Circuit Complexity for Coherent-Thermal States in Bosonic String Theory

TL;DR

This paper constructs thermofield double states for bosonic string theory, introduces coherent-thermal states, and calculates their circuit complexity using a geometric approach, revealing insights into quantum state complexity in string theory.

Contribution

It develops a method to compute the circuit complexity of coherent-thermal states in bosonic string theory using covariance matrices and geometric techniques.

Findings

Derived the covariance matrix for coherent-thermal string states

Calculated the minimal geodesics for complexity measurement

Provided a framework for complexity analysis in string theory

Abstract

In this paper, we first construct thermofield double states for bosonic string theory in the light-cone gauge. We then obtain a coherent-thermal string state and a thermal-coherent string state. We use the covariance matrix approach to calculate the circuit complexity of coherent-thermal string states. In this approach, we generate the optimal geodesics by a horizontal string generator, and then obtain the circuit complexity using the length of the minimal geodesics in the group manifold.