Abstract
We investigate the possibility of spontaneous supersymmetry breaking in a class of zero-dimensional ${\cal N} = 2$ supersymmetric quantum field theories, with complex actions, using complex Langevin dynamics and stochastic quantization. Our simulations successfully capture the presence or absence of supersymmetry breaking in these models. The expectation value of the auxiliary field under twisted boundary conditions was used as an order parameter to capture spontaneous supersymmetry breaking in these models.
Highlights
We can investigate numerous nonperturbative features of quantum field theories using lattice regularized form of the field theory path integral
The basic aim of complex Langevin method [1,2,3,4] is to overcome this problem by extending the idea of stochastic quantization for ordinary field theoretic systems with real actions to the cases with complex actions
This leads to complexification of the real dynamical field variables that appear in the original path integral
Summary
We can investigate numerous nonperturbative features of quantum field theories using lattice regularized form of the field theory path integral. When the action is complex, for example, when studying QCD at finite density or with a theta term, Chern-Simons gauge theories or chiral gauge theories, it is not straightforward to apply path integral Monte Carlo. In these cases we encounter a complex action problem or sign problem. The basic aim of complex Langevin method [1,2,3,4] is to overcome this problem by extending the idea of stochastic quantization for ordinary field theoretic systems with real actions to the cases with complex actions This leads to complexification of the real dynamical field variables that appear in the original path integral. In Appendix B we provide the set of simulation data tables
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