Large N field theories, string theory and gravity

Abstract

We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.

Comments on quantum effects in supergravity theories

“…This derivation is easily generalized to an arbitrary Kähler potential which depends on fields in different representations of the gauge group. Then it leads to a term proportional 5) where the sum over R is over the different representations, T R and d R are the Casimir and dimension of R, and the indices i and i label fields in R and R. The term (4.5) has already been noted in [4]. However, these authors have set M p = 1, and therefore did not stress that this term is independent of M p and hence it is unrelated to gravity!…”

“…We expressed them in terms of the anomalous dimension ∆ φ . 5 This way of writing them can be used to make contact with the formalism based on the conformal compensator.…”

Instantons and conformal holography

“…These equations should be viewed as determining Φ (2) and Φ (3) , etc., once Φ (0) and Φ (1) are provided, as usual. So Φ (0) and Φ (1) have the interpretations as source/operator in the instanton background.…”

“…In particular, classical field dynamics in AdS spaces has enjoyed a large amount of attention over the last few years and an enormous amount of work on classical supergravities in various dimensions has found important applications in classical gravity, Standard Model phenomenology, and Cosmology. Progress, however, has been limitied by what is also one of the virtues of AdS/CFT [1,2,3], namely the fact that it is a weak/strong coupling duality. In practice this means that the boundary field theories, being strongly coupled, are usually not under control.…”

Plasma balls/kinks as solitons of largeNconfining gauge theories

“…Various subsequent studies explored this connection to discuss the dynamics and phases of the gauge theory and the physics of black holes [2] - [26].…”