Higher spin entanglement entropy from CFT

Datta, Shouvik; David, Justin R.; Ferlaino, Michael; Kumar, S. Prem

doi:10.1007/jhep06(2014)096

Cited by 43 publications

(107 citation statements)

References 79 publications

(258 reference statements)

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“…Here 11) are the rescaled conformal dimensions of the operators O(x i ), and c i are auxiliary parameters related to the conformal blocks f (x i ) through a derivative…”

Section: Virasoro Algebramentioning

confidence: 99%

“…In the notation (5.4) the zeroth order piece (which is independent of ε) is 11) and the fundamental matrix associated to the zeroth order equation is …”

Section: Jhep07(2015)168mentioning

confidence: 99%

“…Another is to the case of higher spin gravity, which is the case that we focus on here, in particular its 3d version and corresponding 2d CFT dual. The study of entanglement entropy in higher spin theories was initiated in [7,8] and further work appears in [9][10][11][12][13][14][15][16][17]. Our two main goals are the following: first to attempt to derive from first principles the prescriptions advanced in [7,8], 1 and second to extend these considerations to the case of Rényi entropy in higher spin theories.…”

Section: Jhep07(2015)168 1 Introductionmentioning

confidence: 99%

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Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks

Boer

Castro

Hijano

et al. 2015

J. High Energ. Phys.

158

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Two-dimensional conformal field theories with extended W-symmetry algebras have dual descriptions in terms of weakly coupled higher spin gravity in AdS 3 at large central charge. Observables that can be computed and compared in the two descriptions include Rényi and entanglement entropies, and correlation functions of local operators. We develop techniques for computing these, in a manner that sheds light on when and why one can expect agreement between such quantities on each side of the duality. We set up the computation of excited state Rényi entropies in the bulk in terms of Chern-Simons connections, and show how this directly parallels the CFT computation of correlation functions. More generally, we consider the vacuum conformal block for general operators with ∆ ∼ c. When two of the operators obey ∆ c ≪ 1, we show by explicit computation that the vacuum conformal block is computed by a bulk Wilson line probing an asymptotically AdS 3 background with higher spin fields excited, the latter emerging as the effective bulk description of the excited state produced by the heavy operators. Among other things, this puts a previous proposal for computing higher spin entanglement entropy via Wilson lines on firmer footing, and clarifies its relation to CFT. We also study the corresponding computation in Toda theory and find that this provides yet another independent way to arrive at the same result.

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“…Here 11) are the rescaled conformal dimensions of the operators O(x i ), and c i are auxiliary parameters related to the conformal blocks f (x i ) through a derivative…”

Section: Virasoro Algebramentioning

confidence: 99%

“…In the notation (5.4) the zeroth order piece (which is independent of ε) is 11) and the fundamental matrix associated to the zeroth order equation is …”

Section: Jhep07(2015)168mentioning

confidence: 99%

Section: Jhep07(2015)168 1 Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks

Boer

Castro

Hijano

et al. 2015

J. High Energ. Phys.

158

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“…Though there are divergences in the global contribution [31], such divergences can be regulated appropriately. Actually there are various definite extensive examples [34][35][36][37][38] to show that global contribution is finite. Actually, we can get a more general conformal transformation for the operators, which is an expansion for the previous result Open Access.…”

Section: Jhep10(2015)173mentioning

confidence: 99%

Entanglement entropy for descendent local operators in 2D CFTs

Chen

Guo

et al. 2015

J. High Energ. Phys.

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We mainly study the Rényi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and Rényi entropy for a class of descendent operators, which are generated by L (−)L(−) onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the Rényi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the Rényi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by d {n i }{n j } ( i L −n i jL −n j ) on the primary operator. For these operators, the entanglement entropy and Rényi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the Rényi entropy of the excited operators in deformed CFT. The Rényi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.

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“…The first non-trivial correction to the Rényi entropies in the deformed theory is therefore determined by the four point correlator involving the twist-anti-twist pair and two W -currents. Importantly, the twist operators and their action can be made explicit only for free theories and consequently the correlators explicitly evaluated for these examples [8]. We will now argue that the singularity structure of the correlator, relevant for RE evaluation, is determined in complete generality by the W W operator product expansion (OPE).…”

mentioning

confidence: 99%

Universal correction to higher spin entanglement entropy

et al. 2014

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We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a chemical potential µ for the spin-three current. We show that the order µ 2 correction to the Rényi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. This explains the recently found agreement of the order µ 2 correction across distinct free field CFTs and higher spin black hole solutions holographically dual to CFTs with W-symmetry.

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Higher spin entanglement entropy from CFT

Cited by 43 publications

References 79 publications

Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks

Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks

Entanglement entropy for descendent local operators in 2D CFTs

Universal correction to higher spin entanglement entropy

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