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arXiv:1907.12603 · Journal of High Energy Physics

Correlation functions, entanglement and chaos in the $$ T\overline{T}/J\overline{T} $$-deformed CFTs

Song He, Hongfei Shu

Published Feb 1, 2020• 81 citations
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Abstract

Abstract In this paper, we regard the $$ T\overline{T}/J\overline{T} $$ T T ¯ / J T ¯ -deformed CFTs as perturbation theories and calculate the first order correction of the correlation functions due to the $$ T\overline{T}/J\overline{T} $$ T T ¯ / J T ¯ ­deformation. As applications, we study the Rényi entanglement entropy of excited state in the $$ T\overline{T}/J\overline{T} $$ T T ¯ / J T ¯ -deformed two-dimensional CFTs. We find, up to the first order perturbation of the deformation, the Rényi entanglement entropy of locally excited states will acquire a non­trivial time dependence. The excess of the Rényi entanglement entropy of locally excited state is changed up to order O(c). Furthermore, the out of time ordered correlation function is investigated to confirm that the $$ T\overline{T}/J\overline{T} $$ T T ¯ / J T ¯ -deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.

DOI
10.1007/jhep02(2020)088

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Various aspects of warped conformal field theories (WCFTs) are studied including entanglement entropy on excited states, the Renyi entropy after a local quench, and out-of-time-order four-point functions. Assuming a large central charge and dominance of the vacuum block in the conformal block expansion, (i) we calculate the single-interval entanglement entropy on an excited state, matching previous finite temperature results by changing the ensemble; and (ii) we show that WCFTs are maximally chaotic, a result that is compatible with the existence of black holes in the holographic duals. Finally, we relax the aforementioned assumptions and study the time evolution of the Renyi entropy after a local quench. We find that the change in the Renyi entropy is topological, vanishing at early and late times, and nonvanishing in between only for charged states in spectrally-flowed WCFTs.
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