Complexity of warped conformal field theory

Bhattacharyya, Arpan and Katoch, Gaurav and Roy, Shubho R. (2023) Complexity of warped conformal field theory. The European Physical Journal C, 83 (1). ISSN 1434-6052

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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 AdS3 spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT2 s using 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 CFT2 and has a very complicated dependence on the Virasoro central charge c and the U(1) Kac–Moody level parameter k. 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 c, k, while c/k remains finite and small) both the holographic volume complexity and circuit complexity scales with k.

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