Dynamical Symmetry and the Thermofield State at Large $N$

TL;DR

This paper explores the dynamical symmetry of Thermofield Double states in large N quantum field theories, revealing a degeneracy of solutions and explicitly constructing the Thermofield Double State in real time.

Contribution

It introduces a dynamical symmetry in large N QFTs on the real-time Schwinger-Keldysh contour and constructs the Thermofield Double State explicitly within this framework.

Findings

Identifies a dynamical symmetry generating solution degeneracy.

Constructs the Thermofield Double State in large N QFTs.

Demonstrates the symmetry in an O(N) vector model.

Abstract

We discus Thermofield Double QFT at real time, in the large $N$ limit. First, we establish a (dynamical) symmetry which we argue holds in general on the real time portion of the Schwinger-Kelydish contour. At large $N$ this symmetry is seen to generate a one parameter degeneracy of stationary collective solutions. The construction is explicitly worked out on the example of $O(N)$ vector QFT. As a nontrivial application we describe construction of the corresponding (large $N$) Thermofield Double State in real time collective formalism.