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DBranes And KTheory In 2D Topological Field Theory,” hepth/0609042; see also lectures by G. Moore, at http://online.itp.ucsb.edu/online/mp01
"... This expository paper describes sewing conditions in twodimensional open/closed topological field theory. We include a description of the Gequivariant case, where G is a finite group. We determine the category of boundary conditions in the case that the closed string algebra is semisimple. In this ..."
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This expository paper describes sewing conditions in twodimensional open/closed topological field theory. We include a description of the Gequivariant case, where G is a finite group. We determine the category of boundary conditions in the case that the closed string algebra is semisimple. In this case we find that sewing constraints – the most primitive form of worldsheet locality – already imply that Dbranes are (Gtwisted) vector bundles on spacetime. We comment on extensions to cochainvalued theories and various applications. Finally, we give uniform proofs of all relevant sewing theorems using Morse theory. August
Discrete torsion, nonAbelian orbifolds and the Schur multiplier,” hepth/0010023
"... Preprint typeset in JHEP style. HYPER VERSION ..."
On Algebraic Singularities, Finite Graphs and DBrane Gauge Theories: A String Theoretic Perspective
, 2002
"... In this writing we shall address certain beautiful interrelations between the construction of 4dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such ..."
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In this writing we shall address certain beautiful interrelations between the construction of 4dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such as orbifolds, symplectic quotients and quiver representations, as well as the physics, such as gauged linear sigma models, geometrical engineering, HananyWitten setups and Dbrane probes. We investigate aspects of worldvolume gauge dynamics using Dbrane resolutions of various CalabiYau singularities, notably Gorenstein quotients and toric singularities. Attention will be paid to the general methodology of constructing gauge theories for these singular backgrounds, with and without the presence of the NSNS Bfield, as well as the Tduals to brane setups and branes wrapping cycles in the mirror geometry. Applications of such diverse and elegant mathematics as crepant resolution of algebraic singularities, representation of finite groups and finite graphs, modular invariants of affine Lie algebras, etc. will naturally arise. Various viewpoints and generalisations of McKay’s Correspondence will also be considered. The present work is a transcription of excerpts from the first three volumes of the author’s PhD thesis which was written under the direction of Prof. A. Hanany to whom he is much indebted at the Centre for Theoretical Physics of MIT, and which, at the suggestion of friends, he posts to the ArXiv pro hac vice; it is his sincerest wish that the ensuing pages might be of some small use to the beginning student.
Discrete Torsion, Covering Groups and Quiver Diagrams
, 2001
"... Preprint typeset in JHEP style. HYPER VERSION ..."
Dbranes in nonabelian orbifolds with discrete torsion
, 2001
"... hepth/0109170 ..."
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Notes on discrete torsion in orientifolds
, 2009
"... In this short note we discuss discrete torsion in orientifolds. In particular, we apply the physical understanding of discrete torsion worked out several years ago, as group actions on B fields, to the case of orientifolds, and recover some old results of Braun and Stefanski concerning group cohomol ..."
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In this short note we discuss discrete torsion in orientifolds. In particular, we apply the physical understanding of discrete torsion worked out several years ago, as group actions on B fields, to the case of orientifolds, and recover some old results of Braun and Stefanski concerning group cohomology and twisted equivariant K theory. We also derive new results
Discrete Torsion and Shift Orbifolds
, 2003
"... In this paper we make two observations related to discrete torsion. First, we observe that an old obscure degree of freedom (momentum/translation shifts) in (symmetric) string orbifolds is related to discrete torsion. We point out how our previous derivation of discrete torsion from orbifold group a ..."
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In this paper we make two observations related to discrete torsion. First, we observe that an old obscure degree of freedom (momentum/translation shifts) in (symmetric) string orbifolds is related to discrete torsion. We point out how our previous derivation of discrete torsion from orbifold group actions on B fields includes these momentum lattice shift phases, and discuss how they are realized in terms of orbifold group actions on Dbranes. Second, we describe the M theory dual of IIA discrete torsion, a duality relation to our knowledge not previously understood. We show that IIA discrete torsion is encoded in analogues of the