Complexity of warped conformal field theory
Arpan Bhattacharyya, Gaurav Katoch, Shubho Roy
Abstract
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 $$_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msub> </mml:math> spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> 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 CFT $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> 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 .