Related papers: Five-Branes in M-Theory and a Two-Dimensional Geom…
We argue that the moduli space for the Bagger-Lambert A_4 theory at level k is (R^8 \times R^8)/D_{2k}, where D_{2k} is the dihedral group of order 4k. We conjecture that the theory describes two M2-branes on a Z_{2k} ``M-fold'', in which a…
We clarify some ambiguous points in a derivation of duality via brane exchange using M-theory language, and propose a ``proof'' of duality in MQCD. Actually, duality in MQCD is rather trivial and does not need a complicated proof. The…
We give a review of truncated L$_\infty$ algebras, as used in the study of higher gauge theory. These structures are believed to hold the correct properties to adequately describe gauge theory of extended objects. We discuss how to…
We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to junctions of two boundary conditions in a 4d…
Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…
We study the T duality between a set of type IIB D3 branes atnon-orbifold threefold singularities, and type IIA configurations of D4 branes stretched between relatively rotated NS fivebranes. The four-dimensional N=1 field theories on the…
We consider four dimensional supersymmetric gauge field theories from brane configurations with the matter content given by semi-infinite D4 branes ending on both sides of NS branes. In M theory configuration, we discuss the splitting of…
Using brane quantization, we study the representation theory of the spherical double affine Hecke algebra of type $A_1$ in terms of the topological A-model on the moduli space of flat SL(2,C)-connections on a once-punctured torus. In…
We review aspects of N=1 duality between the heterotic string and F-theory. After a description of string duality intended for the non-specialist the framework and the constraints for heterotic/F-theory compactifications are presented. The…
We discuss the geometry of string and M-theory gauge fields in Deligne cohomology. In particular, we show how requiring string structure (or loop space Spin-C structure) on the five-brane leads to topological conditions on the flux in the…
We engineer a large new set of four-dimensional N=1 superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS_5 M-theory backgrounds which describe these fixed points at large N, and then…
Extending previous work that involved D3-branes ending on a fivebrane with $\theta_{\mathrm{YM}}\not=0$, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional…
This thesis first gives a background and review of the article hep-th/0102038, where we substantiated a conjectured duality between two a priori unrelated gauge theories, N=2 quiver theory and N=2 Seiberg-Witten theory. These gauge theories…
T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory…
This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to…
We obtain singularity resolutions for various overlapping brane configurations, including those of two heterotic 5-branes, type II 5-branes or D4-branes. In these solutions, the ``harmonic'' function H for each brane component depends only…
By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology of the hypermultiplet moduli space M_H in Calabi-Yau compactifications of type II string theories at fixed value of the dilaton and of the…
Given a compact Riemann surface $X$ and a complex reductive Lie group $G$ equipped with real structures, we define antiholomorphic involutions on the moduli space of $G$-Higgs bundles over $X$. We investigate how the various components of…
The global geometric Langlands correspondence relates Hecke eigensheaves on the moduli stack of G-bundles on a smooth projective algebraic curve X and holomorphic G'-bundles with connection on X, where G' is the Langlands dual group of G.…
We study the dimensional reduction of M5-branes wrapping special Lagrangian 3-cycles of a Calabi-Yau manifold and show explicitly that they result in 2-branes coupled to the hypermultiplets of ungauged N=2 D=5 supergravity theory. In…