From One to Eight: Supersymmetry Restoration in Lattice 3D N = 4 Super Yang--Mills · arXivDesk
2608.05099Aug 5, 20266 pages, 1 figure. Contribution to the 70th Annual Conference of the South African Institute of Physics (SAIP2026), 6-10 July 2026
From One to Eight: Supersymmetry Restoration in Lattice 3D N=4 Super Yang--Mills
Topological twisting provides a powerful framework for constructing lattice formulations of supersymmetric gauge theories. In three dimensions, a twisted version of N=4 super Yang--Mills theory can be discretized so that one nilpotent scalar supersymmetry is preserved exactly at nonzero lattice spacing. The remaining seven supersymmetries are broken by lattice artifacts of O(a), where a is the lattice spacing. An important question is whether these supersymmetries are automatically restored in the continuum limit a→0
Nearby in the stack
, or whether fine-tuning of the lattice couplings is required. In this work, we derive the additional twisted supersymmetries by combining discrete
R
-symmetries of the continuum theory with the action of the scalar supercharge. This construction suggests that restoration of rotational symmetry in the continuum limit implies restoration of
R
-symmetry, leading to an automatic enhancement to the full
N=4
supersymmetry without further tuning. These results may enable nonperturbative lattice studies of three-dimensional supersymmetric gauge theories relevant to string theory and mirror symmetry.