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24
Exactly marginal deformations of N = 4 SYM and of its supersymmetric orbifold descendants
 JHEP 0205
, 2002
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Nonabelian phenomena on Dbranes
, 2003
"... Abstract. A remarkable feature of Dbranes is the appearance of a nonabelian gauge theory in the description of several (nearly) coincident branes. This nonabelian structure plays an important role in realizing various geometric effects with Dbranes. In particular, the branes ’ transverse displacem ..."
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Cited by 14 (1 self)
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Abstract. A remarkable feature of Dbranes is the appearance of a nonabelian gauge theory in the description of several (nearly) coincident branes. This nonabelian structure plays an important role in realizing various geometric effects with Dbranes. In particular, the branes ’ transverse displacements are described by matrixvalued scalar fields and so noncommutative geometry naturally appears in this framework. I review the action governing this nonabelian theory, as well as various related physical phenomena such as the dielectric effect, giant gravitons and fuzzy funnels.
Discrete torsion, nonAbelian orbifolds and the Schur multiplier,” hepth/0010023
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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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Cited by 11 (8 self)
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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.
Lectures on Dbranes, gauge theories and CalabiYau singularities
, 2004
"... These lectures, given at the Chinese Academy of Sciences for the BeiJing/HangZhou International Summer School in Mathematical Physics, are intended to introduce, to the beginning student in string theory and mathematical physics, aspects of the rich and beautiful subject of Dbrane gauge theories co ..."
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Cited by 11 (6 self)
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These lectures, given at the Chinese Academy of Sciences for the BeiJing/HangZhou International Summer School in Mathematical Physics, are intended to introduce, to the beginning student in string theory and mathematical physics, aspects of the rich and beautiful subject of Dbrane gauge theories constructed from local CalabiYau spaces. Topics such as orbifolds, toric singularities, del Pezzo surfaces as well as chaotic duality will be covered.
Noncommutative moduli spaces, Dielectric Tori and Tduality
"... We review and extend recent work on the application of the noncommutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N = 4 super YangMills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds so ..."
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Cited by 8 (4 self)
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We review and extend recent work on the application of the noncommutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N = 4 super YangMills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the Dbrane bubbles. Different regions of moduli space are associated with D5branes of various topologies; singularities in the moduli space are associated with topology change. Tduality on toroidal topologies maps between mirror string realizations of the field theory.
Discrete Torsion, Covering Groups and Quiver Diagrams
, 2001
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Winding String Condensation and Noncommutative Deformation of Spacelike Singularity
"... In a previous paper (hepth/0509067) using matrix model, we showed that closed string tachyons can resolve spacelike singularity in one particular class of Misner space (with antiperiodic boundary conditions for fermions around the spatial circle). In this note, we show that for Misner space withou ..."
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Cited by 6 (0 self)
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In a previous paper (hepth/0509067) using matrix model, we showed that closed string tachyons can resolve spacelike singularity in one particular class of Misner space (with antiperiodic boundary conditions for fermions around the spatial circle). In this note, we show that for Misner space without closed string tachyons, there also exists a mechanism to resolve the singularity in the context of the matrix model, namely cosmological winding string production. We show that here space and time also become noncommutative due to these winding strings. Employing optical theorem, we study the bulk boundary coupling by calculating the fouropenstring cylinder amplitudes.
Rashkov, Threepoint correlators: Examples from LuninMaldacena background, Phys
 Rev. D
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Toric Varieties with NC Toric Actions: NC Type IIA Geometry, Nucl.Phys
 B677 (2004) 587613, hepth/0312200, NC CalabiYau Manifolds in Toric Varieties with NC Torus fibration, Phys.Lett. B550 (2002) 108116, hepth/0210073 El Hassan Saidi, NC Geometry and Fractional
"... Extending the usual C ∗r actions of toric manifolds by allowing asymmetries between the various C ∗ factors, we build a class of non commutative (NC) toric varieties V (nc) d+1. We construct NC complex d dimension CalabiYau manifolds embedded in V (nc) d+1 by using the algebraic geometry method. Re ..."
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Cited by 3 (2 self)
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Extending the usual C ∗r actions of toric manifolds by allowing asymmetries between the various C ∗ factors, we build a class of non commutative (NC) toric varieties V (nc) d+1. We construct NC complex d dimension CalabiYau manifolds embedded in V (nc) d+1 by using the algebraic geometry method. Realizations of NC C ∗r toric group are given in presence and absence of quantum symmetries and for both cases of discrete or continuous spectrums. We also derive the constraint eqs for NC CalabiYau backgrounds M nc d embedded in V nc d+1 and work out their solutions. The latters depend on the CalabiYau condition ∑ i qa i = 0, q a i being the charges of C ∗r; but also on