Complexity of warped conformal field theory
Abstract
Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro-Kac-Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT\,s using \emph{circuit complexity} as a tool. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT and has a very complicated dependence on the Virasoro central charge and the Kac-Moody level parameter . Next we consider circuit complexity based on Virasoro-Kac-Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro-Kac-Moody group. We consider a special solution to extremization equations for which complexity scales linearly with ``time''. In the semiclassical limit (large , while remains finite and small) both the holographic volume complexity and circuit complexity scales linearly with .
Keywords
Cite
@article{arxiv.2202.09350,
title = {Complexity of warped conformal field theory},
author = {Arpan Bhattacharyya and Gaurav Katoch and Shubho R. Roy},
journal= {arXiv preprint arXiv:2202.09350},
year = {2023}
}
Comments
34 pages, New references added; revised discussions of Virasoro-Kac-Moody circuits in section 3 although the final conclusions remain unchanged; updated discussion of complexity for warped conformal field theory. Version accepted for publication in EPJC