Four dimensional non-critical strings

TL;DR

This paper discusses the gauge/string duality and non-critical string theories, emphasizing a matrix model approach to four-dimensional non-critical strings, providing explicit non-perturbative definitions and insights into gauge theories.

Contribution

It introduces a generalized matrix model approach for four-dimensional non-critical strings, offering explicit non-perturbative definitions and calculations of supersymmetry and central charges.

Findings

Derived exact formulas for space-time supersymmetry central charge.

Included both perturbative and non-perturbative string effects.

Showed instantons induce a non-trivial 1/N expansion at strong coupling.

Abstract

This is a set of lectures on the gauge/string duality and non-critical strings, with a particular emphasis on the discretized, or matrix model, approach. After a general discussion of various points of view, I describe the recent generalization to four dimensional non-critical (or five dimensional critical) string theories of the matrix model approach. This yields a fully non-perturbative and explicit definition of string theories with eight (or more) supercharges that are related to four dimensional CFTs and their relevant deformations. The space-time as well as world-sheet dimensions of the supersymmetry preserving world-sheet couplings are obtained. Exact formulas for the central charge of the space-time supersymmetry algebra as a function of these couplings are calculated. They include infinite series of string perturbative contributions as well as all the non-perturbative effects. An important insight on the gauge theory side is that instantons yield a non-trivial 1/N expansion at strong coupling, and generate open string contributions, in addition to the familiar closed strings from Feynman diagrams. We indicate various open problems and future directions of research.