I argue that the simulations of supersymmetric field theories on the lattice necessarily suffer from a fermion sign problem whenever supersymmetry is spontaneously broken. I discuss this in the context of supersymmetric quantum mechanics and the N=1 Wess-Zumino model. I show how the sign problem can be circumvented by using the fermion loop aka canonical formulation in which the fermion number is kept fixed. Using the explicit construction of transfer matrices in separate canonical sectors allows to extend this approach successfully to supersymmetric Yang-Mills gauge theories which are conjectured to describe the thermodynamics of certain black holes through the gauge/gravity duality conjecture. On the way, I discuss several interesting nonperturbative results that can be obtained through numerical simulations once the sign problem is under control.
Friday, May 17, 2019 - 13:00
Supersymmetric field theories on the lattice - avoiding the sign problem in the canonical formulation