Exact amplitudes in four dimensional non-critical string theories

TL;DR

This paper explores the connection between four-dimensional non-critical string theories and supersymmetric Yang-Mills theory, showing how certain amplitudes can be computed and related to matrix models, extending lower-dimensional string approaches.

Contribution

It introduces a method to compute amplitudes in 4D non-critical string theories via Seiberg-Witten integrals, extending matrix model techniques beyond one dimension.

Findings

Explicit calculation of amplitudes at multicritical points.

Identification of universal limits near singularities.

Extension of matrix model methods to four-dimensional strings.

Abstract

The large Nc expansion of N=2 supersymmetric Yang-Mills theory with gauge group SU(Nc) has recently been shown to break down at singularities on the moduli space. We conjecture that by taking Nc to infinity and approaching the singularities in a correlated way, all the observables of the theory have a finite universal limit yielding amplitudes in string theories dual to field theories describing the light degrees of freedom. We explicitly calculate the amplitudes corresponding to the Seiberg-Witten period integrals for an A_{n-1} series of multicritical points as well as for other critical points exhibiting a scaling reminiscent of the c=1 matrix model. Our results extend the matrix model approach to non-critical strings in less than one dimension to non-critical strings in four dimensions.