Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres

Abstract

We study a 4d supersymmetric matrix model with a cubic term, which incorporates fuzzy spheres as classical solutions, using Monte Carlo simulations and perturbative calculations. The fuzzy sphere in the supersymmetric model turns out to be always stable if the large-N limit is taken in such a way that various correlation functions scale. This is in striking contrast to analogous bosonic models, where the fuzzy sphere decays into the pure Yang-Mills vacuum due to quantum effects when the coefficient of the cubic term becomes smaller than a critical value. We also find that the power-law tail of the eigenvalue distribution, which exists in the supersymmetric model without the cubic term, disappears in the presence of the fuzzy sphere in the large-N limit. Coincident fuzzy spheres turn out to be unstable, which implies that the dynamically generated gauge group is U(1).

27 pages, 15 figures, (v2) some typos corrected

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• Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM
• Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model
• Dynamical aspects of the plane-wave matrix model at finite temperature
• Lectures on Matrix Field Theory I
• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
• Four-dimensional N=1 super Yang-Mills from matrix model
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• A practical solution to the sign problem in a matrix model for dynamical compactification
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory
• The instability of intersecting fuzzy spheres
• Little IIB Matrix Model
• Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models