Ayan Mukhopadhyay

Bio: Ayan Mukhopadhyay is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Tensor & Physics. The author has an hindex of 16, co-authored 59 publications receiving 714 citations. Previous affiliations of Ayan Mukhopadhyay include Centre national de la recherche scientifique & University of Crete.

Holographic perfect fluidity, Cotton energy-momentum duality and transport properties

Abstract: We investigate background metrics for 2+1-dimensional holographic theories where the equilibrium solution behaves as a perfect fluid, and admits thus a thermodynamic description. We introduce stationary perfect-Cotton geometries, where the Cotton--York tensor takes the form of the energy--momentum tensor of a perfect fluid, i.e. they are of Petrov type D_t. Fluids in equilibrium in such boundary geometries have non-trivial vorticity. The corresponding bulk can be exactly reconstructed to obtain 3+1-dimensional stationary black-hole solutions with no naked singularities for appropriate values of the black-hole mass. It follows that an infinite number of transport coefficients vanish for holographic fluids. Our results imply an intimate relationship between black-hole uniqueness and holographic perfect equilibrium. They also point towards a Cotton/energy--momentum tensor duality constraining the fluid vorticity, as an intriguing boundary manifestation of the bulk mass/nut duality.

Worldsheet properties of extremal correlators in AdS/CFT

Abstract: We continue to investigate planar four point worldsheet correlators of string theories which are conjectured to be duals of free gauge theories. We focus on the extremal correlators langleTr(ZJ1(x))Tr(ZJ2(y))Tr(ZJ3(z))Tr(bar ZJ(0)))rangle of Script N = 4 SYM theory, and construct the corresponding worldsheet correlators in the limit when the Ji >> 1. The worldsheet correlator gets contributions, in this limit, from a whole family of Feynman graphs. We find that it is supported on a curve in the moduli space parametrized by the worldsheet crossratio. In a further limit of the spacetime correlators we find this curve to be the unit circle. In this case, we also check that the entire worldsheet correlator displays the appropriate crossing symmetry. The non-renormalization of the extremal correlators in the 't Hooft coupling offers a potential window for a comparison of these results with those from strong coupling.

Time-dependence of the holographic spectral function: Diverse routes to thermalisation

Abstract: We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quench duration, the spectral function indeed follows the thermal form at the instantaneous effective temperature adiabatically, although with a slight initial time delay and a bit premature thermalisation. At shorter quench durations, several new non-adiabatic features appear: (i) time-dependence of the spectral function is seen much before than that in the effective temperature (advanced time-dependence), (ii) a big transfer of spectral weight to frequencies greater than the initial temperature occurs at an intermediate time (kink formation) and (iii) new peaks with decreasing amplitudes but in greater numbers appear even after the effective temperature has stabilised (persistent oscillations). We find four broad routes to thermalisation for lower values of spatial momenta. At higher values of spatial momenta, kink formations and persistent oscillations are suppressed, and thermalisation time decreases. The general thermalisation pattern is globally top-down, but a closer look reveals complexities.

Time-dependent N A d S 2 holography with applications

Abstract: We develop a method for obtaining exact time-dependent solutions in Jackiw-Teitelboim gravity coupled to nonconformal matter and study consequences for $N{AdS}_{2}$ holography. We study holographic quenches in which we find that the black hole mass increases. A semiholographic model composed of an infrared $N{AdS}_{2}$ holographic sector representing the mutual strong interactions of trapped impurities confined at a spatial point is proposed. The holographic sector couples to the position of a displaced impurity acting as a self-consistent boundary source. This effective $0+1$-dimensional description has a total conserved energy. Irrespective of the initial velocity of the particle, the black hole mass initially increases, but after the horizon runs away to infinity in the physical patch, the mass vanishes in the long run. The total energy is completely transferred to the kinetic energy or the self-consistent confining potential energy of the impurity. For initial velocities below a critical value determined by the mutual coupling, the black hole mass changes sign in finite time. Above this critical velocity, the initial condition of the particle can be retrieved from the $SL(2,R)$ invariant exponent that governs the exponential growth of the bulk gravitational $SL(2,R)$ charges at late time.

Holography as a highly efficient renormalization group flow. II. An explicit construction

Abstract: We complete the reformulation of the holographic correspondence as a highly efficient renormalization group (RG) flow that can also determine the UV data in the field theory in the strong-coupling and large-$N$ limit. We introduce a special way to define operators at any given scale in terms of appropriate coarse-grained collective variables, without requiring the use of the elementary fields. The Wilsonian construction is generalized by promoting the cutoff to a functional of these collective variables. We impose three criteria to determine the coarse-graining. The first criterion is that the effective Ward identities for local conservation of energy, momentum, etc. should preserve their standard forms, but in new scale-dependent background metric and sources which are functionals of the effective single-trace operators. The second criterion is that the scale-evolution equations of the operators in the actual background metric should be state-independent, implying that the collective variables should not explicitly appear in them. The final required criterion is that the end point of the scale-evolution of the RG flow can be transformed to a fixed point corresponding to familiar nonrelativistic equations with a finite number of parameters, such as incompressible nonrelativistic Navier-Stokes, under a certain universal rescaling of the scale and of the time coordinate. Using previous work, we explicitly show that in the hydrodynamic limit each such highly efficient RG flow reproduces a unique classical gravity theory with precise UV data that satisfy our IR criterion and also lead to regular horizons in the dual geometries. We obtain the explicit coarse-graining which reproduces Einstein's equations. In a simple example, we are also able to construct a low-energy effective action and compute the beta function. Finally, we show how our construction can be interpolated with the traditional Wilsonian RG flow at a suitable scale and can be used to develop new nonperturbative frameworks for QCD-like theories.

Thermodynamical aspects of gravity: new insights

Abstract: The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses certain aspects of this topic, concentrating on new insights gained from some recent work. After a brief introduction of the overall perspective, sections 2 and 3 provide the pedagogical background on the geometrical features of bifurcation horizons, path integral derivation of horizon temperature, black hole evaporation, structure of Lanczos-Lovelock models, the concept of Noether charge and its relation to horizon entropy. Section 4 discusses several conceptual issues introduced by the existence of temperature and entropy of the horizons. In section 5 we take up the connection between horizon thermodynamics and gravitational dynamics and describe several peculiar features which have no simple interpretation in the conventional approach. The next two sections describe the recent progress achieved in an alternative perspective of gravity. In section 6 we provide a thermodynamic interpretation of the field equations of gravity in any diffeomorphism invariant theory and in section 7 we obtain the field equations of gravity from an entropy maximization principle. The last section provides a summary.

Black holes as mirrors: quantum information in random subsystems

Abstract: We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.

Exact Space-Times in Einstein's General Relativity

Abstract: The title immediately brings to mind a standard reference of almost the same title [1]. The authors are quick to point out the relationship between these two works: they are complementary. The purpose of this work is to explain what is known about a selection of exact solutions. As the authors state, it is often much easier to find a new solution of Einstein's equations than it is to understand it. Even at first glance it is very clear that great effort went into the production of this reference. The book is replete with beautifully detailed diagrams that reflect deep geometric intuition. In many parts of the text there are detailed calculations that are not readily available elsewhere. The book begins with a review of basic tools that allows the authors to set the notation. Then follows a discussion of Minkowski space with an emphasis on the conformal structure and applications such as simple cosmic strings. The next two chapters give an in-depth review of de Sitter space and then anti-de Sitter space. Both chapters contain a remarkable collection of useful diagrams. The standard model in cosmology these days is the ICDM model and whereas the chapter on the Friedmann-Lema?tre?Robertson?Walker space-times contains much useful information, I found the discussion of the currently popular a representation rather too brief. After a brief but interesting excursion into electrovacuum, the authors consider the Schwarzschild space-time. This chapter does mention the Swiss cheese model but the discussion is too brief and certainly dated. Space-times related to Schwarzschild are covered in some detail and include not only the addition of charge and the cosmological constant but also the addition of radiation (the Vaidya solution). Just prior to a discussion of the Kerr space-time, static axially symmetric space-times are reviewed. Here one can find a very interesting discussion of the Curzon?Chazy space-time. The chapter on rotating black holes is rather brief and, for example, does not contain reference to the insights found by Pretorius and Israel [2]. This is perhaps justifiable in view of the many specialized texts devoted to the Kerr space-time (e.g. [3]). The large clear diagrams that one becomes accustomed to in this book show off the Taub-NUT (and related) space-times in the next chapter. After perhaps a somewhat standard discussion of stationary axially symmetric space-times, there is a very informative discussion of accelerating black holes. For example, the global structure of the C-metric is considered in detail. This is followed by a brief discussion of solutions for uniformly accelerating particles. The discussion of the Pleba?ski-Demia?ski solutions contains two very useful flow charts that help to systematize two rather complex families of solutions. After a somewhat brief discussion of plane and pp-waves, the authors give an extensive discussion of the Kunt solutions. I note here that after this text was in production the importance of the Kunt space-times as regards the characterization of space-times by scalar curvature invariants was made clear [4]. The discussion of the Robinson-Trautman solutions that follows is extensive, containing, for example, details of the singularity structure and of the global structure. The final formal chapter in this text covers colliding plane waves. This contains, for example, discussions of the Khan?Penrose, Ferrari?Iba?ez and Chandrasekhar?Xanthopoulos solutions. The text ends with a `final miscellany'. This covers a number of interesting topics, but I found the discussion of the Lema?tre?Tolman solutions rather weak (compare e.g. [5]). The book has two quite useful appendices covering 2-spaces and 3-spaces of constant curvature. To conclude, I will quote from the dust jacket: `The book is an invaluable resource for both graduate students and academic researchers working in gravitational physics'. I highly recommend it. References [1] Stephani H, Kramer D, MacCallum M, Hoenselaers C and Herlt E 2003 Exact Solutions of Einstein's Field Equations (Second Edition) (Cambridge: Cambridge University Press) [2] Pretorius F and Israel W 1998 Class. Quantum Grav.15 2289 [3] Wiltshire D, Visser M and Scott S (ed) 2008 The Kerr Spacetime: Rotating Black Holes in General Relativity (Cambridge: Cambridge University Press) [4] Coley A, Hervik S and Pelavas N 2009 Class. Quantum Grav. 26 025013 [5] Pleba?ski J and Krasi?ski A 2006 An Introduction to General Relativity and Cosmology (Cambridge: Cambridge University Press)

Holographic Duality with a View Toward Many-Body Physics

Abstract: These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.

Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe

Abstract: It is shown that the differential form of Friedmann equation of a FRW universe can be rewritten as the first law of thermodynamics $dE=TdS+WdV$ at apparent horizon, where $E=\ensuremath{\rho}V$ is the total energy of matter inside the apparent horizon, $V$ is the volume inside the apparent horizon, $W=(\ensuremath{\rho}\ensuremath{-}P)/2$ is the work density, $\ensuremath{\rho}$ and $P$ are energy density and pressure of matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon ${\stackrel{\texttildelow{}}{r}}_{A}$ has associated entropy $S=A/4G$ and temperature $T=\ensuremath{\kappa}/2\ensuremath{\pi}$ in Einstein general relativity, where $A$ is the area of apparent horizon and $\ensuremath{\kappa}$ is the surface gravity at apparent horizon of FRW universe. We extend our procedure to the Gauss-Bonnet gravity and more general Lovelock gravity and show that the differential form of Friedmann equations in these gravities can also be written as $dE=TdS+WdV$ at the apparent horizon of FRW universe with entropy $S$ being given by expression previously known via black hole thermodynamics.