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.

http://iopscience.iop.org/article/10.1088/0034-4885/73/4/046901/pdf

Thermodynamical aspects of gravity: new insights

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.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2007-003180.pdf

Black holes as mirrors: quantum information in random subsystems

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)

Exact Space-Times in Einstein's General Relativity

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.

Holographic Duality with a View Toward Many-Body Physics

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.

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

In this article we have studied the transverse momentum distribution of the pseudo-scalar Higgs boson at the Large Hadron Collider (LHC). The small $\pt$ region which provides the bulk of the cross section is not accessible to fixed order perturbation theory due to the presence of large logarithms in the series. Using the universal infrared behaviour of the QCD we resum these large logarithms up to next-to-next-to-leading logarithmic (NNLL) accuracy. We observe a significant reduction in theoretical uncertainties due to the unphysical scales at NNLL level compared to the previous order. We present the $p_T$ distribution matched to NNLO$_A$+NNLL, valid for the whole $p_T$ region and provide a detailed phenomenological study in the context of both 14 TeV and 13 TeV LHC using different choices of masses, scales and parton distribution functions which will be useful for the search of such particle at the LHC in near future.

/pdf/resummed-transverse-momentum-distribution-of-pseudo-scalar-3fele7u5k1.pdf

Resummed transverse momentum distribution of pseudo-scalar Higgs boson at NNLO$_A$+NNLL

Over the last twenty five years, holographic duality has revolutionised our understanding of gauge theories, quantum many-body systems and also quantum black holes. This topical issue is a collection of review articles on recent advances in fundamentals of holographic duality and its applications with special focus on a few areas where it is inter-disciplinary to a large measure. The aim is to provide a sufficient background on relevant phenomenology and other theoretical areas such as quantum information theory to researchers whose primary expertise is in quantum fields, strings and gravity, and also the necessary concepts and methods of holography to researchers in other fields, so that these recent developments could be grasped and hopefully further developed by a wider community. The topics relating to fundamental aspects include understanding of bulk spacetime reconstruction in holography in the framework of quantum error correction along with the spectacular advances in resolution of the information paradoxes of quantum black holes; quantum complexity and its fundamental role in connecting holography with quantum information theory; theoretical and experimental advances in quantum simulators for information mirroring and scrambling in quantum black holes, and teleportation via wormholes; and a pedagogical review on wormholes also. The topics related to applied holography include applications to hydrodynamic attractor and its phenomenological implications, modelling of equation of state of QCD matter in neutron stars, and finally estimating hadronic contribution to light-by-light scattering for theoretical computation of the muon's $g-2$. 

/pdf/editorial-new-frontiers-in-holographic-duality-1cq771wx.pdf

Editorial: New frontiers in holographic duality

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 of $N = 4$ SYM theory, and construct the corresponding worldsheet correlators in the limit when the $J_i >> 1$. The worldsheet correlator gets contributions, in this limit, from a whole family of Feynman graphs. We find that it is supported on a {\it curve} in the moduli space parametrised 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.

Worldsheet Properties of Extremal Correlators in AdS/CFT

Investigating principles for storage of quantum information at finite temperature with minimal need for active error correction is an active area of research. We bear upon this question in two-dimensional holographic conformal field theories via the quantum null energy condition that we have shown earlier to implement the restrictions imposed by quantum thermodynamics on such many-body systems. We study an explicit encoding of a logical qubit into two similar chirally propagating excitations of finite von Neumann entropy on a finite temperature background whose erasure can be implemented by an appropriate inhomogeneous and instantaneous energy-momentum inflow from an infinite energy memoryless bath due to which the system transits to a thermal state. Holographically, these fast erasure processes can be depicted by generalized AdS-Vaidya geometries described previously in which no assumption of specific form of bulk matter is needed. We show that the quantum null energy condition gives analytic results for the minimal finite temperature needed for the deletion which is larger than the initial background temperature in consistency with Landauer's principle. In particular, we find a simple expression for the minimum final temperature needed for the erasure of a large number of encoding qubits. We also find that if the encoding qubits are localized over an interval shorter than a specific localization length, then the fast erasure process is impossible, and furthermore this localization length is the largest for an optimal amount of encoding qubits determined by the central charge. We estimate the optimal encoding qubits for realistic protection against fast erasure. We discuss possible generalizations of our study for novel constructions of fault-tolerant quantum gates operating at finite temperature.

Erasure Tolerant Quantum Memory and the Quantum Null Energy Condition in Holographic Systems.

Sutapa Samanta, ∗ Hareram Swain, † Benôıt Douçot, ‡ Giuseppe Policastro, § and Ayan Mukhopadhyay ¶ Department of Physics and Astronomy, Western Washington University, 516 High Street, Bellingham, Washington 98225,USA Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India Laboratoire de Physique Théorique et Hautes Energies, Sorbonne Université and CNRS UMR 7589, 4 place Jussieu, 75252 Paris Cedex 05, France Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, 24 rue Lhomond, F-75005 Paris, France (Dated: June 6, 2022)

Ayan Mukhopadhyay

Papers

Resummed transverse momentum distribution of pseudo-scalar Higgs boson at NNLO$_A$+NNLL

Editorial: New frontiers in holographic duality

Worldsheet Properties of Extremal Correlators in AdS/CFT

Erasure Tolerant Quantum Memory and the Quantum Null Energy Condition in Holographic Systems.

A simple model for strange metallic behavior