Suvankar Dutta

Hydrodynamics from charged black branes

We extend the recent work on fluid-gravity correspondence to charged black-branes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.

Un)attractor black holes in higher derivative AdS gravity

We investigate five-dimensional static (non-)extremal black hole solutions in higher derivative Anti-de Sitter gravity theories with neutral scalars non-minimally coupled to gauge fields. We explicitly identify the boundary counterterms to regularize the gravi- tational action and the stress tensor. We illustrate these results by applying the method of holographic renormalization to computing thermodynamical properties in several con- crete examples. We also construct numerical extremal black hole solutions and discuss the attractor mechanism by using the entropy function formalism.

Euclidean and Noetherian entropies in AdS space

We examine the Euclidean action approach, as well as that of Wald, to the entropy of black holes in asymptotically AdS spaces. From the point of view of holography these two approaches are somewhat complementary in spirit and it is not obvious why they should give the same answer in the presence of arbitrary higher derivative gravity corrections. For the case of the AdS{sub 5} Schwarzschild black hole, we explicitly study the leading correction to the Bekenstein-Hawking entropy in the presence of a variety of higher derivative corrections studied in the literature, including the Type IIB R{sup 4} term. We find a nontrivial agreement between the two approaches in every case. Finally, we give a general way of understanding the equivalence of these two approaches.

Free fermions and thermal AdS/CFT

The dynamics of finite temperature U(N) gauge theories on S3 can be described, at weak coupling, by an effective unitary matrix model. Here we present an exact solution to these models, for any value of N, in terms of a sum over representations. Taking the large N limit of this solution provides a new perspective on the deconfinement transition which is supposed to be dual to the Hawking-Page transition. The large N phase transition manifests itself here in a manner similar to the Douglas-Kazakov phase transition in 2d Yang-Mills theory. We carry out a complete analysis of the saddle representation in the simplest case involving only the order parameter TrU. We find that the saddle points corresponding to thermal AdS, the small black hole and the large black hole can all be described in terms of free fermions. They all admit a simple phase space description a la the BPS geometries of Lin, Lunin and Maldacena.

Dyonic black hole and holography.

A bstractWe study thermodynamic properties of dyonic black hole and its dual field theory. We observe that the phase diagram of a dyonic black hole in constant electric potential and magnetic charge ensemble is similar to that of a Van der Waals fluid with chemical potential. Phase transitions and other critical phenomena have been studied in presence of magnetic charge and chemical potential. We also analyse magnetic properties of dual conformal field theory and observe a ferromagnetic like behavior of boundary theory when the external magnetic field vanishes. Finally, we compute susceptibility of different phases of boundary CFT and find that, depending on the strength of the external magnetic field and temperature, these phases are either paramagnetic or diamagnetic.

Phase Transition of Electrically Charged Ricci-flat Black Holes

We study phase transition between electrically charged Ricci-flat black holes and AdS soliton spacetime of Horowitz and Myers in five dimensions. Boundary topology for both of them is S1 × S1 × R2. We consider AdS-Reissner-Nordstrom black hole and R-charged black holes and find that phase transition of these black holes to AdS soliton spacetime depends on the relative size of two boundary circles. We also perform the stability analysis for these black holes. In order to use the AdS/CFT correspondence, we work in the grand canonical ensemble.

Null Fluids - A New Viewpoint of Galilean Fluids

current up to anomalies. We construct a relativistic system, which we call a null fluid and show that it is in one-to-one correspondence with a Galilean fluid living in one lower dimension. The correspondence is based on light cone reduction, which is known to reduce the Poincare symmetry of a theory to Galilean in one lower dimension. We show that the proposed null fluid and the corresponding Galilean fluid have exactly same symmetries, thermodynamics, constitutive relations, and equilibrium partition to all orders in the derivative expansion. We also devise a mechanism to introduce U(1) anomaly in even dimensional Galilean theories using light cone reduction, and study its effect on the constitutive relations of a Galilean fluid.

Entropy current for non-relativistic fluid.

A bstractWe 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 non-relativistic 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.

Equilibrium partition function for nonrelativistic fluids.

We construct an equilibrium partition function for a nonrelativistic fluid and use it to constrain the dynamics of the system. The construction is based on light cone reduction, which is known to reduce the Poincare symmetry to Galilean in one lower dimension. We modify the constitutive relations of a relativistic fluid, and find that its symmetry broken phase—“null fluid” is equivalent to the nonrelativistic fluid. In particular, their symmetries, thermodynamics, constitutive relations, and equilibrium partition function match exactly to all orders in derivative expansion.

First order Galilean superfluid dynamics.

We study dynamics of an (anomalous) Galilean superfluid up to first order in derivative expansion, both in parity-even and parity-odd sectors. We construct a relativistic system—null superfluid, which is a null fluid (introduced in N. Banerjee, S. Dutta, and A. Jain Akash, [Phys. Rev. D 93, 105020 (2016).]) with a spontaneously broken global U(1) symmetry. A null superfluid is in one-to-one correspondence with a Galilean superfluid in one lower dimension; i.e., they have the same symmetries, thermodynamics, constitutive relations and are related to each other by a mere choice of basis. The correspondence is based on null reduction, which is known to reduce the Poincare symmetry of a theory to Galilean symmetry in one lower dimension. To perform this analysis, we use off-shell formalism of (super)fluid dynamics, adopting it appropriately to null (super)fluids. We also verify these results via c → ∞ limit of a parent relativistic system.