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545
Chiral rings and anomalies in supersymmetric gauge theory
 JHEP
, 2002
"... Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loo ..."
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Cited by 160 (7 self)
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Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of “integration constants. ” From this, we can derive the DijkgraafVafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of N = 1 super YangMills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.
Nonlinear Instantons from Supersymmetric Pbranes
, 1999
"... Supersymmetric configurations of type II Dbranes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the κsymmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtai ..."
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Cited by 152 (6 self)
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Supersymmetric configurations of type II Dbranes with nonzero gauge field strengths in general supersymmetric backgrounds with nonzero B fields are analyzed using the κsymmetric worldvolume action. It is found in dimension four or greater that the usual instanton equation for the gauge field obtains a nonlinear deformation. The deformation is parameterized by the topological data of the Bfield, the background geometry and the cycle wrapped by the brane. In the appropriate dimensions, limits and settings these equations reduce to deformed instanton equations recently found in the context of noncommutative geometry as well as those following from Lagrangians based on BottChern forms. We further consider instantons comprised of M5branes wrapping a CalabiYau space with nonvanishing threeform field strengths. It is shown that the instanton equations for the threeform are related to the KodairaSpencer equations.
Fourdimensional String Compactifications with DBranes, Orientifolds and Fluxes
"... This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with Dbranes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct fourdimensional orientifold vacua, with the final aim to ..."
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Cited by 149 (15 self)
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This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with Dbranes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct fourdimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric Standard Model. Furthermore, we outline the available methods to derive the resulting fourdimensional effective action. Finally, we summarize recent attempts to address the
Disk instantons, mirror symmetry and the duality web
, 2001
"... We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of Dbranes wrapped over Lagrangian cycles of noncompact CalabiYau 3folds. Along the way we clarify the notion of “flat coordinates” for the boundary theory. We also discover ..."
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Cited by 137 (25 self)
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We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of Dbranes wrapped over Lagrangian cycles of noncompact CalabiYau 3folds. Along the way we clarify the notion of “flat coordinates” for the boundary theory. We also discover an integer IR ambiguity needed to define the quantum theory of Dbranes wrapped over noncompact Lagrangian submanifolds. In the large N dual ChernSimons theory, this ambiguity is mapped to the UV choice of the framing of the knot. In a type IIB dual description involving (p, q) 5branes, disk instantons of type IIA get mapped to (p, q) string instantons. The Mtheory lift of these results lead to computation of superpotential terms generated by M2 brane instantons wrapped over 3cycles of certain manifolds of G2 holonomy.
Knot invariants and topological strings
 Nucl. Phys. B
, 2000
"... We find further evidence for the conjecture relating large N ChernSimons theory on S3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S3 (for any representation) agrees to all orders in N with the corresponding quantity on the ..."
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Cited by 135 (19 self)
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We find further evidence for the conjecture relating large N ChernSimons theory on S3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S3 (for any representation) agrees to all orders in N with the corresponding quantity on the topological string side. For a general knot, we find a reformulation of the knot invariant in terms of new integral invariants, which capture the spectrum (and spin) of M2 branes ending on M5 branes embedded in the resolved conifold geometry. We also find an intriguing link between knot invariants and superpotential terms generated by worldsheet instantons in N = 1 supersymmetric theories in 4 dimensions.
Matrix Model as a Mirror of ChernSimons Theory
, 2002
"... Using mirror symmetry, we show that ChernSimons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of ChernSimons theory. ..."
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Cited by 134 (17 self)
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Using mirror symmetry, we show that ChernSimons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of ChernSimons theory. Moreover, large N dualities in this context lead to computation of all genus Amodel topological amplitudes on toric CalabiYau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these CalabiYau manifolds with wrapped D6 branes (which are dual to Mtheory on G2 manifolds) this leads to engineering and solving Fterms for N = 1 supersymmetric gauge theories with superpotentials involving certain multitrace operators
Mirror principle
 I. Asian J. Math
, 1997
"... Abstract. We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich’s stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As applications, we compute the equivariant Euler classes of ..."
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Cited by 127 (13 self)
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Abstract. We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich’s stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As applications, we compute the equivariant Euler classes of obstruction bundles induced by any concavex bundles – including any direct sum of line bundles – on Pn. This includes proving the formula of Candelasde la OssaGreenParkes hence completing the program of Candelas et al, Kontesevich, Manin, and Givental, to compute rigorously the instanton prepotential function for the quintic in P4. We derive, among many other examples, the multiple cover formula for GromovWitten invariants of P1, computed earlier by MorrisonAspinwall and by Manin in different approaches. We also prove a formula for enumerating Euler classes which arise in the socalled local mirror symmetry for some noncompact CalabiYau manifolds. At the end we interprete an infinite dimensional transformation group, called the mirror group, acting on Euler data, as a certain duality group of the linear sigma
Perturbative computation of glueball superpotentials,” hepth/0211017
"... Using N = 1 superspace techniques in four dimensions we show how to perturbatively compute the superpotential generated for the glueball superfield upon integrating out massive charged fields. The technique applies to arbitrary gauge groups and representations. Moreover we show that for U(N) gauge t ..."
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Cited by 111 (6 self)
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Using N = 1 superspace techniques in four dimensions we show how to perturbatively compute the superpotential generated for the glueball superfield upon integrating out massive charged fields. The technique applies to arbitrary gauge groups and representations. Moreover we show that for U(N) gauge theories admitting a large N expansion the computation dramatically simplifies and we prove the validity of the recently proposed recipe for computation of this quantity in terms of planar diagrams of matrix integrals. November
The effective action of type IIA CalabiYau orientifolds
"... The N = 1 effective action for generic type IIA CalabiYau orientifolds in the presence of background fluxes is computed from a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determined in terms of geometrical data of the CalabiYau ..."
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Cited by 97 (6 self)
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The N = 1 effective action for generic type IIA CalabiYau orientifolds in the presence of background fluxes is computed from a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determined in terms of geometrical data of the CalabiYau orientifold and the background fluxes. The moduli space is found to be a Kähler subspace of the N = 2 moduli space and shown to coincide with the moduli space arising in compactification of Mtheory on a specific class of G2 manifolds. The superpotential depends on all geometrical moduli and vanishes at leading order when background fluxes are turned off. The N = 1 chiral coordinates linearize the appropriate instanton actions such that instanton effects can lead to holomorphic corrections of the superpotential. Mirror symmetry between type IIA and type IIB orientifolds is shown to hold at the level of the effective action in the large volume – large complex structure limit.