arXiv subjects

Shiraz Minwalla

Publications and source records attributed to Shiraz Minwalla.

At least 55 records · Page 3Linked 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

Chern-Simons Theory with Vector Fermion Matter

We study three dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R^2 as a function of the 't Hooft coupling lambda=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |lambda|=1; the conformal theory does not exist for |lambda|>1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W-infinity algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.

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arXiv2012

Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions

Following up on recent work in the context of ordinary fluids, we study the equilibrium partition function of a 3+1 dimensional superfluid on an arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We argue that this partition function is generated by a 3 dimensional Euclidean effective action for the massless Goldstone field. We parameterize the general form of this action at first order in the derivative expansion. We demonstrate that the constitutive relations of relativistic superfluid hydrodynamics are significantly constrained by the requirement of consistency with such an effective action. At first order in the derivative expansion we demonstrate that the resultant constraints on constitutive relations coincide precisely with the equalities between hydrodynamical transport coefficients recently derived from the second law of thermodynamics.

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arXiv2011

The fluid/gravity correspondence

We review the fluid/gravity correspondence which relates the dynamics of Einstein's equations (with negative cosmological constant) to the dynamics of relativistic Navier-Stokes equations.

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arXiv2011

Supersymmetric States in Large N Chern-Simons-Matter Theories

In this paper we study the spectrum of BPS operators/states in N=2 superconformal U(N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersymmetric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N=2 theory with no superpotential, we study the renormalization of R-charge at finite 't Hooft coupling using "Z-minimization". A particularly intriguing result is found in the case of one adjoint matter.

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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

Small Hairy Black Holes in $AdS_5 \times S^5$

We study small hairy black holes in a consistent truncation of ${\cal N}=8$ gauged supergravity that consists of a single charged scalar field interacting with the metric and a U(1) gauge field. Small very near extremal RNAdS black holes in this system are unstable to decay by superradiant emission. The end point of this instability is a small hairy black hole that we construct analytically in a perturbative expansion in its charge. Unlike their RNAdS counterparts, hairy black hole solutions exist all the way down to the BPS bound, demonstrating that ${\cal N}=4$ Yang Mills theory has an ${\cal O}(N^2)$ entropy at all energies above supersymmetry. At the BPS bound these black holes reduce to previously discussed regular, supersymmetric horizon free solitons. We use numerical methods to continue the construction of these solitons to large charges and find that the line of soliton solutions terminates at a singular solution $S$ at a finite charge. We conjecture that a one parameter family of singular supersymmetric solutions, which emerges out of $S$, constitutes the BPS limit of hairy black holes at larger values of the charge. At leading order in their charge, the thermodynamics of the small hairy black holes constructed in this paper turns out to be correctly reproduced by modeling these objects as a non interacting mix of an RNAdS black hole and the supersymmetric soliton in thermal equilibrium. Assuming that a similar non interacting model continues to apply upon turning on angular momentum, we also predict a rich family of rotating hairy black holes, including new hairy supersymmetric black holes. This analysis suggests interesting structure for the space of (yet to be constructed) hairy charged rotating black holes in $AdS_5\times S^5$, particularly in the near BPS limit.

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arXiv2009

Weak Field Black Hole Formation in Asymptotically AdS Spacetimes

We use the AdS/CFT correspondence to study the thermalization of a strongly coupled conformal field theory that is forced out of its vacuum by a source that couples to a marginal operator. The source is taken to be of small amplitude and finite duration, but is otherwise an arbitrary function of time. When the field theory lives on $R^{d-1,1}$, the source sets up a translationally invariant wave in the dual gravitational description. This wave propagates radially inwards in $AdS_{d+1}$ space and collapses to form a black brane. Outside its horizon the bulk spacetime for this collapse process may systematically be constructed in an expansion in the amplitude of the source function, and takes the Vaidya form at leading order in the source amplitude. This solution is dual to a remarkably rapid and intriguingly scale dependent thermalization process in the field theory. When the field theory lives on a sphere the resultant wave either slowly scatters into a thermal gas (dual to a glueball type phase in the boundary theory) or rapidly collapses into a black hole (dual to a plasma type phase in the field theory) depending on the time scale and amplitude of the source function. The transition between these two behaviors is sharp and can be tuned to the Choptuik scaling solution in $R^{d,1}$.

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arXiv2009

The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity

We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to `accelerated boost' symmetries of the Navier-Stokes equations, uncovering a possibly new conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

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arXiv2009

Forced Fluid Dynamics from Gravity

We generalise the computations of arXiv:0712.2456 to generate long wavelength, asymptotically locally AdS_5 solutions to the Einstein-dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity, our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parametrised by four-velocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS_5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.

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arXiv2008

Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions

We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdS_{d+1} long wavelength solutions of Einstein's equations with a negative cosmological constant, for all d>2. We find simple explicit expressions for the stress tensor (slightly generalizing the recent result by Haack and Yarom (arXiv:0806.4602)), the full dual bulk metric and an entropy current of this strongly coupled conformal fluid, to second order in the derivative expansion, for arbitrary d>2. We also rewrite the well known exact solutions for rotating black holes in AdS_{d+1} space in a manifestly fluid dynamical form, generalizing earlier work in d=4. To second order in the derivative expansion, this metric agrees with our general construction of the metric dual to fluid flows.

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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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arXiv2008

Large rotating AdS black holes from fluid mechanics

We use the AdS/CFT correspondence to argue that large rotating black holes in global AdS(D) spaces are dual to stationary solutions of the relativistic Navier-Stokes equations on S**(D-2). Reading off the equation of state of this fluid from the thermodynamics of non-rotating black holes, we proceed to construct the nonlinear spinning solutions of fluid mechanics that are dual to rotating black holes. In all known examples, the thermodynamics and the local stress tensor of our solutions are in precise agreement with the thermodynamics and boundary stress tensor of the spinning black holes. Our fluid dynamical description applies to large non-extremal black holes as well as a class of large non-supersymmetric extremal black holes, but is never valid for supersymmetric black holes. Our results yield predictions for the thermodynamics of all large black holes in all theories of gravity on AdS spaces, for example, string theory on AdS(5) x S**5 and M theory on AdS(4) x S**7 and AdS(7) x S**4.

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arXiv2008

Nonlinear Fluid Dynamics from Gravity

Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields -- arbitrary functions of the coordinates on the boundary of AdS5 -- we use Einstein's equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.

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arXiv2008

Local Fluid Dynamical Entropy from Gravity

Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed.

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arXiv2008

Comments on 1/16 BPS Quantum States and Classical Configurations

We formulate the problem of counting 1/16 BPS states of N = 4 Yang Mills theory as the enumeration of the local cohomology of an operator acting on holomorphic fields on C^2. We study aspects of the enumeration of this cohomology at finite N, especially for operators constructed only out of products of covariant derivatives of scalar fields, and compare our results to the states obtained from the quantization of giant gravitons and dual giants. We physically interpret the holomorphic fields that enter our conditions for supersymmetry semi-classically by deriving a set of Bogomolnyi equations for 1/16-BPS bosonic field configurations in N = 4 Yang Mills theory on R^4 with reality properties and boundary conditions appropriate to radial quantization. An arbitrary solution to these equations in the free theory is parameterized by holomorphic data on C^2 and lifts to a nearby solution of the interacting Bogomolnyi equations only when the constraints equivalent to Q cohomology are obeyed.

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