Complexity of warped conformal field theory Article Swipe
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· 2023
· Open Access
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· DOI: https://doi.org/10.1140/epjc/s10052-023-11212-8
· OA: W4316881890
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 .
