2025/04/08 by Mohamed M. Anber, Anber, Mohamed M., Andrew A. Cox +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2504.06344
The moduli space of self-dual SU(N) Yang-Mills instantons on \mathbb T4 of topological charge Q = r/N, 1 ≤ r ≤ N-1, is of current interest, yet is not fully understood. In this paper, starting from 't Hooft's constant field strength (F) instantons, the only known exact solutions on \mathbb T4, we explore the moduli space via analytical and lattice tools. These solutions are characterized by two positive integers k, ℓ, k+ℓ=N, and are self-dual for \mathbb T4 sides Lμ tuned to k L1 L2 = r ℓ L3 L4. For gcd(k,r) = r, we show, analytically and numerically (for N = 3) that the constant-F solutions are the only self-dual solutions on the tuned \mathbb T4, with 4r holonomy moduli. In contrast, when gcd(k,r) ≠ r, we argue that the self-dual constant-F solutions acquire, in addition to the 4gcd(k,r) holonomies, 4r - 4gcd(k,r) extra moduli, whose turning on makes the field strength nonabelian and non-constant. Thus, for gcd(k,r) ≠ r, 't Hooft's constant-F solutions are a measure-zero subset of the moduli space on the tuned \mathbb T4, a fact explaining a puzzle encountered in arXiv:2307.04795. We also show that, for r = k = 2, N = 3, the agreement between the approximate analytic solutions on the slightly detuned \mathbb T4 and the Q=2/3 self-dual configurations obtained by minimizing the lattice action is remarkable.