By Aharony, Gubser, Maldacena, Ooguri, Oz.

We evaluation the holographic correspondence among box theories and string/M thought, concentrating on the relation among compactifications of string/M idea on Anti-de Sitter areas and conformal box theories. We evaluation the historical past for this correspondence and talk about its motivations and the facts for its correctness. We describe the most effects which were derived from the correspondence within the regime that the sphere conception is approximated by means of classical or semiclassical gravity. We concentrate on the case of the supersymmetric gauge thought in 4 dimensions, yet we speak about additionally box theories in different dimensions, conformal and non-conformal, without or with supersymmetry, and particularly the relation to QCD. We additionally speak about a few implications for black gap physics.

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**Extra resources for Large N field theories, string theory and gravity**

**Example text**

A string stretching between the brane probe and the N branes appears in the gravity description as a string stretching between the D3-brane and the horizon of AdS. This seems a bit surprising at "rst since the proper distance to the horizon is in"nite. However, we get a "nite result for the energy of this state once we remember to include the redshift factor. The D3-branes in AdS (like any D3-branes in string theory) are described at low energies by the Born}Infeld action, which is the Yang}Mills action plus some higher derivative corrections.

1. The correspondence In this section we will present an argument connecting type IIB string theory compacti"ed on AdS ;S to N"4 super-Yang}Mills theory [5]. Let us start with type IIB string theory in #at, ten dimensional Minkowski space. Consider N parallel D3 branes that are sitting together or very close to each other (the precise meaning of `very closea will be de"ned below). The D3 branes are extended along a (3#1) dimensional plane in (9#1)-dimensional space time. String theory on this background contains two kinds of perturbative excitations, closed strings and open strings.

3), since the superconformal algebra has twice as many fermionic generators as the corresponding Poincare superalgebra. We also have an SO(6) symmetry which rotates the S. This can be identi"ed with the S;(4) R-symmetry 0 group of the "eld theory. In fact, the whole supergroup is the same for the N"4 "eld theory and the AdS ;S geometry, so both sides of the conjecture have the same spacetime symmetries. 2. 1 that we could also think of the conformal "eld theory as de"ned on S;1 by rede"ning the Hamiltonian.