Abstract
Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions. The models we consider are invariant under the combined operation of parity and time reversal, in addition to supersymmetry. When actions are complex traditional Monte Carlo methods based on importance sampling fail. Models with dynamically broken supersymmetry can exhibit sign problem due to the vanishing of the partition function. Complex Langevin method can successfully evade the sign problem. Our simulations suggest that complex Langevin method can reliably predict the absence or presence of dynamical supersymmetry breaking in these one-dimensional models with complex actions.
Highlights
Our simulations suggest that complex Langevin method can reliably predict the absence or presence of dynamical supersymmetry breaking in these one-dimensional models with complex actions
Taylor series expansion [3], methods based on the complexification of the integration variables such as the Lefschetz thimble method [4] and the complex Langevin (CL) method [5,6,7,8,9]. (See refs. [10,11,12,13,14,15] for simulations based on the Lefschetz thimble method.) The CL method is based on stochastic quantization, and it is a straightforward generalization of the real Langevin method into complexified field configurations
Our simulations show that the bosonic and fermionic contributions cancel each other out within statistical errors, and the Ward identities are satisfied. All these results clearly suggest that SUSY is preserved in models with parity and time reversal (PT) -symmetry inspired δ-even potentials
Summary
Let us consider the action S[φ, ψ, ψ] of a supersymmetric quantum mechanics with a general superpotential W (φ). The Q transformation of B in eq (2.2) and the fact that the ground state is annihilated by the supercharges together imply that in the absence of SUSY breaking the normalized expectation value of the auxiliary field vanishes. In a system with broken SUSY, the normalized expectation of auxiliary field admit a 0/0 indefinite form. [43] Kuroki and Sugino introduced a regulator that explicitly breaks SUSY and resolves the degeneracy by fixing a single vacuum state in which SUSY is broken This regulator α (the twist parameter) can be implemented by imposing twisted boundary conditions (TBC) for fermions. [43] that for a non-zero α, the partition function does not vanish, and the normalized expectation value of the auxiliary field is well-defined. In our lattice analysis, we will use eq (2.15) as the continuum target theory
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