Asymptotically free AdS3/CFT2

We propose a new AdS3/CFT2 duality, in which the bulk string theory has a target spacetime AdS3 times a squashed three-sphere $$ {\mathbbm{S}}_{\flat}^3 $$ S ♭ 3 , and the dual CFT2 is a symmetric product of sigma models on ℝϕ×$$ {\mathbbm{S}}_{\flat}^3 $$ S ♭ 3 , deformed by a ϕ-dependent ℤ2 twist operator. The duality maps the asymptotic region of AdS3 to the region ϕ → ∞, where the twist interaction in the CFT2 turns off. The AdS3 backgrounds in question have RAdS< ℓs, and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in AdS3 rather than an ensemble of BTZ black holes. This property allows us to derive the dual CFT2 by a systematic analysis of the worldsheet string theory on AdS3.

Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms

We show that the entanglement entropy of D = 4 linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on S1× AdS3. The mass of the constant mode on S1 saturates the Brietenholer-Freedman bound in AdS3. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on S1× AdS5 and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal p-forms in even dimensions it obeys the expected relations with the coefficients determining the 3-point function of the stress tensor of these fields.

MAPS AND TWISTS RELATING U(sl(2)) AND THE NONSTANDARD Uh(sl(2)): UNIFIED CONSTRUCTION

A general construction is given for a class of invertible maps between the classical U ( sl (2)) and the Jordanian U h( sl (2)) algebras. Here the role of the maps is studied in the context of construction of twist operators relating the cocommutative and non-cocommutative coproducts of the U(sl(2)) and U h( sl (2)) algebras respectively. It is shown that a particular map called the "minimal twist map" implements the simplest twist given directly by the factorized form of the ℛh matrix of Ballesteros–Herranz. For a "non-minimal" map the twist has an additional factor obtainable in terms of the similarity transformation relating the map in question to the minimal one. Our general prescription may be used to evaluate the series expansion in powers of h of the twist operator corresponding to an arbitrary "non-minimal" map. The classical and the Jordanian antipode maps may also be interrelated by suitable similarity transformations.