We show that all half-BPS Wilson loop operators in N = 4 SYM -which are labeled by Young tableaus -have a gravitational dual description in terms of D5-branes or alternatively in terms of D3-branes in AdS 5 ×S 5 . We prove that the insertion of a half-BPS Wilson loop operator in the N = 4 SYM path integral is achieved by integrating out the degrees of freedom on a configuration of bulk D5-branes or alternatively on a configuration of bulk D3-branes. The bulk D5-brane and D3-brane descriptions are related by bosonization. 4/20061 jgomis@perimeterinstitute.ca 2 Filippo.Passerini@fys.kuleuven.be

We prove that the half-BPS Wilson loop operator of N = 4 SYM in a symmetric representation of the gauge group has a bulk gravitational description in terms of a single D3-brane in AdS 5 ×S 5 , as argued in hep-th/0604007. We also show that a half-BPS Wilson loop operator in an arbitrary representation is described by the D3-brane configuration proposed in hep-th/0604007. This is demonstrated by explicitly integrating out the degrees of freedom on the D3-branes and showing that they insert a half-BPS Wilson loop operator into the N = 4 SYM path integral in the desired representation. 12/20061 jgomis@perimeterinstitute.ca 2 fpasserini@perimeterinstitute.ca

Three dimensional field theories admit disorder line operators, dubbed vortex loop operators. They are defined by the path integral in the presence of prescribed singularities along the defect line. We study half-BPS vortex loop operators for N = 2 supersymmetric theories on S 3 , its deformation S 3 b and S 1 × S 2 . We construct BPS vortex loops defined by the path integral with a fixed gauge or flavor holonomy for infinitesimal curves linking the loop. It is also possible to include a singular profile for matter fields. For vortex loops defined by holonomy, we perform supersymmetric localization by calculating the fluctuation modes, or alternatively by applying the index theory for transversally elliptic operators. We clarify how the latter method works in situations without fixed points of relevant isometries. Abelian mirror symmetry transforms Wilson and vortex loops in a specific way. In particular an ordinary Wilson loop transforms into a vortex loop for a flavor symmetry. Our localization results confirm the predictions of abelian mirror symmetry.

We compute the expectation value of the circular Wilson loop in N = 2 supersymmetric Yang-Mills theory with N f = 2N hypermultiplets. Our results indicate that the string tension in the dual string theory scales as the logarithm of the 't Hooft coupling.

Recently Alday and Tachikawa [1] proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal N = 2 SU(2) quiver gauge theories in the presence of a certain surface operator. In this paper we extend this proposal to a relation between conformal blocks in theories with affine sl(N ) symmetry and instanton partition functions in conformal N = 2 SU(N ) quiver gauge theories in the presence of a surface operator. We also discuss the extension to non-conformal N = 2 SU(N ) theories.

© 2014, Springer Science+Business Media Dordrecht. 3d (Formula Presented.) partition functions on the squashed three-sphere (Formula Presented.) and on the twisted product (Formula Presented.) have been shown to factorize into sums of squares of solid tori partition functions, the so-called holomorphic blocks. The same set of holomorphic blocks realizes (Formula Presented.) and (Formula Presented.) partition functions but the two cases involve different inner products, the S-pairing and the id-pairing, respectively. We define a class of q-deformed CFT correlators where chiral blocks are controlled by a deformation of Virasoro symmetry and are paired by S-pairing and id-pairing, respectively. Applying the bootstrap approach to a class of degenerate correlators we are able to derive three-point functions. We show that degenerate correlators can be mapped to 3d partition functions while the crossing symmetry of correlators corresponds to the flop symmetry of 3d gauge theories. We explore how non-degenerate q-deformed correlators are related to 5d partition functions. We argue that id-pairing correlators are associated with the superconformal index on (Formula Presented.) while S-pairing three-point function factors capture the one-loop part of S5 partition functions. This is consistent with the interpretation of (Formula Presented.) and (Formula Presented.) gauge theories as codimension two defect theories inside (Formula Presented.) and S5, respectively

We analyze N = 1 theories on S 5 and S 4 × S 1 , showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We demonstrate that, when the 5d mass parameters are analytically continued to suitable values, the S 5 and S 4 × S 1 partition functions degenerate to those for S 3 and S 2 × S 1 . We explain this mechanism via the recently proposed correspondence between 5d partition functions and correlators with underlying q-Virasoro symmetry. From the q-Virasoro 3-point functions, we axiomatically derive a set of associated reflection coefficients, and show that they can be geometrically interpreted in terms of Harish-Chandra c-functions for quantum symmetric spaces. We link these particular c-functions to the types appearing in the Jost functions encoding the asymptotics of the scattering in integrable spin-chains, obtained taking different limits of the XYZ model to XXZ-type.

We write down a maximally supersymmetric one parameter deformation of the field theory action of Bagger and Lambert. We show that this theory on R × T 2 is invariant under the superalgebra of the maximally supersymmetric Type IIB plane wave. It is argued that this theory holographically describes the Type IIB plane wave in the discrete light-cone quantization (DLCQ). 04/2008a jgomis@perimeterinstitute.ca b ajafarisalim@perimeterinstitute.ca c fpasserini@perimeterinstitute.ca