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N = 2 dualities
A bstractWe study the generalization of S-duality and Argyres-Seiberg duality for a large class of N = 2 superconformal gauge theories. We identify a family of strongly interacting SCFTs and use themExpand
Liouville Correlation Functions from Four-Dimensional Gauge Theories
We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain classExpand
S-duality of boundary conditions in N=4 super Yang-Mills theory
By analyzing brane configurations in detail, and extracting general lessons, we develop methods for analyzing S-duality of supersymmetric boundary conditions in N=4 super Yang-Mills theory. In theExpand
Generalized global symmetries
A bstractA q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have qExpand
Wall-crossing, Hitchin Systems, and the WKB Approximation
We consider BPS states in a large class of d = 4,N = 2 eld theories, obtained by reducing six-dimensional (2; 0) superconformal eld theories on Riemann surfaces, with defect operators inserted atExpand
Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
We give a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories. In the process we give an exact description of the BPS instantonExpand
Framed BPS states
We consider a class of line operators in d = 4,N = 2 supersymmetric field theories which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we callExpand
Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
Recently, a duality between Liouville theory and four dimensional $ \mathcal{N} = 2 $ gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory,Expand
The gravity duals of N=2 superconformal field theories
We study the gauge/gravity duality for theories with four dimensional ${\cal N}=2$ supersymmetries. We consider the large class of generalized quiver field theories constructed recently by one of usExpand
Notes on superconformal Chern-Simons-Matter theories
The three dimensional = 2 supersymmetric Chern-Simons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with LagrangianExpand