Path-Integral Complexity for Perturbed CFTs
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.
Cite
@article{arxiv.1804.01999,
title = {Path-Integral Complexity for Perturbed CFTs},
author = {Arpan Bhattacharyya and Pawel Caputa and Sumit R. Das and Nilay Kundu and Masamichi Miyaji and Tadashi Takayanagi},
journal= {arXiv preprint arXiv:1804.01999},
year = {2018}
}
Comments
27 pages, 1 figure; citation and clarifying text added; version to appear in JHEP