Large N Reductions and Holography

TL;DR

This paper explores the connection between large N gauge theory reductions and holography, extending to generalized models with T-duality, and introduces a new method for calculating correlation functions from these models.

Contribution

It identifies large N reductions with dimensional reductions and extends them to generalized models incorporating T-duality, linking gauge theories to dual supergravity solutions.

Findings

Large N reductions correspond to dimensional reductions with homogeneous eigenvalue distributions.

Generalized reductions relate to T-duality between different supergravity backgrounds.

A new technique for computing correlation functions from reduced models is proposed.

Abstract

The large $N$ reductions in gauge theories are identified with dimensional reductions with homogeneous distribution of the eigenvalues of the gauge field, and it is used to identify the corresponding closed string descriptions in the Maldacena duality. When one does not take the zero-radii limit, the large $N$ reductions are naturally extended to the equivalences between the gauge theories and the "generalized" reduced models, which naturally contain the notion of T-dual equivalence. In the dual gravitational description, T-duality relates two type IIB supergravity solutions, the near horizon geometry of D3-branes, and the near horizon geometry of D-instantons densely and homogeneously distributing on the dual torus. This is the holographic description of the generalized large $N$ reductions. A new technique for calculating correlation functions of local gauge invariant single trace operators from the reduced models is also given.