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

Qudit Dicke states are higher-dimensional analogues of an important class of highly-entangled quantum states known as (qubit) Dicke states. A circuit for preparing arbitrary qudit Dicke states deterministically is formulated. An explicit decomposition of the circuit in terms of elementary gates is presented.

Qudit Dicke state preparation

After a brief review of integrability, first in the absence and then in the presence of a boundary, I outline the construction of actions for the N=1 and N=2 boundary sine-Gordon models. The key point is to introduce Fermionic boundary degrees of freedom in the boundary actions.

Integrability + Supersymmetry + Boundary: Life on the edge is not so dull after all!

https://iopscience.iop.org/article/10.1088/1751-8113/47/7/079501/pdf

Corrigendum: Boundary energy of the open XXX chain with a non-diagonal boundary term (2014 J. Phys. A: Math.Theor. 47 032001)

We use boundary quantum group symmetry to obtain recursion formulas which determine nondiagonal solutions of the boundary Yang-Baxter equation (reflection equation) of the XXZ type for any spin j.

Solutions of the boundary Yang-Baxter equation for arbitrary spin

We prove an inversion identity for the open AdS/CFT SU(1|1) quantum spin chain which is exact for finite size. We use this identity, together with an analytic ansatz, to determine the eigenvalues of the transfer matrix and the corresponding Bethe ansatz equations. We also solve the closed chain by algebraic Bethe ansatz.

Rafael I. Nepomechie

Papers

Qudit Dicke state preparation

Integrability + Supersymmetry + Boundary: Life on the edge is not so dull after all!

Corrigendum: Boundary energy of the open XXX chain with a non-diagonal boundary term (2014 J. Phys. A: Math.Theor. 47 032001)

Solutions of the boundary Yang-Baxter equation for arbitrary spin

Analytical Bethe ansatz for the open AdS/CFT SU(1|1) spin chain