Path-Integral Complexity for Perturbed CFTs

TL;DR

This paper develops a path-integral optimization framework for perturbed 2D conformal field theories, linking complexity minimization to holographic duals and RG flows, with perturbative calculations matching AdS/CFT predictions.

Contribution

It introduces a novel path-integral complexity functional for perturbed CFTs and demonstrates its consistency with holographic geometries and RG flow arguments.

Findings

Optimal metrics match hyperbolic slices in AdS with scalar perturbations

Complexity contributions from relevant operators are estimated

Validation through free field theory calculations and RG flow arguments

Abstract

In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field theories as well as general arguments of RG flows in field theories. Our optimization is performed by minimizing the path-integral complexity functional that depends on the metric and also on the relevant couplings. Then, we compute the optimal metric perturbatively and find that it agrees with the time slice of the hyperbolic metric perturbed by a scalar field in the AdS/CFT correspondence. Last but not the least, we estimate contributions to complexity from relevant perturbations.