Papers by Nabamita Banerjee
The European Physical Journal C
The W(a, b) and $$W(a,b;\bar{a},\bar{b})$$ W ( a , b ; a ¯ , b ¯ ) algebras are deformations of $... more The W(a, b) and $$W(a,b;\bar{a},\bar{b})$$ W ( a , b ; a ¯ , b ¯ ) algebras are deformations of $$\mathfrak {bms}_{3}$$ bms 3 and $$\mathfrak {bms}_{4}$$ bms 4 algebras, respectively. We present a $$\mathcal {N}=2$$ N = 2 supersymmetric extension of both algebras in the presence of Rsymmetry generators that rotates the two supercharges. Our construction provides the most generic central extensions of the W(a, b) algebra. In particular, we find that $$\mathcal {N}=2$$ N = 2 $$\mathfrak {bms}_{3}$$ bms 3 algebra admits a new central extension. On the other hand, we explicitly demonstrate that an infinite $$U(1)_V \times U(1)_A$$ U ( 1 ) V × U ( 1 ) A extension of the $$W(a,b;\bar{a},\bar{b})$$ W ( a , b ; a ¯ , b ¯ ) algebra corresponding to the $$R-$$ R - symmetry is not possible for linear and quadratic structure constants with generic deformation parameters. This also implies that the infinite R symmetry considered in our analysis is broken for the $$\mathcal {N}=2 \, \mathfrak {bm...
Journal of High Energy Physics, 2021
We have studied scattering of a probe particle by a four dimensional AdS-Schwarzschild black hole... more We have studied scattering of a probe particle by a four dimensional AdS-Schwarzschild black hole at large impact factor. Our analysis is consistent perturbatively to leading order in the AdS radius and black hole mass parameter. Next we define a proper “soft limit” of the radiation and extract out the “soft factor” from it. We find the correction to the well known flat space Classical Soft graviton theorem due to the presence of an AdS background.
A systematic off-shell reduction scheme from five to four space-time dimensions is presented for ... more A systematic off-shell reduction scheme from five to four space-time dimensions is presented for supergravity theories with eight supercharges. It is applicable to theories with higher-derivative couplings and it is used to address a number of open questions regarding BPS black holes in five dimensions. Under this reduction the 5D Weyl multiplet becomes reducible and decomposes into the 4D Weyl multiplet and an extra Kaluza-Klein vector multiplet. The emergence of the pseudoscalar field of the latter multiplet and the emergence of the 4D R-symmetry group are subtle features of the reduction. The reduction scheme enables to determine how a 5D supersymmetric Lagrangian with higher-derivative couplings decomposes upon dimensional reduction into a variety of independent 4D supersymmetric invariants, without the need for imposing field equations. In this way we establish, for example, the existence of a new N=2 supersymmetric invariant that involves the square of the Ricci tensor. Finally we resolve the questions associated with the 5D Chern-Simons terms for spinning BPS black holes and their relation to the corresponding 4D black holes.
Research in the Mathematical Sciences
Black holes in a class of string compactifications, known as STU models, carry four electric and ... more Black holes in a class of string compactifications, known as STU models, carry four electric and four magnetic charges. Furthermore a duality group, given by the product of three congruence subgroups of SL(2,Z), acts on these integer valued charges. By placing these eight charges at the eight corners of a Bhargava cube, we provide a classification of the duality orbits in these theories.
Journal of High Energy Physics
We study the effect of electromagnetic interactions on the classical soft theorems on an asymptot... more We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l. This identifies 1/l2 perturbative corrections to the known asymptotically flat spacetime leading and subleading soft factors. Our analysis is only valid to leading order in 1/l2. The leading soft factor can be expected to be universal and holds beyond tree level. This allows us to derive a 1/l2 corrected Ward identity, following the known equivalence between large gauge Ward identities and soft theorems in asymptotically flat spacetimes.
Journal of High Energy Physics
Maximally $$ \mathcal{N} $$ N extended 2 + 1 dimensional flat supergravity theories exist for a c... more Maximally $$ \mathcal{N} $$ N extended 2 + 1 dimensional flat supergravity theories exist for a class of super-Poincaré algebras for arbitrary $$ \mathcal{N} $$ N . They have rich asymptotic structures and contain all interesting topological supergravity solutions in presence of non-trivial holonomy. For the asymptotic symmetry algebra being a suitable flat limit of the superconformal algebra, which is an infinite dimensional extension of two copies of Osp($$ \mathcal{N} $$ N |2; R) group, we have found the 1 + 1 dimensional chiral WZW model as the dual quantum field theory that describes the dynamics of these solutions. In the Hamiltonian analysis, the reduced phase space resembles a flat super Liouville theory.
arXiv (Cornell University), Dec 22, 2011
We review recent developments in holographic hydrodynamics. We start from very basic discussion o... more We review recent developments in holographic hydrodynamics. We start from very basic discussion on hydrodynamic systems and motivate why string theory is an essential tool to deal with these systems when they are strongly coupled. The main purpose of this review article is to understand different holographic techniques to compute transport coefficients (first order and higher order) and their corrections in presence of higher derivative terms in the bulk Lagrangian. We also mention some open challenges in this subject.
Journal of High Energy Physics, 2019
We have constructed a two dimensional theory dual to 3D asymptotically flat Supergravity in prese... more We have constructed a two dimensional theory dual to 3D asymptotically flat Supergravity in presence of two supercharges with(out) internal R-symmetry. The duals in both the cases are identified with chiral Wess-Zumino-Witten models. Further gauging the theories, we show that the dual of the one without R-symmetry is invariant under the well known $$ \mathcal{N} $$ N = 2 SuperBMS3 introduced in Banerjee et al. arXiv:1609.09210, while for the one with R-symmetry, the dual is invariant under the most generic, so far unknown, quantum $$ \mathcal{N} $$ N = 2 SuperBMS3 symmetry. We have also commented on the phase space description of the duals.
Physical Review D, 2019
N =2 three dimensional Supergravity with internal R−symmetry generators can be understood as a tw... more N =2 three dimensional Supergravity with internal R−symmetry generators can be understood as a two dimensional chiral Wess-Zumino-Witten model. In this paper, we present the reduced phase space description of the theory, which turns out to be flat limit of a generalised Liouville theory, up to zero modes. The reduced phase space description can also be explained as a gauged chiral Wess-Zumino-Witten model. We show that both these descriptions possess identical gauge and global (quantum N =2 superBMS 3) symmetries.
Journal of High Energy Physics, 2018
We show that the one-loop on-shell four-point scattering amplitude of massless ϕ 4 scalar field t... more We show that the one-loop on-shell four-point scattering amplitude of massless ϕ 4 scalar field theory in 4D Minkowski space time, when Mellin transformed to the Celestial sphere at infinity, transforms covariantly under the global conformal group (SL(2, ℂ)) on the sphere. The unitarity of the four-point scalar amplitudes is recast into this Mellin basis. We show that the same conformal structure also appears for the two-loop Mellin amplitude. Finally we comment on some universal structure for all loop four-point Mellin amplitudes specific to this theory.
Journal of High Energy Physics, 2019
We consider the maximal $$ \mathcal{N} $$ N -extended supergravity theory in 3 dimensions with fe... more We consider the maximal $$ \mathcal{N} $$ N -extended supergravity theory in 3 dimensions with fermionic generators transforming under real but non necessarily irreducible representations of the internal algebra. We obtain the symmetry algebra at null infinity preserving boundary conditions of asymptotically flat solutions, i.e. the maximal $$ \mathcal{N} $$ N -extended super-BMS3 algebra, which possesses non-linear correction in the anti-commutators of supercharges. We present the supersymmetric energy bound and derive the explicit form of the asymptotic Killing spinors. We also find the most generic circular symmetric ground state of the theory, which corresponds to a non-supersymmetric cosmological solutions and derive their entropy.
Current Science, 2017
We present the dynamics of a most generic uncharged dissipative parity, even Galilean fluid, to t... more We present the dynamics of a most generic uncharged dissipative parity, even Galilean fluid, to the first derivative order. The construction is embedded in a symmetry broken phase of one higher dimensional relativistic system, namely the null fluid. Both the null fluid and the Galilean fluid have identical symmetries, thermodynamics and constitutive relations to all order in derivative expansion. Finally, we present the number of transport coefficients for most generic charged Galilean fluid and Galilean Superfluid.
Journal of High Energy Physics, 2016
We study N = (2, 4, 8) supersymmetric extensions of the three dimensional BMS algebra (BMS 3) wit... more We study N = (2, 4, 8) supersymmetric extensions of the three dimensional BMS algebra (BMS 3) with most generic possible central extensions. We find that Nextended supersymmetric BMS 3 algebras can be derived by a suitable contraction of two copies of the extended superconformal algebras. Extended algebras from all the consistent contractions are obtained by scaling left-moving and right-moving supersymmetry generators symmetrically, while Virasoro and R-symmetry generators are scaled asymmetrically. On the way, we find that the BMS/GCA correspondence does not in general hold for supersymmetric systems. Using the β-γ and the b-c systems, we construct free field realisations of all the extended super-BMS 3 algebras.
Journal of High Energy Physics, 2016
We construct an explicit realisation of the BMS 3 algebra with nonzero central charges using holo... more We construct an explicit realisation of the BMS 3 algebra with nonzero central charges using holomorphic free fields. This can be extended by the addition of chiral matter to a realisation having arbitrary values for the two independent central charges. Via the introduction of additional free fields, we extend our construction to the minimally supersymmetric BMS 3 algebra and to the nonlinear higher-spin BMS 3-W 3 algebra. We also describe an extended system that realises both the SU(2) current algebra as well as BMS 3 via the Wakimoto representation, though in this case introducing a central extension also brings in new non-central operators.
Physical Review D, 2009
We study higher derivative corrections to the statistical entropy function and the statistical en... more We study higher derivative corrections to the statistical entropy function and the statistical entropy for five dimensional BMPV black holes by doing the asymptotic expansion of the partition function. This enables us to evaluate entropy for a large range of charges, even out of Cardy (Farey tail) limit.
Journal of High Energy Physics, 2009
The shear viscosity coefficient of strongly coupled boundary gauge theory plasma depends on the h... more The shear viscosity coefficient of strongly coupled boundary gauge theory plasma depends on the horizon value of the effective coupling of transverse graviton moving in a black hole background. The proof for the above statement is based on the canonical form of graviton's action. But in presence of generic higher derivative terms in the bulk Lagrangian the action is no longer canonical. We give a procedure to find an effective action for graviton (to first order in coefficient of higher derivative term) in canonical form in presence of any arbitrary higher derivative terms in the bulk. From that effective action we find the effective coupling constant for transverse graviton which in general depends on the radial coordinate r. We also argue that horizon value of this effective coupling is related to the shear viscosity coefficient of the boundary fluid in higher derivative gravity. We explicitly check this procedure for two specific examples: (1) four derivative action and (2) eight derivative action (W eyl 4 term). For both cases we show that our results for shear viscosity coefficient (upto first order in coefficient of higher derivative term) completely agree with the existing results in the literature.
Journal of High Energy Physics, 2013
We discuss the fate of flat directions in higher derivative gravity by studying two explicit exam... more We discuss the fate of flat directions in higher derivative gravity by studying two explicit examples, namely higher derivative gauged supergravity in five dimensions and higher derivative type IIB string theory in ten dimensions. In the first case, the supersymmetric spinning black hole solution in asymptotically AdS spacetime, found by Gutowski and Reall, is analyzed. In this case we find that the flat direction at the two derivative level is not lifted after addition of higher derivative terms, and as it turns out, this result holds even for non-supersymmetric deformations of the higher derivative action. For the rotating D3-brane solutions in type IIB theory, the dilaton parametrizes a flat direction at leading order, but its fate changes upon including order (α ′) 3 supersymmetric higher derivative corrections to the type IIB action, i.e. its leading value gets fixed.
Journal of High Energy Physics, 2011
We investigate the thermodynamic and hydrodynamic properties of 4dimensional gauge theories with ... more We investigate the thermodynamic and hydrodynamic properties of 4dimensional gauge theories with finite electric charge density in the presence of a constant magnetic field. Their gravity duals are planar magnetically and electrically charged AdS black holes in theories that contain a gauge Chern-Simons term. We present a careful analysis of the near horizon geometry of these black branes at finite and zero temperature for the case of a scalar field non-minimally coupled to the electromagnetic field. With the knowledge of the near horizon data, we obtain analytic expressions for the shear viscosity coefficient and entropy density, and also study the effect of a generic set of four derivative interactions on their ratio. We also comment on the attractor flows of the extremal solutions.
Classical and Quantum Gravity, 2014
We study the effect of a bulk Chern-Simons (CS) term on (3 + 1) dimensional type II superconducto... more We study the effect of a bulk Chern-Simons (CS) term on (3 + 1) dimensional type II superconductor in the context of the AdS/CFT correspondence. We holographically compute the super-current and find that it is non-local in nature. It receives non trivial corrections due to presence of the CS term. Considering a large limit of a parameter λ (we call this limit as long wave length limit), which is effectively the high temperature limit of the theory, we find that this non-local super-current boils down to a local quantity. The leading term (without the CS term) of this current matches with the result of Ginzburg-Landau (GL) theory. We compute the effect of the CS term on GL current and find that the effect is highly suppressed at large temperature (1 T 4). Finally, free energy of the vortex configuration has been calculated. The free energy also receives non trivial correction at the order of 1/λ 2 in the long wave length approximation.
Journal of High Energy Physics, 2014
We study transport properties of a parity-odd, non-relativistic charged fluid in presence of back... more We study transport properties of a parity-odd, non-relativistic charged fluid in presence of background electric and magnetic fields. To obtain stress tensor and charged current for the nonrelativistic system we start with the most generic relativistic fluid, living in one higher dimension and reduce the constituent equations along the light-cone direction. We also reduce the equation satisfied by the entropy current of the relativistic theory and obtain a consistent entropy current for the non-relativistic system (we call it "canonical form" of the entropy current). Demanding that the non-relativistic fluid satisfies the second law of thermodynamics we impose constraints on various first order transport coefficients. For parity even fluid, this is straight forward; it tells us positive definiteness of different transport coefficients like viscosity, thermal conductivity, electric conductivity etc. However for parity-odd fluid, canonical form of the entropy current fails to confirm the second law of thermodynamics. Therefore, we need to add two parity-odd vectors to the entropy current with arbitrary coefficients. Upon demanding the validity of second law, we see that one can fix these two coefficients exactly.
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Papers by Nabamita Banerjee