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).

A practical solution to the sign problem in a matrix model for dynamical compactification

“…It is essentially the hybrid Monte Carlo (HMC) algorithm, which has been applied in similar models in refs. [21,22,24,25,39]. The computational effort grows as O(N 3 ) in the present model.…”

Lectures on Matrix Field Theory

“…These models present an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early universe. Impact of supersymmetry is to stabilize the geometry further against quantum fluctuations [235]. …”

The numerical approach to quantum field theory in a noncommutative space

“…This approach has been successfully pursued in a number of studies [117,118,119,120,121,122,123,124,125,126,127,128,129,130]. As an example of results, the left-hand-side panel of fig.…”