2023/07/10 by Mohamed M. Anber, Anber, Mohamed M., Erich Poppitz +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2307.04795
We construct analytical self-dual Yang-Mills fractional instanton solutions on a four-torus \mathbbT4 with 't Hooft twisted boundary conditions. These instantons possess topological charge Q=(r)/(N), where 1≤ r< N. To implement the twist, we employ SU(N) transition functions that satisfy periodicity conditions up to center elements and are embedded into SU(k)× SU(ℓ)× U(1)⊂ SU(N), where ℓ+k=N. The self-duality requirement imposes a condition, k L1L2=rℓ L3L4, on the lengths of the periods of \mathbbT4 and yields solutions with abelian field strengths. However, by introducing a detuning parameter Δ≡ (rℓ L3L4-k L1 L2)/√(L1 L2L3L4), we generate self-dual nonabelian solutions on a general \mathbbT4 as an expansion in powers of Δ. We explore the moduli spaces associated with these solutions and find that they exhibit intricate structures. Solutions with topological charges greater than (1)/(N) and k≠ r possess non-compact moduli spaces, along which the O(Δ) gauge-invariant densities exhibit runaway behavior. On the other hand, solutions with Q=(r)/(N) and k=r have compact moduli spaces, whose coordinates correspond to the allowed holonomies in the SU(r) color space. These solutions can be represented as a sum over r lumps centered around the r distinct holonomies, thus resembling a liquid of instantons. In addition, we show that each lump supports 2 adjoint fermion zero modes.