Euclidean lattice simulation for the dynamical supersymmetry breaking

Abstract

The global supersymmetry is spontaneously broken if and only if the ground-state energy is strictly positive. We propose to use this fact to observe the spontaneous supersymmetry breaking in euclidean lattice simulations. For lattice formulations that possess a manifest fermionic symmetry, there exists a natural choice of a hamiltonian operator that is consistent with a topological property of the Witten index. We confirm validity of our idea in models of the supersymmetric quantum mechanics. We then examine a possibility of a dynamical supersymmetry breaking in the two-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory with the gauge group $\SU(2)$, for which the Witten index is unknown. Differently from a recent conjectural claim, our numerical result tempts us to conclude that supersymmetry is not spontaneously broken in this system.

5 pages, 4 figures, the final version to appear in Phys. Rev. D

References in corpus (3)

• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Towards lattice simulation of the gauge theory duals to black holes and hot strings
• Two-dimensional N=(2,2) super Yang-Mills theory on computer

Cited by in corpus (7)

• Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
• Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• Observing dynamical SUSY breaking with lattice simulation