Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of ${\cal N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the ${\cal N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

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Anti De Sitter Space And Holography

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

Anti de sitter space and holography

Extended Theories of Gravity

Black holes in higher dimensional space-times

Unity of superstring dualities

We investigate the open spin chain describing the scalar sector of the Y = 0 giant graviton brane at weak coupling. We provide a direct proof of integrability in the SU(2) and SU(3) sectors by constructing the transfer matrices. We determine the eigenvalues of these transfer matrices in terms of roots of the corresponding Bethe ansatz equations (BAEs). Based on these results, we propose BAEs for the full SO(6) sector. We find that, in the weak-coupling limit, the recently-proposed all-loop BAEs essentially agree with those proposed in the present work.

Bethe ansatz equations for open spin chains from giant gravitons

We extend Sklyanin's construction of commuting open-chain transfer matrices to the SU(2|2) bulk and boundary S-matrices of AdS/CFT. Using the graded version of the S-matrices leads to a transfer matrix of particularly simple form. We also find an SU(1|1) boundary S-matrix which has one free boundary parameter.

Open-chain transfer matrices for AdS/CFT

Soliton s matrices for the critical a(1)n-1 chain

We formulate a systematic Bethe ansatz approach for computing bound-state (`breather') S matrices for integrable quantum spin chains We use this approach to calculate the breather boundary S matrix for the open XXZ spin chain with diagonal boundary fields We also compute the soliton boundary S matrix in the critical regime

Rafael I. Nepomechie

Papers

Bethe ansatz equations for open spin chains from giant gravitons

Open-chain transfer matrices for AdS/CFT

Soliton s matrices for the critical a(1)n-1 chain

Direct calculation of breather S matrices

The scaling supersymmetric Yang–Lee model with boundary