Complex matrix model duality

TL;DR

This paper explores a duality between two complex matrix models, linking tachyon scattering in non-critical string theory and correlation functions in super-Yang-Mills, revealing a deep connection via Feynman diagram duality.

Contribution

It introduces a duality between two complex matrix models, connecting different physical theories and their diagrammatic representations, with implications for string theory and gauge theory.

Findings

Duality between two complex matrix models established.

Correlation functions expressed as sums over moduli space points.

Feynman diagram duality reflects the theoretical equivalence.

Abstract

The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super-Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich-Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces.