We study operator insertions into the 1/2 BPS Wilson loop in N = 4 SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension insertions and relies on known results for the expectation value of a smooth Wilson loop. In addition to the particular coefficients that we calculate, our study elucidates the connection between deformations of the line and operator insertions and between the vacuum expectation value of the line and the CFT data of the insertions. a cookepm@tcd.ie

We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma-models on AdS backgrounds with Ramond-Ramond fluxes in various dimensions. We show that sigma-models based on supercosets of PSU supergroups, such as AdS 2 × S 2 and AdS 3 × S 3 are self-dual under fermionic T-duality, while supercosets of OSp supergroups such as non-critical AdS 2 and AdS 4 models, and the critical AdS 4 × CP 3 background are not. We present a general algebraic argument to when a supercoset is expected to have a fermionic T-duality symmetry, and when it will fail to have one.

We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: non-critical superstrings on AdS 2d and critical superstrings on AdS p × S p × CY . We work both in the Green-Schwarz and in the pure spinor formalisms. We construct a one-parameter family of flat currents (a Lax connection), leading to an infinite number of conserved non-local charges, which imply the classical integrability of both sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigma-model. We discuss how classical κ-symmetry implies one-loop conformal invariance. We consider the addition of space-filling D-branes to the pure spinor formalism.

Abstract:We study superstrings on AdS 3 × S 3 × T 4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and write down a set of finite-gap equations that describe the massive part of the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-FrolovStaudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantisation of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.