Supersymmetry Breaking in Low Dimensional Models

Abstract

We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting supersymmetric models onto the lattice. We compare our lattice results (built upon the non-local SLAC derivative) with numerically exact results obtained within the Hamiltonian approach. A particular emphasis is put on the discussion of boundary conditions. We investigate the ground state structure, mass spectrum, effective potential and Ward identities and conclude that lattice methods are suitable to derive the physical properties of supersymmetric quantum mechanics, even with broken supersymmetry. Based on this result we analyse the two dimensional N=1 Wess-Zumino model with spontaneous supersymmetry breaking. First we show that (in agreement with earlier analytical and numerical studies) the SLAC derivative is a sensible choice in the quenched model, which is nothing but the two dimensional phi^4 model. Then, we present the very first computation of a renormalised critical coupling for the complete supersymmetric model. This calculation makes use of Binder cumulants and is supported by a direct comparison to Ward identity results, both in the continuum and infinite volume limit. The physical picture is completed by masses at two selected couplings, one in the supersymmetric phase and one in the supersymmetry broken phase. Signatures of the Goldstino in the fermionic correlator are clearly visible in the broken case.

33 pages, 28 figures

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Cited by in corpus (26)

• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• Monte Carlo determination of the critical coupling in ${\varphi }_2^4$ theory
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• New MC determination of the critical coupling in ${\varphi }_2^4$ theory
• Convergence of Derivative Expansion in Supersymmetric Functional RG Flows
• Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases
• Matrix algorithm for solving Schroedinger equations with position-dependent mass or complex optical potentials
• Supersymmetry on the lattice
• Critical mass renormalization in renormalized phi4 theories in two and three dimensions
• Lattice studies of supersymmetric gauge theories
• Spontaneous supersymmetry breaking in the two-dimensional N=1 Wess-Zumino model
• Supersymmetric quantum mechanics on the lattice: I. Loop formulation
• Supersymmetric Nonlinear O(3) Sigma Model on the Lattice
• Supersymmetric quantum mechanics on the lattice: II. Exact results
• Direct computational approach to lattice supersymmetric quantum mechanics
• Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms
• Symmetries of Thirring models on 3d lattices
• Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics
• Supersymmetric probability distributions
• Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on lattice
• Application of tensor network method to two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• Probing Non-perturbative Supersymmetry Breaking through Lattice Path Integrals