Lattice studies of supersymmetric gauge theories

Abstract

Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model. Lattice field theory provides a non-perturbative regularization suitable for strongly interacting systems. This invited review briefly summarizes significant recent progress in lattice investigations of supersymmetric field theories, as well as some of the challenges that remain to be overcome. I focus on progress in three areas: supersymmetric Yang–Mills (SYM) theories in fewer than four space-time dimensions, as well as both minimal $${\mathcal {N}} = 1$$ N = 1 SYM and maximal $${\mathcal {N}} = 4$$ N = 4 SYM in four dimensions. I also highlight superQCD and sign problems as prominent challenges that will be important to address in future work.

Quantum Computing for the Wess-Zumino Model

“…Of course there have been prior investigations of dynamical supersymmetry breaking both for the 1+1d Wess-Zumino model [7][8][9][10][11][12][13] as well as for more complicated 1+1d systems including super-Yang-Mills [16], super-QCD [17] and the supersymmetric Gross-Neveu-Yukawa model [18]. A persistent challenge in such studies is the severe sign problem associated with spontaneous supersymmetry breaking [2,3], which has motivated the development of fermion loop [13], tensor network [14] and conformal truncation [18] techniques.…”

“…While Monte Carlo importance sampling studies of supersymmetric lattice QFTs have been performed for many years (see Refs. [1][2][3] for recent reviews), sign problems can prevent this approach from considering key dynamical phenomena including real-time evolution and spontaneous supersymmetry breaking [2,3]. Quantum computing in principle provides a novel means to study these phenomena without introducing sign problems.…”

Quantum Computing for the Wess–Zumino Model

“…Of course there have been prior investigations of dynamical supersymmetry breaking both for the 1+1d Wess-Zumino model [7][8][9][10][11][12][13] as well as for more complicated 1+1d systems including super-Yang-Mills [16], super-QCD [17] and the supersymmetric Gross-Neveu-Yukawa model [18]. A persistent challenge in such studies is the severe sign problem associated with spontaneous supersymmetry breaking [2,3], which has motivated the development of fermion loop [13], tensor network [14] and conformal truncation [18] techniques.…”

Lattice Studies of 3D Maximally Supersymmetric Yang–Mills

“…Supersymmetry is quite prominent in modern theoretical physics and in recent years there has been considerable interest and progress in the use of lattice field theory to study supersymmetric quantum field theories non-pertubatively -see Ref. [1] for a recent review.…”