N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories

Abstract

We show how the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c=1 non-critical bosonic string theory, and express them in a quiver or, equivalently, super matrix model. Moreover we relate, by deconstruction, the uncompactified c=1 theory to the six-dimensional conformal (2,0) theory. Furthermore, we show how we can use the idea of deconstruction to connect 4+k dimensional supersymmetric gauge theories to a k-dimensional internal bosonic gauge theory, generalizing the relation between 4d theories and matrix models. Examples of such bosonic systems include unitary matrix models and gauged matrix quantum mechanics, which deconstruct 5-dimensional supersymmetric gauge theories, and Chern-Simons gauge theories, which deconstruct gauge theories living on branes wrapped over cycles in Calabi-Yau threefolds.

arXiv comment34 pages

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• Normal random matrix ensemble as a growth problem
• Ghost D-branes
• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Flux Backgrounds in 2D String Theory
• Exact results on ABJ theory and the refined topological string
• Direct derivation of "mirror" ABJ partition function
• ABJM Wilson Loops in Arbitrary Representations
• Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills
• Dijkgraaf-Vafa theory as large-N reduction
• Matrix Quantum Mechanics and Two-dimensional String Theory in Non-trivial Backgrounds
• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• Holography and the Higgs branch of N=2 SYM theories
• Topological Matrix Models, Liouville Matrix Model and c=1 String Theory
• Properties of Chiral Wilson Loops
• Boundary Ground Ring in 2D String Theory
• Chern-Simons Theory in Lens Spaces from 2d Yang-Mills on the Cylinder
• Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy
• Less is More: Non-renormalization Theorems from Lower Dimensional Superspace
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• Branched Matrix Models and the Scales of Supersymmetric Gauge Theories
• Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Conifold geometries, topological strings and multi-matrix models
• The C-Deformation of Gluino and Non-planar Diagrams
• Large N limit of 2D Yang-Mills Theory and Instanton Counting
• Super instanton counting and localization
• The Off-shell M5-brane and Non-Perturbative Gauge Theory
• Supersymmetric large-N reduced model with multiple matter
• Two-Dimensional Gauge Theory and Matrix Model
• On Type II Strings in Two Dimensions
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Topological B-model and $\hat{c}=1$ String Theory
• The Glueball Superpotential
• c=1 from c<1: Bulk and boundary correlators
• Direct derivation of the Veneziano-Yankielowicz superpotential from matrix model
• Conifold geometries, matrix models and quantum solutions
• Localization on the D-brane, two-dimensional gauge theory and matrix models
• On Graviphoton F-terms of N=1 SU(N) SYM with Fundamental Matter
• Five-Dimensional Gauge Theories and Unitary Matrix Models
• Geometric Engineering of Seiberg-Witten Theories with Massive Hypermultiplets
• Gravitational F-terms of N=1 Supersymmetric Gauge Theories