On the next-to-leading holographic entanglement entropy in AdS 3 /CFT 2

Abstract:We extend and refine recent results on Rényi entropy in two-dimensional conformal field theories at large central charge. To do so, we examine the effects of higher spin symmetry and of allowing unequal left and right central charges, at leading and subleading order in large total central charge. The result is a straightforward generalization of previously derived formulae, supported by both gravity and CFT arguments. The preceding statements pertain to CFTs in the ground state, or on a circle at unequal left-and right-moving temperatures. For the case of two short intervals in a CFT ground state, we derive certain universal contributions to Rényi and entanglement entropy from Virasoro primaries of arbitrary scaling weights, to leading and next-to-leading order in the interval size; this result applies to any CFT. When these primaries are higher spin currents, such terms are placed in one-to-one correspondence with terms in the bulk 1-loop determinants for higher spin gauge fields propagating on handlebody geometries.

Section: Jhep05(2014)052mentioning

confidence: 84%

Comments on Rényi entropy in AdS3/CFT2

Perlmutter

2014

“…Especially for the large c CFT dual to the AdS 3 gravity, the vacuum module contribution dominates the partition function in the large central charge limit. This leads to a lot of study on the two-interval Rényi entropy in the large c CFTs, which sheds new light on the AdS 3 /CFT 2 correspondence [28][29][30][31][32][33][34][35][36]. Some relevant discussions on entanglement entropy of 2D quantum field theory can be found in [37][38][39][40][41][42][43][44][45][46][47].…”

Section: Jhep06(2017)096mentioning

confidence: 99%

On the mutual information in conformal field theory

Chen

Hao

et al. 2017

Abstract:In this work, we study the universal behaviors in the mutual information of two disjoint spheres in a conformal field theory (CFT). By using the operator product expansion of the spherical twist operator in terms of the conformal family, we show that the large distance expansion of the mutual information can be cast in terms of the conformal blocks. We develop the 1/n prescription to compute the coefficients before the conformal blocks. For a single conformal family, the leading nonvanishing contribution to the mutual information comes from the bilinear operators. We show that the coefficients of these operators take universal forms and such universal behavior persists in the bilinear operators with derivatives as well. Consequently the first few leading order contributions to the mutual information in CFT take universal forms. To illustrate our framework, we discuss the free scalars and free fermions in various dimensions. For the free scalars, we compute the mutual information to the next-to-leading order and find good agreement with the improved numerical lattice result. For the free fermion, we compute the leading order result, which is of universal form, and find the good match with the numerical study. Our formalism could be applied to any CFT potentially.

“…the spectrum of the operators and the OPE coefficients [20] (see also [21][22][23][24] and for related work [25][26][27][28][29]). One may ask whether a similar approach can be useful in the computation of entanglement negativity, and if the holographic prescription can be inferred from it.…”

Section: Jhep09(2014)010mentioning

confidence: 99%

Conformal blocks and negativity at large central charge

Kulaxizi

Parnachev

Policastro

2014

141

We consider entanglement negativity for two disjoint intervals in 1+1 dimensional CFT in the limit of large central charge. As the two intervals get close, the leading behavior of negativity is given by the logarithm of the conformal block where a set of approximately null descendants appears in the intermediate channel. We compute this quantity numerically and compare with existing analytic methods which provide perturbative expansion in powers of the cross-ratio.