Entanglement and chaos in warped conformal field theories

Abstract

Various aspects of warped conformal field theories (WCFTs) are studied including entanglement entropy on excited states, the Rényi 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 Rényi entropy after a local quench. We find that the change in the Rényi entropy is topological, vanishing at early and late times, and nonvanishing in between only for charged states in spectrally-flowed WCFTs. and f (x + ) and g(x + ) are two arbitrary functions. Unlike standard conformal transformations, the warped conformal symmetries are generated by a left-moving Virasoro-Kac-Moody algebra. Notably, the SL(2, R) L × U (1) R global symmetries of the theory feature translations and chiral scale transformations, but do not include Lorentz transformations. Known examples of WCFT include chiral Liouville gravity [3], free Weyl fermions [4], and

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

“…Moreover, the Rényi entanglement entropy has been used as a very helpful quantity to measure the properties of the vacuum state and excited states [55][56][57][58][59][60][61][62][63][64][65][66]. In the undeformed CFTs, the nth Rényi entanglement entropy S (n) A has been extensively studied in the literature [58][59][60][61][64][65][66][67][68][69][70][71][72][73][74]. In rational CFTs, it has been shown that the excess of the Rényi entanglement entropy has to be the logarithmic of quantum dimension [59] of the corresponding local operator.…”

“…As applications, we employ the formula to investigate the Rényi entanglement entropy in two-dimensional CFTs perturbatively. We just put a local primary operator following the procedure in [59][60][61][64][65][66] to obtain a locally excited state. With time evolution, the excess of Rényi entanglement entropy of deformed two-dimensional CFTs has been calculated in this paper.…”

Warped symmetries of the Kerr black hole

“…Many of their unique field theoretic properties have been uncovered in recent years [16][17][18][19][20][21][22][23][24][25][26][27]. In a holographic context, their natural counterparts are gravitational theories that admit Warped AdS 3 (WAdS 3 ) spacetimes as solutions [28][29][30][31].…”

Entanglement Entropy after Double Excitation as an Interaction Measure

“…In CFT, this quantity can be calculated in terms of a correlator [7,8] and has already studied in RCFTs [9,10], holographic CFTs [11,12], and also non-perturbatively in pure CFTs [1,13,14]. (See also [11,[15][16][17][18][19][20], which revealed the growth of the entanglement entropy after a local quench in other setups.) It is interesting to note that the entanglement growth in RCFTs approaches constant in the late time limit, on the other hand, the entanglement entropy in holographic CFTs shows a logarithmic growth.…”