arXiv subjects

Jyotirmoy Bhattacharya

Publications and source records attributed to Jyotirmoy Bhattacharya.

27 records · Page 2Linked to original sources

arXiv2012

Constraints on Fluid Dynamics from Equilibrium Partition Functions

We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with the constraints described in this paper.

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arXiv2012

Soliton Stars as Holographic Confined Fermi Liquids

In this paper, we study a holographic dual of a confined fermi liquid state by putting a charged fluid of fermions in the AdS soliton geometry. This can be regarded as a confined analogue of electron stars. Depending on the parameters such as the mass and charge of the bulk fermion field, we found three different phase structures when we change the values of total charge density at zero temperature. In one of the three cases, our confined solution (called soliton star) is always stable and this solution approaches to the electron star away from the tip. In both the second and third case, we find a confinement/deconfinement phase transition. Moreover, in the third one, there is a strong indication that the soliton star decays into an inhomogeneous solution. We also analyze the probe fermion equations (in the WKB approximation) in the background of this soliton star geometry to confirm the presence of many fermi-surfaces in the system.

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arXiv2011

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.

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arXiv2011

Dissipative superfluid dynamics from gravity

Charged asymptotically AdS black branes in five dimensions are sometimes unstable to the condensation of charged scalar fields. For fields of infinite charge and squared mass -4 Herzog was able to analytically determine the phase transition temperature and compute the endpoint of this instability in the neighborhood of the phase transition. We generalize Herzog's construction by perturbing away from infinite charge in an expansion in inverse charge and use the solutions so obtained as input for the fluid gravity map. Our tube wise construction of patched up locally hairy black brane solutions yields a one to one map from the space of solutions of superfluid dynamics to the long wavelength solutions of the Einstein Maxwell system. We obtain explicit expressions for the metric, gauge field and scalar field dual to an arbitrary superfluid flow at first order in the derivative expansion. Our construction allows us to read off the the leading dissipative corrections to the perfect superfluid stress tensor, current and Josephson equations. A general framework for dissipative superfluid dynamics was worked out by Landau and Lifshitz for zero superfluid velocity and generalized to nonzero fluid velocity by Clark and Putterman. Our gravitational results do not fit into the 13 parameter Clark-Putterman framework. Purely within fluid dynamics we present a consistent new generalization of Clark and Putterman's equations to a set of superfluid equations parameterized by 14 dissipative parameters. The results of our gravitational calculation fit perfectly into this enlarged framework. In particular we compute all the dissipative constants for the gravitational superfluid.

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arXiv2010

Small Hairy Black Holes in Global AdS Spacetime

We study small charged black holes in global AdS spacetime in the presence of a charged massless minimally coupled scalar field. In a certain parameter range these black holes suffer from well known superradiant instabilities. We demonstrate that the end point of the resultant tachyon condensation process is a hairy black hole which we construct analytically in a perturbative expansion in the black hole radius. At leading order our solution is a small undeformed RNAdS black hole immersed into a charged scalar condensate that fills the AdS `box'. These hairy black hole solutions appear in a two parameter family labelled by their mass and charge. Their mass is bounded from below by a function of their charge; at the lower bound a hairy black hole reduces to a regular horizon free soliton which can also be thought of as a nonlinear Bose condensate. We compute the microcanonical phase diagram of our system at small mass, and demonstrate that it exhibits a second order `phase transition' between the RNAdS black hole and the hairy black hole phases.

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arXiv2010

Lumps of plasma in arbitrary dimensions

We use the AdS/CFT correspondence in a regime in which the field theory reduces to fluid dynamics to construct an infinite class of new black objects in Scherk-Schwarz compactified AdS(d+2) space. Our configurations are dual to black objects that generalize black rings and have horizon topology S^(d-n) x T^n, for n less than or equal to (d-1)/2. Locally our fluid configurations are plasma sheets that curve around into tori whose radii are large compared to the thickness of the sheets (the ratio of these radii constitutes a small parameter that permits the perturbative construction of these configurations). These toroidal configurations are stabilized by angular momentum. We study solutions whose dual horizon topologies are S^3 x S^1, S^4 x S^1 and S^3 x T^2 in detail; in particular we investigate the thermodynamic properties of these objects. We also present a formal general construction of the most general stationary configuration of fluids with boundaries that solve the d-dimensional relativistic Navier-Stokes equation.

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arXiv2009

Thermodynamics of Plasmaballs and Plasmarings in 3+1 Dimensions

We study localized plasma configurations in 3+1 dimensional massive field theories obtained by Scherk-Schwarz compactification of 4+1 dimensional CFT to predict the thermodynamic properties of localized blackholes and blackrings in Scherk-Schwarz compactified $AdS_6$ using the AdS/CFT correspondence. We present an exact solution to the relativistic Navier-Stokes equation in the thin ring limit of the fluid configuration. We also perform a thorough numerical analysis to obtain the thermodynamic properties of the most general solution. Finally we compare our results with the recent proposal for the phase diagram of blackholes in six flat dimensions and find some similarities but other differences.

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arXiv2008

Indices for Superconformal Field Theories in 3,5 and 6 Dimensions

We present a trace formula for a Witten type Index for superconformal field theories in d=3,5 and 6 dimensions, generalizing a similar recent construction in d=4. We perform a detailed study of the decomposition of long representations into sums of short representations at the unitarity bound to demonstrate that our trace formula yields the most general index (i.e. quantity that is guaranteed to be protected by superconformal symmetry alone) for the corresponding superalgebras. Using the dual gravitational description, we compute our index for the theory on the world volume of N M2 and M5 branes in the large N limit. We also compute our index for recently constructed Chern Simons theories in three dimensions in the large N limit, and find that, in certain cases, this index undergoes a large N phase transition as a function of chemical potentials.

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arXiv2008

Superconformal Indices for ${\cal N}=6$ Chern Simons Theories

Aharony, Bergman, Jafferis and Maldacena have recently proposed a dual gravitational description for a family of superconformal Chern Simons theories in three spacetime dimensions. In this note we perform the one loop computation that determines the field theory superconformal index of this theory and compare with the index computed over the Fock space of dual supersymmetric gravitons. In the appropriate limit (large $N$ and large $k$) we find a perfect match.

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