the magnetic theory. In particular, it gives a clear description of the emergence of new massless degrees of freedom in the electric theory.
We propose a number of new Seiberg dualities of N = 1 quiver gauge theories. The new Seiberg dual... more We propose a number of new Seiberg dualities of N = 1 quiver gauge theories. The new Seiberg dualities originate in new S-dualities of N = 2 superconformal field theories recently proposed by Gaiotto. N = 2 S-dual theories deformed by suitable mass terms flow to our N = 1 Seiberg dual theories. We show that the number of exactly marginal operators is universal for these Seiberg dual theories and the 't Hooft anomaly matching holds for these theories. These provide strong evidence for the new Seiberg dualities. Furthermore, we study in detail the Klebanov-Witten type theory and its dual as a concrete example. We show that chiral operators and their non-linear relations match between these theories. These arguments also give non-trivial consistency checks for our proposal.
We construct Seiberg-Witten curves for 5d N = 1 gauge theories whose Type IIB 5-brane configurati... more We construct Seiberg-Witten curves for 5d N = 1 gauge theories whose Type IIB 5-brane configuration involves an O7-plane and discuss an intriguing relation between theories with an O7 +-plane and those with an O7 −-plane and 8 D7-branes. We claim that 5-brane configurations with an O7 +-plane can be effectively understood as 5-brane configurations with a set of an O7 −-plane and eight D7-branes with some special tuning of their masses such that the D7-branes are frozen at the O7 −-plane. We check this equivalence between SU(N) gauge theory with a symmetric hypermultiplet and SU(N) gauge theory with an antisymmetric with 8 fundamentals, and also between SO(2N) gauge theory and Sp(N) gauge theory with eight fundamentals. We also compute the Seiberg-Witten curves for non-Lagrangian theories with a symmetric hypermultiplet, which includes the local P 2 theory with an adjoint.
Progress of theoretical and experimental physics, Aug 1, 2015
We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume... more We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local 1 2 K3 surface.
In this article we explore the duality between the low energy effective theory of fivedimensional... more In this article we explore the duality between the low energy effective theory of fivedimensional N = 1 SU (N) M −1 and SU (M) N −1 linear quiver gauge theories compactified on S 1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.
We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiple... more We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to propose (naively) inequivalent magnetic quivers, which will turn out to have the same moduli spaces of vacua, at least locally around their most singular loci. We encounter several interesting new phenomena occurring in the magnetic quivers, such as hypermultiplets between neighbouring symplectic gauge nodes and matter in two-index representations of unitary nodes. We also give a prescription for ...
For any 5d N=1 superconformal field theory, we propose a "complete" prepotential which ... more For any 5d N=1 superconformal field theory, we propose a "complete" prepotential which reduces to the perturbative prepotential for any of its possible gauge theory realizations, manifests its global symmetry when written in terms of the invariant Coulomb branch parameters, and is valid for the whole parameter region. As concrete examples, we consider SU(2) gauge theories with up to 7 flavors, Sp(2) gauge theories with up to 9 flavors, and Sp(2) gauge theories with 1 antisymmetric tensor and up to 7 flavors, as well as their dual gauge theories.
We study the Coulomb branch of class $\mathcal{S}_k$ $\mathcal{N} = 1$ SCFTs by constructing and ... more We study the Coulomb branch of class $\mathcal{S}_k$ $\mathcal{N} = 1$ SCFTs by constructing and analyzing their spectral curves.
In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors ... more In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-...
We show how to map Grothendieck’s dessins d’enfants to algebraic curves as Seiberg-Witten curves,... more We show how to map Grothendieck’s dessins d’enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d$$ \mathcal{N} $$N= 2 supersymmetric instanton partition functions and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent dessins with 4 punctures on the sphere. We find that the parametrizations obtained from a dessin should be related by certain duality for gauge theories. Then we will discuss that some dessins could correspond to conformal blocks satisfying certain rules in different minimal models.
We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, ortho... more We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $$ \mathcal{N} $$ N = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expa...
We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifo... more We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in [1], by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and ℤ2 gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.
We discuss Type IIB 5-brane configurations for 5d $$ \mathcal{N}=1 $$ N = 1 gauge theories with h... more We discuss Type IIB 5-brane configurations for 5d $$ \mathcal{N}=1 $$ N = 1 gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow from a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these SU(6) gauge theories.
We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are class... more We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are classified recently by geometry in [1]. We propose all the 5-brane web diagrams for these rank 2 theories and show dualities between some of different gauge theories with explicit duality map of mass parameters and Coulomb branch moduli. In particular, we explicitly construct 5-brane configurations for G 2 gauge theory with six flavors and its dual Sp(2) and SU(3) gauge theories. We also present 5-brane webs for SU(3) theories of Chern-Simons level greater than 5.
We consider 5d $$ \mathcal{N} $$ N = 1 Sp(1) gauge theory based on a brane configuration with an ... more We consider 5d $$ \mathcal{N} $$ N = 1 Sp(1) gauge theory based on a brane configuration with an O5-plane. At the UV fixed point, the theory with no matter enjoys enhanced global symmetry SU(2) or U(1) depending on the discrete theta angle θ = 0, π (mod 2π). A naive brane configuration with an O5-plane, however, does not distinguish two different theories, as it describes the weak coupling region. We devise a technique for computing 5d Seiberg-Witten curve of the two theories from the brane web with an O5-plane. Their Seiberg-Witten curves show that their M5 configurations under the presence of OM5-planes are different. The decompactification limit of each Seiberg-Witten curve also shows distinct phase structures in their Coulomb branch leading to significantly different (p, q) 5-brane configurations with an O5-plane in the strong coupling region.
We study the Coulomb branch of class S k N = 1 SCFTs by constructing and analyzing their spectral... more We study the Coulomb branch of class S k N = 1 SCFTs by constructing and analyzing their spectral curves.
We propose new five-dimensional gauge theory descriptions of six-dimensional N = (1, 0) superconf... more We propose new five-dimensional gauge theory descriptions of six-dimensional N = (1, 0) superconformal field theories arising from type IIA brane configurations including an ON 0-plane. The new five-dimensional gauge theories may have SO, Sp, and SU gauge groups and further broaden the landscape of ultraviolet complete five-dimensional N = 1 supersymmetric gauge theories. When we include an O8 −-plane in addition to an ON 0-plane, T-duality yields two O7 −-planes at the intersections of an ON 0-plane and two O5 0-planes. We propose a novel resolution of the O7 −-plane with four D7-branes in such a configuration, which enables us to obtain three different types of five-dimensional gauge theories, depending on whether we resolve either none or one or two O7 −-planes. Such different possibilities yield a new five-dimensional duality between a D-type SU quiver and an SO − Sp quiver theories. We also claim that a twisted circle compactification of a six-dimensional superconformal field theory may lead to a five-dimensional gauge theory different from those obtained through a simple circle compactification.
We calculate the fluctuations from the classical multiple M5-brane solution of ABJM action which ... more We calculate the fluctuations from the classical multiple M5-brane solution of ABJM action which we found in the previous paper. We obtain D4-brane-like action but the gauge coupling constant depends on the spacetime coordinate. This is consistent with the expected properties of M5-brane action, although we will need to take into account the monopole operators in order to fully understand M5-branes. We also see that the Nambu-Poisson bracket is hidden in the solution.
Progress of Theoretical and Experimental Physics, 2015
We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume... more We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local 1 2 K3 surface.
We study four-dimensional N = 1 Spin(10) gauge theory with a single spinor and N Q vectors at the... more We study four-dimensional N = 1 Spin(10) gauge theory with a single spinor and N Q vectors at the superconformal fixed point via the electric-magnetic duality and amaximization. When gauge invariant chiral primary operators hit the unitarity bounds, we find that the theory with no superpotential is identical to the one with some superpotential at the infrared fixed point. The auxiliary field method in the electric theory offers a satisfying description of the infrared fixed point, which is consistent with the better picture in the magnetic theory. In particular, it gives a clear description of the emergence of new massless degrees of freedom in the electric theory.
We propose a number of new Seiberg dualities of N = 1 quiver gauge theories. The new Seiberg dual... more We propose a number of new Seiberg dualities of N = 1 quiver gauge theories. The new Seiberg dualities originate in new S-dualities of N = 2 superconformal field theories recently proposed by Gaiotto. N = 2 S-dual theories deformed by suitable mass terms flow to our N = 1 Seiberg dual theories. We show that the number of exactly marginal operators is universal for these Seiberg dual theories and the 't Hooft anomaly matching holds for these theories. These provide strong evidence for the new Seiberg dualities. Furthermore, we study in detail the Klebanov-Witten type theory and its dual as a concrete example. We show that chiral operators and their non-linear relations match between these theories. These arguments also give non-trivial consistency checks for our proposal.
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Papers by Futoshi Yagi