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Quiver theories from D6branes via mirror symmetry
 JHEP 0204 (2002) 009 [arXiv:hepth/0108137
"... Abstract: We study N = 1 four dimensional quiver theories arising on the worldvolume of D3branes at del Pezzo singularities of CalabiYau threefolds. We argue that under local mirror symmetry D3branes become D6branes wrapped on a three torus in the mirror manifold. The Type IIB (p, q) 5brane web ..."
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Cited by 67 (24 self)
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Abstract: We study N = 1 four dimensional quiver theories arising on the worldvolume of D3branes at del Pezzo singularities of CalabiYau threefolds. We argue that under local mirror symmetry D3branes become D6branes wrapped on a three torus in the mirror manifold. The Type IIB (p, q) 5brane web description of the local del Pezzo, being closely related to the geometry of its mirror manifold, encodes the geometry of 3cycles and is used to obtain gauge groups, quiver diagrams and the charges of the fractional branes. 1 Contents
Reverse geometric engineering of singularities
 JHEP 0204 (2002) 052 [arXiv:hepth/0201093
"... Abstract: One can geometrically engineer supersymmetric field theories theories by placing Dbranes at or near singularities. The opposite process is described, where one can reconstruct the singularities from quiver theories. The description is in terms of a noncommutative quiver algebra which is c ..."
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Cited by 41 (10 self)
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Abstract: One can geometrically engineer supersymmetric field theories theories by placing Dbranes at or near singularities. The opposite process is described, where one can reconstruct the singularities from quiver theories. The description is in terms of a noncommutative quiver algebra which is constructed from the quiver diagram and the superpotential. The center of this noncommutative algebra is a commutative algebra, which is the ring of holomorphic functions on a variety V. If certain algebraic conditions are met, then the reverse geometric engineering produces V as the geometry that Dbranes probe. It is also argued that the identification of V is invariant under Seiberg dualities. Contents
Quantum moduli spaces from matrix models,” arXiv:hepth/0210183
"... Abstract: In this paper we show that the matrix model techniques developed by Dijkgraaf and Vafa can be extended to compute quantum deformed moduli spaces of vacua in four dimensional supersymmetric gauge theories. The examples studied give the moduli space of a bulk Dbrane probe in geometrically e ..."
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Cited by 38 (4 self)
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Abstract: In this paper we show that the matrix model techniques developed by Dijkgraaf and Vafa can be extended to compute quantum deformed moduli spaces of vacua in four dimensional supersymmetric gauge theories. The examples studied give the moduli space of a bulk Dbrane probe in geometrically engineered theories, in the presence of fractional branes at singularities.
Sklyanin algebras and Hilbert schemes of points
"... We construct projective moduli spaces for torsionfree sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual (commutative) projective ..."
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Cited by 20 (2 self)
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We construct projective moduli spaces for torsionfree sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual (commutative) projective plane P 2. The generic noncommutative plane corresponds to the Sklyanin algebra S = Skl(E, σ) constructed from an automorphism σ of infinite order on an elliptic curve E ⊂ P 2. In this case, the fine moduli space of line bundles over S with first Chern class zero and Euler characteristic 1 − n provides a symplectic variety that is a deformation of the Hilbert scheme of n points on P² \ E.
On the universality class of the conifold
 JHEP 0111
, 2001
"... Abstract: The possibility of having discrete degrees of freedom at singularities associated to ‘conifolds with discrete torsion ’ is studied. We find that the field theory of Dbrane probes near these singularities is identical to ordinary conifolds, so that there are no additional discrete degrees ..."
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Cited by 15 (6 self)
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Abstract: The possibility of having discrete degrees of freedom at singularities associated to ‘conifolds with discrete torsion ’ is studied. We find that the field theory of Dbrane probes near these singularities is identical to ordinary conifolds, so that there are no additional discrete degrees of freedom located at the singularity. We shed light on how the obstructions to resolving the singularity are global topological issues rather that local obstrucions at the singularity itself. We also analyze the geometric transitions and duality cascades when one has fractional branes at the singularity and compute the moduli space of an arbitrary number of probes in the geometry. We provide some evidence for a conjecture that there are no discrete degrees of freedom localized at any CalabiYau singularity that can not be guessed from topological data away from the singularity. Keywords: Dbranes, AdS/CFT, Calabi Yau singularities.Contents 1. Dbranes and the conifold algebra 4 1.1 On the fate of the U(1)’s 7 1.2 Representations of the conifold algebra 8 1.3 The resolved conifold 9
Open strings in simple current orbifolds
"... We study branes and open strings in a large class of orbifold backgrounds using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex operators for such branes. Applications include branes in Z2 orbifolds of ..."
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Cited by 11 (2 self)
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We study branes and open strings in a large class of orbifold backgrounds using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex operators for such branes. Applications include branes in Z2 orbifolds of the SU(2) WZW model and in the Dseries of unitary minimal models considered previously by Runkel.
Parameter space of quiver gauge theories
"... Placing a set of branes at a CalabiYau singularity leads to an N = 1 quiver gauge theory. We analyze Fterm deformations of such gauge theories. A generic deformation can be obtained by making the CalabiYau noncommutative. We discuss noncommutative generalisations of wellknown singularities suc ..."
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Cited by 11 (0 self)
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Placing a set of branes at a CalabiYau singularity leads to an N = 1 quiver gauge theory. We analyze Fterm deformations of such gauge theories. A generic deformation can be obtained by making the CalabiYau noncommutative. We discuss noncommutative generalisations of wellknown singularities such as the Del Pezzo singularities and the conifold. We also introduce new techniques for deriving superpotentials, based on quivers with ghosts and a notion of generalised Seiberg duality. The curious gauge structure of quivers with ghosts is most naturally described using the BV formalism. Finally we suggest a new approach to Seiberg duality by adding fields and ghostfields whose effects cancel each other. Contents 1 Parameter space of quiver gauge theories 2 2 Large volume construction of quiver theories 4
RUNHETC200914 BPS State Counting in Local Obstructed Curves from Quiver Theory and Seiberg Duality
, 908
"... In this paper we study the BPS state counting in the geometry of local obstructed curve with normal bundle O ⊕ O(−2). We find that the BPS states have a framed quiver description. Using this quiver description along with the Seiberg duality and the localization techniques, we can compute the BPS sta ..."
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In this paper we study the BPS state counting in the geometry of local obstructed curve with normal bundle O ⊕ O(−2). We find that the BPS states have a framed quiver description. Using this quiver description along with the Seiberg duality and the localization techniques, we can compute the BPS state indices in different chambers dictated by stability parameter assignments. This provides a welldefined method to compute the generalized DonaldsonThomas invariants. This method can be generalized to other affine ADE quiver theories.