2025/08/29 by Mohamed M. Anber, Anber, Mohamed M., Erich Poppitz +1
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2509.00157
openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study SU(N) super Yang-Mills theory with a small gaugino mass m and vacuum angle θ on the four-torus \mathbbT4 with 't Hooft twisted boundary conditions. Introducing a detuning parameter Δ, which measures the deviation from an exactly self-dual \mathbbT4, and working in the limits mLN ≪ ΛLN ≪ 1 and ((N-1) m2 L2)/(4 π) ≪ Δ≪ 1, where L is the torus size and Λ the strong-coupling scale, we compute the scalar and pseudo-scalar condensates to leading order in m2L2/Δ. The twists generate fractional-charge instantons, and we show that summing over all such contributions is crucial for reproducing the correct physical observables in the decompactified strong-coupling regime. From a Hamiltonian perspective, the sum over twisted sectors, already at small torus size, projects in the m=0 limit onto a definite superselection sector of the ℝ4 theory. In the massless limit, we recover the exact value of the gaugino condensate |⟨ λλ⟩| = 16π2 Λ3, and demonstrate how a spurious U(1) symmetry eliminates all CP-violating effects. Our results are directly testable in lattice simulations, and our method extends naturally to non-supersymmetric gauge theories.