Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices
arXiv:hep-th/0602294 · doi:10.1016/j.nuclphysb.2006.07.003
Abstract
We study superpotential perturbations of q deformed N=4 Yang-Mills for q a root of unity. This is a special case whose geometry is associated to an orbifold with three lines of codimension two singularities meeting at the origin. We perform field theory perturbations that leave only co-dimension three singularities of conifold type in the geometry. We show that there are two "fractional brane" solutions of the F-term equations for each singularity in the deformed geometry, and that the number of complex deformations of that geometry also matches the number of singularities. This proves that for this case there are no local or non-local obstructions to deformation. We also show that the associated Dijkgraaf-Vafa matrix model has a solvable sector, and that the loop equations in this sector encode the full deformed geometry of the theory.
27 pages, uses JHEP3. v2: changes in formatting
References in corpus (45)
- Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
- Supergravity and a Confining Gauge Theory: Duality Cascades and SB-Resolution of Naked Singularities
- Deforming field theories with global symmetry and their gravity duals
- Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
- The String Dual of a Confining Four-Dimensional Gauge Theory
- Chiral Rings and Anomalies in Supersymmetric Gauge Theory
- Gauge Theories from Toric Geometry and Brane Tilings
- A Perturbative Window into Non-Perturbative Physics
- A Large N Duality via a Geometric Transition
- A Geometric Unification of Dualities
- Perturbative Computation of Glueball Superpotentials
- D-branes and Discrete Torsion II
- Deformations of N=4 SYM and integrable spin chain models
- Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
- On the Moduli Space of the Cascading SU(M+p)xSU(p) Gauge Theory
- Fractional Branes and Dynamical Supersymmetry Breaking
- Supersymmetry Breaking from a Calabi-Yau Singularity
- Geometric Transitions and N=1 Quiver Theories
- Discrete Torsion, AdS/CFT and duality
- N=1 and N=2 Geometry from Fluxes
- On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5
- Supersymmetry breaking at the end of a cascade of Seiberg dualities
- The Power of Holomorphy -- Exact Results in 4D SUSY Field Theories
- S-duality of the Leigh-Strassler Deformation via Matrix Models
- The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
- M-Theory and Topological Strings--I
- Combinatorial Solution of the Two-Matrix Model
- Comments on N=2 AdS Orbifolds
- The Toric Phases of the Y^{p,q} Quivers
- Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories
- Reverse geometric engineering of singularities
- D-branes and Discrete Torsion
- On Conformal Deformations
- Quantum moduli spaces from matrix models
- Resolution of Stringy Singularities by Non-commutative Algebras
- S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills
- On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills
- A New Deconstruction of Little String Theory
- Quantum Deformations from Toric Geometry
- Conifold geometries, topological strings and multi-matrix models
- New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
- On the universality class of the conifold
- D-brane realizations of runaway behavior and moduli stabilization
- Another Leigh-Strassler deformation through the Matrix model
- Solving matrix models using holomorphy