Related papers: Surface operators in four-dimensional topological …
We study 4d $\mathcal{N}=2$ gauge theories with a co-dimension two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure…
We study four-dimensional gauge theories on oriented and non-spin spacetime manifolds. On such manifolds, each line operator arises only either as a boson or a fermion. Based on physical arguments, a method of systematically assigning spin…
We present here a careful study of the holographic duals of BPS surface operators in the 6d ${\cal N}=(2,0)$ theory. Several different classes of surface operators have been recently identified and each class has a specific calibration form…
We give a new, fully mathematical, construction of the space of local operators in the holomorphic-topological twist of 4d $\mathcal N=2$ gauge theories. It is based on computations of morphism spaces in the DG category of line operators,…
The surface operator in an SU(2) gauge field theory is studied. We analyze Abelian projection of the SU(2) symmetry to the U(1) group calculating the surface parameter. The surface parameter dependence on the surface area and volume is…
Surface operators in four-dimensional gauge theories are two-dimensional defects, serving as natural generalizations of Wilson lines and 't Hooft line operators. They act as ideal probes for exploring the non-perturbative structure of the…
In this paper we study surface operators in N=4 supersymmetric Yang-Mills theory. We compute surface operator observables, such as the expectation value of surface operators, the correlation function of surface operators with local…
We show how to use D and NS fivebranes in Type IIB superstring theory to construct large classes of finite N=1 supersymmetric four dimensional field theories. In this construction, the beta functions of the theories are directly related to…
We study rigid surface operators in the $N=4$ supersymmetric Yang-Mills theories with gauge groups $SO(n)$ and $Sp(2n)$. Using maps $X_S$ and $Y_S$ between these two theories, Wyllard made explicit proposals for how the $S$-duality map…
We study a class of dilatation invariant BPS surface operators in 4-dimensional N=4 Super Yang-Mills theory and their holographic duals in type IIB string theory in AdS_5 x S^5. First we take an example of 1/4 BPS surface operator and study…
We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d N=4 gauge theories. We conjecture various relations between these boundary VOA's and properties of the (topologically twisted)…
We study half-BPS surface operators in N=2 supersymmetric QCD in four dimensions with gauge group SU(2) and four fundamental flavours. We compute the twisted chiral superpotential that describes the effective theory on the surface operator…
This is the seventh article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It discusses an interesting class of observables localised on surfaces that attracts steadily growing attention.…
We investigate 1/2 BPS conformal surface operators in the Klebanov-Witten theory. These surface operators preserve certain parts of the conformal symmetry and R-symmetry as well as half of the supersymmetry. We propose the gravity dual of…
This is the sixth article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It is discussed how to use localisation techniques for the calculation of expectation values of Wilson and 't Hooft…
In three dimensions, a free, periodic scalar field is related by duality to an abelian gauge field. Here I explore aspects of this duality when both theories are quantized on a Riemann surface of genus g. At higher genus, duality involves…
Starting with a choice of a gauge group in four dimensions, there is often freedom in the choice of magnetic and dyonic line operators. Different consistent choices of these operators correspond to distinct physical theories, with the same…
A general class of W-algebras can be constructed from the affine sl(N) algebra by (quantum) Drinfeld-Sokolov reduction and are classified by partitions of N. Surface operators in an N=2 SU(N) 4d gauge theory are also classified by…
We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show…
We continue our program initiated in [arXiv:0912.4261] to consider supersymmetric surface operators in a topologically-twisted N=2 pure SU(2) gauge theory, and apply them to the study of four-manifolds and related invariants. Elegant…