Papers by Nakarin Lohitsiri
Journal of High Energy Physics, Aug 1, 2015
In this note we study the effects of a magnetic field on transport using holographic models with ... more In this note we study the effects of a magnetic field on transport using holographic models with broken translational invariance. We show that, after carefully subtracting off non-trivial magnetisation currents, it is possible to express the DC transport currents of the boundary theory in terms of properties of a black hole horizon. This allows us to obtain simple analytic expressions for the electrical, thermoelectric and heat conductivity tensors. Our results apply to both isotropic and anisotropic models, including holographic Q-lattices and to certain theories where translational invariance is broken by linear sources for axions.
Journal of High Energy Physics, Jul 3, 2023
2-group symmetries arise in physics when a 0-form symmetry G [0] and a 1-form symmetry H [1] inte... more 2-group symmetries arise in physics when a 0-form symmetry G [0] and a 1-form symmetry H [1] intertwine, forming a generalised group-like structure. Specialising to the case where both G [0] and H [1] are compact, connected, abelian groups (i.e. tori), we analyse anomalies in such 'toric 2-group symmetries' using the cobordism classification. As a warm up example, we use cobordism to study various 't Hooft anomalies (and the phases to which they are dual) in Maxwell theory defined on non-spin manifolds. For our main example, we compute the 5th spin bordism group of B|G| where G is any 2-group whose 0-form and 1-form symmetry parts are both U(1), and |G| is the geometric realisation of the nerve of the 2-group G. By leveraging a variety of algebraic methods, we show that Ω Spin 5 (B|G|) ∼ = Z/m where m is the modulus of the Postnikov class for G, and we reproduce the expected physics result for anomalies in 2-group symmetries that appear in 4d QED. Moving down two dimensions, we recap that any (anomalous) U(1) global symmetry in 2d can be enhanced to a toric 2-group symmetry, before showing that its associated local anomaly reduces to at most an order 2 anomaly, when the theory is defined with a spin structure.
Journal of High Energy Physics, Sep 19, 2022
We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dime... more We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dimensions. By applying the method of 'anomaly interplay', which uses functoriality of cobordism and naturality of the η-invariant to relate anomalies in a group of interest to anomalies in other (finite or compact Lie) groups, we derive the anomaly for every representation in many examples motivated by flavour physics, including S 3 , A 4 , Q 8 , and SL(2, F 3). In the case of finite abelian groups, it is well known that anomalies can be 'truncated' in a way that has no effect on low-energy physics, by means of a group extension. We extend this idea to non-abelian symmetries. We show, for example, that a system with A 4 symmetry can be rendered anomaly-free, with only one-third as many fermions as naïvely required, by passing to a larger symmetry. As another example, we find that a well-known model of quark and lepton masses utilising the SL(2, F 3) symmetry is anomalous, but that the anomaly can be cancelled by enlarging the symmetry to a Z/3 extension of SL(2, F 3).
Journal of High Energy Physics, 2022
We study two well-known SU(N) chiral gauge theories with fermions in the symmetric, anti-symmetri... more We study two well-known SU(N) chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work argues that these theories exhibit a subtle mod 2 anomaly, ruling out certain phases in which the theories confine without breaking their global symmetry, leaving a gapless composite fermion in the infra-red. We point out that no such anomaly exists. We further exhibit an explicit path to the gapless fermion phase, showing that there is no kinematic obstruction to realising these phases.
SciPost physics, Mar 25, 2021
We give a general description of the interplay that can occur between local and global anomalies,... more We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordismbased version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.
Journal of High Energy Physics, Jul 1, 2020
We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond... more We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond the Standard Model (BSM) theories. We begin by considering four distinct, but equally valid, versions of the SM, in which the gauge group is taken to be G = G SM /Γ n , with G SM = SU(3) × SU(2) × U(1) and Γ n isomorphic to Z/n where n ∈ {1, 2, 3, 6}. In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the SU(3) × SU(2) factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups Ω Spin 5 (BG) using the Atiyah-Hirzebruch spectral sequence. In two cases we show that there are no global anomalies beyond the Witten anomaly, while in the other cases we show that there are no global anomalies at all, illustrating the subtle interplay between local and global anomalies. While freedom from global anomalies has been previously shown for the specific fermion content of the SM by embedding the SM in an anomaly-free SU(5) GUT, our results here remain true when the SM fermion content is extended arbitrarily. Going beyond the SM gauge groups, we show that there are no new global anomalies in extensions of the (usual) SM gauge group by U(1) m for any integer m, which correspond to phenomenologically well-motivated BSM theories featuring multiple Z bosons. Nor do we find any new global anomalies in various grand unified theories, including Pati-Salam and trinification models. We also consider global anomalies in a family of theories with gauge group SU(N) × Sp(M) × U(1), which share the phase structure of the SM for certain (N, M). Lastly, we discuss a BSM theory in which the SM fermions are defined using a spin c structure, for example by gauging B − L. Such a theory may be extended to all orientable four-manifolds, and we find no global anomalies.
arXiv (Cornell University), Jun 2, 2023
We study 4-dimensional SU(N) gauge theory with one adjoint Weyl fermion and fundamental matter-ei... more We study 4-dimensional SU(N) gauge theory with one adjoint Weyl fermion and fundamental matter-either bosonic or fermionic. Symmetries, their 't Hooft anomalies, and the Vafa-Witten-Weingarten theorems strongly constrain the possible bulk phases. The first part of the paper is dedicated to a single fundamental fermion or boson. As long as the adjoint Weyl fermion is massless, this theory always possesses a Z χ 2N chiral symmetry, which breaks spontaneously, supporting N vacua and domain walls between them for a generic mass of the matter fields. We argue, however, that the domain walls generically undergo a phase transition, and we establish the corresponding 3d gauge theories on the walls. The rest of the paper is dedicated to studying the multi-flavor fundamental matter. Here, the phases crucially depend on the ratio of the number of colors and the number of fundamental flavors. We also discuss the limiting scenarios of heavy adjoint and fundamentals, which align neatly with our current understanding of QCD and N = 1 super Yang-Mills theory.
Journal of High Energy Physics, Oct 12, 2022
't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. I... more 't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. In 3d one common anomaly is the parity anomaly in a T-symmetric theory where one cannot gauge the global symmetry group without breaking the time-reversal symmetry. We find that a T-symmetric SU(N) gauge theory with either fermionic or bosonic matter in the fundamental representation of the gauge group has a parity anomaly between the flavor group and T-symmetry provided that there is also a massless Majorana fermion in the adjoint representation of the gauge group. In particular, there is always a mixed anomaly between T and U(1) baryon symmetry. We then analyze the parity anomaly in this theory, together with the more recent mod 16 time-reversal anomaly, and give some free fermion proposals as candidates for the low energy phases consistent with the anomalies. We make brief comments about the large N limit and the T-broken regimes in the conclusion as well as related anomalies in 4d.
Journal of High Energy Physics, Apr 1, 2018
Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We constru... more Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.
Journal of High Energy Physics, May 1, 2020
We discuss anomaly cancellation in U(2) gauge theories in four dimensions. For a U(2) gauge theor... more We discuss anomaly cancellation in U(2) gauge theories in four dimensions. For a U(2) gauge theory defined with a spin structure, the vanishing of the bordism group Ω Spin 5 (BU(2)) implies that there can be no global anomalies, in contrast to the related case of an SU(2) gauge theory. We show explicitly that the familiar SU(2) global anomaly is replaced by a local anomaly when SU(2) is embedded in U(2). There must be an even number of fermions with isospin 2r +1/2, for r ∈ Z ≥0 , for this local anomaly to cancel. The case of a U(2) theory defined without a choice of spin structure but rather using a spin-U(2) structure, which is possible when all fermions (bosons) have half-integer (integer) isospin and odd (even) U(1) charge, is more subtle. We find that the recently-discovered 'new SU(2) global anomaly' is also equivalent, though only at the level of the partition function, to a perturbative anomaly in the U(2) theory, which is this time a combination of a mixed gauge anomaly with a gauge-gravity anomaly. This perturbative anomaly vanishes if there is an even number of fermions with isospin 4r + 3/2, for r ∈ Z ≥0 , recovering the condition for cancelling the new SU(2) anomaly. Alternatively, this perturbative anomaly can be cancelled by a Wess-Zumino term, leaving a low-energy theory with a global anomaly, which can itself be cancelled by coupling to topological degrees of freedom.
Journal of High Energy Physics, Jul 1, 2017
Within holography the DC conductivity can be obtained by solving a system of Stokes equations for... more Within holography the DC conductivity can be obtained by solving a system of Stokes equations for an auxiliary fluid living on the black hole horizon. We show that these equations can be derived from a novel variational principle involving a functional that depends on the fluid variables of interest as well as the time reversed quantities. This leads to simple derivation of the Onsager relations for the conductivity. We also obtain the relevant Stokes equations for bulk theories of gravity in four dimensions including a ϑF ∧ F term in the Lagrangian, where ϑ is a function of dynamical scalar fields. We discuss various realisations of the anomalous Hall conductivity that this term induces and also solve the Stokes equations for holographic lattices which break translations in one spatial dimension.
Journal of High Energy Physics, May 1, 2021
In this note we review the role of homotopy groups in determining nonperturbative (henceforth 'gl... more In this note we review the role of homotopy groups in determining nonperturbative (henceforth 'global') gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of π d (G) is neither a necessary nor a sufficient condition for there being a possible global anomaly in a ddimensional chiral gauge theory with gauge group G. To showcase the failure of sufficiency, we revisit 'global anomalies' that have been previously studied in 6d gauge theories with G = SU(2), SU(3), or G 2. Even though π 6 (G) = 0, the bordism groups Ω Spin 7 (BG) vanish in all three cases, implying there are no global anomalies. In the case of G = SU(2) we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.
Journal of High Energy Physics
2-group symmetries arise in physics when a 0-form symmetry G[0] and a 1-form symmetry H[1] intert... more 2-group symmetries arise in physics when a 0-form symmetry G[0] and a 1-form symmetry H[1] intertwine, forming a generalised group-like structure. Specialising to the case where both G[0] and H[1] are compact, connected, abelian groups (i.e. tori), we analyse anomalies in such ‘toric 2-group symmetries’ using the cobordism classification. As a warm up example, we use cobordism to study various ’t Hooft anomalies (and the phases to which they are dual) in Maxwell theory defined on non-spin manifolds. For our main example, we compute the 5th spin bordism group of B|𝔾| where 𝔾 is any 2-group whose 0-form and 1-form symmetry parts are both U(1), and |𝔾| is the geometric realisation of the nerve of the 2-group 𝔾. By leveraging a variety of algebraic methods, we show that $$ {\varOmega}_5^{\textrm{Spin}}\left(B\left|\mathbbm{G}\right|\right)\cong \mathbb{Z}/m $$ Ω 5 Spin B G ≅ ℤ / m where m is the modulus of the Postnikov class for 𝔾, and we reproduce the expected physics result for anoma...
Journal of High Energy Physics
't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. I... more 't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. In 3d one common anomaly is the parity anomaly in a T-symmetric theory where one cannot gauge the global symmetry group without breaking the time-reversal symmetry. We find that a T-symmetric SU(N) gauge theory with either fermionic or bosonic matter in the fundamental representation of the gauge group has a parity anomaly between the flavor group and T-symmetry provided that there is also a massless Majorana fermion in the adjoint representation of the gauge group. In particular, there is always a mixed anomaly between T and U(1) baryon symmetry. We then analyze the parity anomaly in this theory, together with the more recent mod 16 time-reversal anomaly, and give some free fermion proposals as candidates for the low energy phases consistent with the anomalies. We make brief comments about the large N limit and the T-broken regimes in the conclusion as well as related anomalies in 4d.
Journal of High Energy Physics
We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dime... more We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dimensions. By applying the method of ‘anomaly interplay’, which uses functoriality of cobordism and naturality of the η-invariant to relate anomalies in a group of interest to anomalies in other (finite or compact Lie) groups, we derive the anomaly for every representation in many examples motivated by flavour physics, including S3, A4, Q8, and SL(2, 𝔽3).In the case of finite abelian groups, it is well known that anomalies can be ‘truncated’ in a way that has no effect on low-energy physics, by means of a group extension. We extend this idea to non-abelian symmetries. We show, for example, that a system with A4 symmetry can be rendered anomaly-free, with only one-third as many fermions as naïvely required, by passing to a larger symmetry. As another example, we find that a well-known model of quark and lepton masses utilising the SL(2, 𝔽3) symmetry is anomalous, but that the anomaly can be ...
Journal of High Energy Physics, 2022
We study two well-known SU(N) chiral gauge theories with fermions in the symmetric, anti-symmetri... more We study two well-known SU(N) chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work argues that these theories exhibit a subtle mod 2 anomaly, ruling out certain phases in which the theories confine without breaking their global symmetry, leaving a gapless composite fermion in the infra-red. We point out that no such anomaly exists. We further exhibit an explicit path to the gapless fermion phase, showing that there is no kinematic obstruction to realising these phases.
First and foremost, I would like to express my enormous gratitude to my supervisor, David Tong. T... more First and foremost, I would like to express my enormous gratitude to my supervisor, David Tong. Through his excellent examples in teaching, writing, and his constant guidance on research, during my PhD years and when I was still an undergraduate, I have learned and enjoyed a lot of physics and gained a glimpse of understanding and experience how to progress in Academia. His delight when discussing physics is extremely contagious, and it has played a significant role to drive me forward. His supportive and caring words have pulled me out whenever I am stuck academically or emotionally. I could not wish for a better supervisor. I would like to thank my collaborators Aristomenis Donos and Joe Davighi. My first taste of theoretical physics research started with Aristos who generously accepted my request for a summer internship to work with him on the subject of holography. His encouragement made me feel a little more confident in myself to carry on along this path. Joe has been my office mate since my first day as a graduate student in DAMTP. His energy for physics and his willingness to share and discuss all sorts of ideas are very stimulating and conducive to doing exciting research.
Journal of High Energy Physics, 2020
We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond... more We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond the Standard Model (BSM) theories. We begin by considering four distinct, but equally valid, versions of the SM, in which the gauge group is taken to be G = GSM/Γn, with GSM = SU(3) × SU(2) × U(1) and Γn isomorphic to ℤ/n where n ∈ {1, 2, 3, 6}. In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the SU(3) × SU(2) factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups $$ {\Omega}_5^{\mathrm{Spin}}(BG) $$ Ω 5 Spin BG using the Atiyah-Hirzebruch spectral sequence. In two cases we show that there are no global anomalies beyond the Witten anomaly, while in the other cases we show that there are no global anomalies at all, illustrating the subtle interplay between local and global anomalies. While freedom from global anomalies has been previously shown for the specific...
Journal of High Energy Physics
In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘g... more In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘global’) gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of πd(G) is neither a necessary nor a sufficient condition for there being a possible global anomaly in a d-dimensional chiral gauge theory with gauge group G. To showcase the failure of sufficiency, we revisit ‘global anomalies’ that have been previously studied in 6d gauge theories with G = SU(2), SU(3), or G2. Even though π6(G) ≠ 0, the bordism groups $$ {\Omega}_7^{\mathrm{Spin}}(BG) $$ Ω 7 Spin BG vanish in all three cases, implying there are no global anomalies. In the case of G = SU(2) we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary cond...
SciPost Physics
We give a general description of the interplay that can occur between local and global anomalies,... more We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.
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Papers by Nakarin Lohitsiri