Universal correction to higher spin entanglement entropy

Abstract

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.

Boundary conditions and partition functions in higher spin AdS3/CFT2

“…Indeed, starting with the proposal of Gaberdiel and Gopakumar [6,7] relating the three-dimensional interacting higher spin theories [8,9] to a family of minimal model coset CFTs with W-symmetry, 1 several results have been obtained that show agreement between quantities computed in CFT and from the bulk duals. These include the spectrum [11][12][13][14][15], partition functions [16][17][18], scalar correlators [19,20], and entanglement entropies [21][22][23], to name a few. While the full realization of the duality also involves matter fields in the bulk, which couple to operators other than conserved currents, the pure higher spin sector of the correspondence already provides an interesting arena where universal aspects of the duality can be explored.…”

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

“…Such operators do not exist in standard Toda theory, where the scalar fields are real, and in order to accommodate such operators one must consider complexified solutions of Toda theory. From (7.11), and with a bit of algebra, we deduce that the stress tensor that appears in the Drinfeld-Sokolov connection is equal to 12) and this is, up to overall normalization, also the stress tensor of the Toda theory. We can evaluate this stress tensor for the saddle-point solution of Toda theory which describes the correlation function of a combination of heavy and light operators, again to first order in the light operators.…”

“…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.…”

Entanglement entropy for descendent local operators in 2D CFTs

“…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.…”

“…The transformation of the energy momentum tensor under the map z(ω) is given by 36) with the Schwarzian derivative…”