Supersymmetric quantum mechanics on the lattice: II. Exact results

Abstract

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper -- the second in a series of three -- we present such an investigation for $\mathcal{N}=2$ supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

39 pages, 29 figures; typos in text, eq.(48) and (49) corrected

References in corpus (9)

• Non-lattice simulation for supersymmetric gauge theories in one dimension
• Low-dimensional Supersymmetric Lattice Models
• Observing dynamical supersymmetry breaking with euclidean lattice simulations
• Efficient simulation of relativistic fermions via vertex models
• Supersymmetric quantum mechanics on the lattice: I. Loop formulation
• Spontaneous supersymmetry breaking in the two-dimensional N=1 Wess-Zumino model
• Loop formulation of supersymmetric Yang-Mills quantum mechanics
• Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms
• Loop formulation of the supersymmetric nonlinear O(N) sigma model

Cited by in corpus (9)

• Progress and prospects of lattice supersymmetry
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• Lattice studies of supersymmetric gauge theories
• Supersymmetric quantum mechanics on the lattice: I. Loop formulation
• Direct computational approach to lattice supersymmetric quantum mechanics
• Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms
• Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on lattice
• A particle in equilibrium with a bath realizes worldline supersymmetry
• Probing Non-perturbative Supersymmetry Breaking through Lattice Path Integrals