Complexity of warped conformal field theory

Arpan Bhattacharyya (Indian Institute of Technology, Gandhinagar, Gujarat, 382355, India) ; Gaurav Katoch (Department of Physics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana, 502285, India) ; Shubho Roy (Department of Physics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana, 502285, India)

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 $$_3$$ 3 spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT $$_2$$ 2 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 $$_2$$ 2 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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      "surname": "Roy", 
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      "value": "Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro\u2013Kac\u2013Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS $$_3$$  <math> <msub> <mrow></mrow> <mn>3</mn> </msub> </math>   spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT $$_2$$  <math> <msub> <mrow></mrow> <mn>2</mn> </msub> </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 $$_2$$  <math> <msub> <mrow></mrow> <mn>2</mn> </msub> </math>   and has a very complicated dependence on the Virasoro central charge c and the U(1) Kac\u2013Moody level parameter k. Next we consider circuit complexity based on Virasoro\u2013Kac\u2013Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro\u2013Kac\u2013Moody group. We consider a special solution to extremization equations for which complexity scales linearly with \u201ctime\u201d. 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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Published on:
17 January 2023
Publisher:
Springer
Published in:
European Physical Journal C , Volume 83 (2023)
Issue 1
Pages 1-14
DOI:
https://doi.org/10.1140/epjc/s10052-023-11212-8
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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