String Perturbation Theory on the Schwinger-Keldysh Time Contour

TL;DR

This paper develops a large-N expansion framework within the Schwinger-Keldysh formalism for non-equilibrium quantum systems, revealing a refined topological genus expansion and insights into dual string theory features.

Contribution

It introduces a novel large-N expansion approach in the Schwinger-Keldysh formalism, uncovering a detailed topological structure of worldsheets in non-equilibrium quantum systems.

Findings

Refined topological genus expansion in Schwinger-Keldysh formalism

Decomposition of worldsheets into classical and quantum parts after Keldysh rotation

Identification of universal features related to dual string theory

Abstract

We perform the large-$N$ expansion in the Schwinger-Keldysh formulation of non-equilibrium quantum systems with matrix degrees of freedom, and study universal features of the anticipated dual string theory. We find a rich refinement of the topological genus expansion: In the original formulation, the future time instant where the forward and backward branches of the Schwinger-Keldysh time contour meet is associated with its own worldsheet genus expansion. After the Keldysh rotation, the worldsheets decompose into a classical and quantum part.