Holography in Einstein Gauss-Bonnet Gravity

We investigate a holographic relation between Einstein Gauss-Bonnet gravity in $n$ dimensions and its dual field theory in ($n-1$) dimensions. We briefly review the AdS/CFT correspondence for the entropy in the $n$-dimensional Einstein gravity and consider its extension to the case of the $n$-dimensional Einstein Gauss-Bonnet gravity. We show that there is a holographic relation between entropies of an Einstein Gauss-Bonnet black hole in the bulk and the corresponding radiation on the brane in the high temperature limit. In particular, we find that the Hubble entropy evaluated when the brane crosses the horizon also coincides with the black hole entropy in the high temperature limit.Comment: 15 pages, LaTeX, references adde

R^4 Corrections to Eleven Dimensional Supergravity via Supersymmetry

By applying Noether method to N=1 local supersymmetry in eleven dimensions, we obtained two candidates of R^4 corrections to the supergravity. The bosonic parts of these two completely match with the results obtained by type IIA string perturbative calculations. We also obtained 13 parameters which relate only fermionic terms.Comment: 9 pages, no figure, note adde

Holographic Entropy on the Brane in de Sitter Schwarzschild Space

The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both for time-like and space-like cases, the entropy of the CFT exactly agrees with the black hole entropy of 5-dimensional AdS Schwarzschild background as it happens in the AdS/CFT correspondence.Comment: 8 pages, LaTeX, Referneces adde

Comments on Large N Matrix Model

The large N Matrix model is studied with attention to the quantum fluctuations around a given diagonal background. Feynman rules are explicitly derived and their relation to those in usual Yang-Mills theory is discussed. Background D-instanton configuration is naturally identified as a discretization of momentum space of a corresponding QFT. The structure of large N divergence is also studied on the analogy of UV divergences in QFT.Comment: 32 pages, 9 figure

A Dynamical Brane in the Gravitational Dual of N=2{\cal N}=2 Sp(N)Sp(N) Superconformal Field Theory

The particular model of d5 higher derivative gravity which is dual to ${\cal N}=2$ $Sp(N)$ SCFT is considered. A (perturbative) AdS black hole in such theory is constructed in the next-to-leading order of the AdS/CFT correspondence. The surface counterterms are fixed by the conditions required for a well-defined variational procedure and the finiteness of AdS space (when the brane goes to infinity). A dynamical brane is realized at the boundary of an AdS black hole with a radius that is larger than the horizon radius. The AdS/CFT correspondence dictates the parameters of the gravitational dual in such a way that the dynamical brane (the observable universe) always occurs outside the horizon.Comment: LaTeX file, 14 pages, minor changes (including title) to match with published versio

Holographic conformal anomaly with bulk scalars potential from d3 and d5 gauged supergravity

d3 and d5 maximally SUSY gauged supergravity is considered in the parametrization (flow) of full scalar coset where the kinetic term for scalars takes the standard field theory form and the bulk potential is an arbitrary one subject to consistent parametrization. From such SG duals we calculate d2 and d4 holographic conformal anomaly which depends on bulk scalars potential. AdS/CFT correspondence suggests that such SG side conformal anomaly should be identified with (non-perturbative) QFT conformal anomaly (taking account of radiative corrections) for the theory living on the boundary of AdS space. In the limit of constant bulk potential and single scalar, d4 result reproduces the known exact conformal anomaly corresponding to maximally SUSY super Yang-Mills theory coupled to ${\cal N}=4$ conformal supergravity.Comment: LaTeX file, 13 pages. minor modification

Axion-Dilatonic Conformal Anomaly from Ads/CFT Correspondence

We discuss general multidimensional axion-dilatonic AdS gravity which may correspond to bosonic sector of Gibbons-Green-Perry (compactified) IIB supergravity with RR-scalar (axion). Using AdS/CFT correspondence the 4d conformal anomaly on axion-dilaton-gravitational background is found from SG side. It is shown that for IIB SG with axion such conformal anomaly coincides with the one obtained from QFT calculation in ${\cal N}=4$ super Yang-Mills theory conformally coupled with ${\cal N}=4$ conformal SG. Brief discussion on possibility to apply these results for gauged SGs is also presented.Comment: LaTeX file, 10 page