Dimensionally Reduced SYM_4 as Solvable Matrix Quantum Mechanics

Abstract

We study the quantum mechanical model obtained as a dimensional reduction of N=1 super Yang-Mills theory to a periodic light-cone "time". After mapping the theory to a cohomological field theory, the partition function (with periodic boundary conditions) regularized by a massive term appears to be equal to the partition function of the twisted matrix oscillator. We show that this partition function perturbed by the operator of the holonomy around the time circle is a tau function of Toda hierarchy. We solve the model in the large N limit and study the universal properties of the solution in the scaling limit of vanishing perturbation. We find in this limit a phase transition of Gross-Witten type.

29 pages, harvmac, 1 figure, formulas in appendices B and C corrected

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Cited by in corpus (27)

• ABJM theory as a Fermi gas
• Non-Perturbative Effects in Matrix Models and D-branes
• Exact Results on the ABJM Fermi Gas
• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• Probing N=4 SYM With Surface Operators
• Convergent Yang-Mills Matrix Theories
• Time-dependent backgrounds of 2D string theory
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Correlators in 2D string theory with vortex condensation
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• String Equation for String Theory on a Circle
• Abstract loop equations, topological recursion, and applications
• Confinement and Mayer cluster expansions
• Yang-Mills Matrix Theory
• N=2 3d-Matrix Integral with Myers Term
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Notes on Mayer Expansions and Matrix Models
• Simulating Simplified Versions of the IKKT Matrix Model
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• Matrix models for topological strings: exact results in the planar limit
• Light-cone SU(2) Yang-Mills theory and conformal mechanics
• Little IIB Matrix Model
• Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models
• High-Precision Bootstrap of Multimatrix Quantum Mechanics