Holographic entropy production
Yu Tian
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Xiao-Ning Wu
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Hongbao Zhang
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Beijing 100190, China
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Institute of Theoretical Physics, Chinese Academy of Sciences
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Theoretische Natuurkunde,
Vrije Universiteit Brussel and The International Solvay Institutes
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Beijing 100049, China
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State Key Laboratory of Theoretical Physics
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Institute of Mathematics, Academy of Mathematics and System Science
, CAS
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School of Physicas, University of Chinese Academy of Sciences
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Open Access, c The Authors
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of Quantum Gravity, Quantum Dissipative Systems
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Pleinlaan 2, B-1050 Brussels,
Belgium
The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson's formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographic dictionary, in particular, we provide a rather general proof of the equality between the entropy production on the boundary and the increase of black hole entropy in the bulk, which can be regarded as strong support to this holographic principle. The entropy production in the familiar holographic superconductors/superfluids is investigated as an important example, where the role played by the holographic renormalization is explained. ArXiv ePrint: 1407.8273
1 Introduction
2 Holographic dictionary and its implementation in the equilibrium thermodynamics 2.1 Thermodynamics dual to the RN bulk space-time
2.2 The general thermodynamics by Hamilton-Jacobi-like analysis
3 Entropy production on the holographic screen and its equality with the 3.1 3.2 4.1
increase of entropy in the bulk
The case without cross-transportation
For more general gravitational theories
3.3 The case with cross-transportation
4 Entropy production in holographic superconductors/superfluids Universal form of the holographic entropy production The second order conserved current From finite cutoff to the conformal boundary
5 Conclusion and discussion A Black-hole thermodynamics with the topological charge B The increase of horizon area from the Raychaudhuri equation 1
Introduction
Evidence has accumulated since the end of last century that quantum gravity is
holographic [1, 2], i.e. quantum gravity in a (d + 1)-dimensional space-time region can be
described by some sort of quantum field theory on the d-dimensional boundary of this
region, especially since the discovery of AdS/CFT correspondence [35] in the framework
of (super)string theory. On one hand, nowadays there have been many generalizations
and/or applications of AdS/CFT correspondence, such as most of the phenomenological
models in AdS/CMT (condensed matter theory), AdS/QCD and so on, which cannot be
embedded in string theory. On the other hand, besides the black hole thermodynamics [6]
that inspires the proposition of holography, there are already various hints from within the
context of Einsteins gravity towards the speculation that gravity is essentially holographic,
where neither string theory nor supersymmetry are involved. Here we would like list three
of them as follows.
Brown-Henneauxs asymptotic symmetry analysis for three dimensional gravity [7].
Brown-Yorks surface tensor formulation of quasilocal energy and conserved
Boussos covariant entropy bound [9].
In particular, Brown-Yorks surface tensor formulation bears a strong resemblance to the
recipe in the dictionary for AdS/CFT correspondence, and has actually been incorporated
into the latter (or its generalizations). Holography could have been explicitly implemented
just in Einsteins gravity, in fact, if one was brave enough to declare that Brown-Yorks
surface tensor is not only for the purpose of the bulk side but also for some sort of system
living on the boundary.
In AdS/CFT, the radial direction of the (asymptotic AdS) bulk space-time corresponds
to the energy scale of the dual field theory [1013] and the change of radial coordinate r
is regarded as equivalent to the corresponding renormalization group (RG) flow [1420],
from this point of view, the RG flows of many important transport coefficients of the
boundary theory (at finite temperature) are trivial, which enables one to compute these
coefficients by the so-called black-hole membrane paradigm [21]. Especially, it is proved
the RG flow, so the universality of this ratio in both the black-hole membrane paradigm
and the standard AdS/CFT follows.
In the above framework of the so-called holographic RG flow, physical quantities can
be defined on any constant r surface (called the finite cutoff surface), while their RG
flows are obtained by changing r. However, the finite cutoff (...truncated)