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

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• Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions
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• Topologically Twisted $N=(2,2)$ Supersymmetric Yang-Mills Theory on Arbitrary Discretized Riemann Surface
• Matrix formulation of superspace on 1D lattice with two supercharges
• Nonperturbative study of dynamical SUSY breaking in $\mathcal{N}=(2,2)$ Yang-Mills
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• Anomaly and Sign problem in $\mathcal{N}=(2,2)$ SYM on Polyhedra : Numerical Analysis
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• Exact Results in Discretized Gauge Theories
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• Ferrara--Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM
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• Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on lattice
• Probing Non-perturbative Supersymmetry Breaking through Lattice Path Integrals
• A one-loop test for construction of 4D N=4 SYM from 2D SYM via fuzzy sphere geometry
• Nonperturbative phase diagram of two-dimensional $\mathcal{N}=(2,2)$ super-Yang--Mills