We study the leading quantum string correction to the dressing phase in the asymptotic Bethe Ansatz system for superstring in AdS 3 × S 3 × T 4 supported by RR flux. We find that the phase should be different from the phase appearing in the AdS 5 ×S 5 case. We use the simplest example of a rigid circular string with two equal spins in S 3 and also consider the general approach based on the algebraic curve description. We also discuss the case of the AdS 3 × S 3 × S 3 × S 1 theory and find the dependence of the 1-loop correction to the effective string tension function h(λ) (expected to enter the magnon dispersion relation) on the parameters α related to the ratio of the two 3-sphere radii. This correction vanishes in the AdS 3 × S 3 × T 4 case.

As was shown earlier, the one-loop correction in 10d supergravity on AdS 5 × S 5 corresponds to the contributions to the vacuum energy and 4d boundary conformal anomaly which are minus the values for one N = 4 Maxwell supermultiplet, thus reproducing the subleading term in the N 2 − 1 coefficient in the dual SU(N ) SYM theory. We perform similar one-loop computations in 11d supergravity on AdS 7 × S 4 and 10d supergravity on AdS 3 × S 3 × T 4 . In the AdS 7 case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2, 0) tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2, 0) theory is 4N 3 − 9/4N − 7/4 and thus vanishes for N = 1. In the AdS 3 case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4, 4) scalar multiplet, i.e. is c = +6. This reproduces the subleading term in the central charge c = 6(Q 1 Q 5 + 1) of the dual 2d CFT describing decoupling limit of D5-D1 system. We also present the expressions for the 6d a-anomaly coefficient and vacuum energy contributions of general-symmetry higher spin field in AdS 7 and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank-2 antisymmetric tensors.

We consider the semiclassical limit of the vacuum Virasoro block describing the diagonal 4-point correlation functions on the sphere. At large central charge c, after exponentiation, it depends on two fixed ratios h H /c and h L /c, where h H,L are the conformal dimensions of the 4-point function operators. The semiclassical block may be expanded in powers of the light ratio h L /c and the leading non-trivial (linear) order is known in closed form as a function of h H /c. Recently, this contribution has been matched against AdS 3 gravity calculations where heavy operators build up a classical geometry corresponding to a BTZ black hole, while the light operators are described by a geodesic in this background. Here, we compute for the first time the next-to-leading quadratic correction O((h L /c) 2 ), again in closed form for generic heavy operator ratio h H /c. The result is a highly nontrivial extension of the leading order and may be relevant for further refined AdS 3 /CFT 2 tests. Applications to the two-interval Rényi entropy are also presented.

In the present paper, which is a sequel to arXiv:1001:4018, we compute the one-loop correction to the energy of pulsating string solutions in AdS 5 × S 5 . We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can be also put into the single-gap Lamé form. A novel aspect of pulsating solutions is that the one-loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the "short string" limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of "small" semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.

We consider the process of associated stop-chargino production in the MSSM at LHC and show that, at the simplest Born level, the production rate is dramatically sensitive to the choice of the benchmark points, oscillating from potentially "visible" maxima of the picobarn size to much smaller, hardly "visible", values. Adopting a canonical choice of SM type CKM matrices, we also show that in some "visible" cases the total rate exhibits a possibly relevant dependence on tan(beta)

We consider integrable superstring theory on AdS 3 × S 3 × M 4 where M 4 = T 4 or M 4 = S 3 × S 1 with generic ratio of the radii of the two 3-spheres. We compute the oneloop energy of a short folded string spinning in AdS 3 and rotating in S 3 . The computation is performed by world-sheet small spin perturbation theory as well as by quantizing the classical algebraic curve characterizing the finite-gap equations. The two methods give equal results up to regularization contributions that are under control. One important byproduct of the calculation is the part of the energy which is due to the dressing phase in the Bethe Ansatz. Remarkably, this contribution E dressing 1 turns out to be independent on the radii ratio. In the M 4 = T 4 limit, we discuss how E dressing 1 relates to a recent proposal for the dressing phase tested in the su(2) sector. We point out some difficulties suggesting that quantization of the AdS 3 classical finite-gap equations could be subtler than the easier AdS 5 × S 5 case.

We consider twist-1, 2 operators in planar AE superconformal Chern-Simons ABJM theory. We derive higher order anomalous dimensions from integrability and test various QCD-inspired predictions known to hold in AE SYM. In particular, we show that the asymptotic anomalous dimensions display intriguing remnants of Gribov-Lipatov reciprocity and Low-Burnett-Kroll logarithmic cancellations. Wrapping effects are also discussed and shown to be subleading at large spin. 5.2 Twist-2 13 6. Conclusions 15 A. On shift symmetries 16 B. Next-to-leading Baxter equation 17 B.1 Twist-1 17 B.2 Twist-2 17

Abstract:We reconsider the one-loop correction to the holographic entanglement entropy in AdS 3 /CF T 2 by analysing the contributions due to a bulk higher spin s current or a scalar field with scaling dimension ∆. We consider the two-interval case and work perturbatively in their small cross ratio x. We provide various results for the entanglement entropy due to the so-called CDW elements of the associated Schottky uniformization group. In particular, in the higher spin current case, we obtain a closed formula for all the contributions of the form O(x 2s+p ) up to O(x 4s ), where 2-CDW elements are relevant. In the scalar field case, we calculate the similar contributions for generic values of ∆. The terms up to O(x 2∆+5 ) are compared with an explicit CFT calculation with full agreement. The analysis exploits various simplifications which are valid in the strict entanglement limit of the Rényi entropy. This allows to identify in a clean way the relevant operators that provide the gravity result. The 2-CDW contributions are also analysed and a closed formula for the leading O(x 4s ) coefficient is presented as a function of the generic spin s. As a specific application, we combine the CDW and 2-CDW calculations and present the complete O(x 4s+2 ) entanglement entropy for a spin s = 2, 3, 4 higher spin currents.