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- W4384111578 abstract "We construct analytical self-dual Yang-Mills fractional instanton solutions on a four-torus $mathbb{T}^4$ with 't Hooft twisted boundary conditions. These instantons possess topological charge $Q=frac{r}{N}$, where $1leq r< N$. To implement the twist, we employ $SU(N)$ transition functions that satisfy periodicity conditions up to center elements and are embedded into $SU(k)times SU(ell)times U(1)subset SU(N)$, where $ell+k=N$. The self-duality requirement imposes a condition, $k L_1L_2=rell L_3L_4$, on the lengths of the periods of $mathbb{T}^4$ and yields solutions with abelian field strengths. However, by introducing a detuning parameter $Deltaequiv (rell L_3L_4-k L_1 L_2)/sqrt{L_1 L_2L_3L_4}$, we generate self-dual nonabelian solutions on a general $mathbb{T}^4$ as an expansion in powers of $Delta$. We explore the moduli spaces associated with these solutions and find that they exhibit intricate structures. Solutions with topological charges greater than $frac{1}{N}$ and $kneq r $ possess non-compact moduli spaces, along which the $O(Delta)$ gauge-invariant densities exhibit runaway behavior. On the other hand, solutions with $Q=frac{r}{N}$ 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." @default.
- W4384111578 created "2023-07-13" @default.
- W4384111578 creator A5079507362 @default.
- W4384111578 creator A5079698615 @default.
- W4384111578 date "2023-07-10" @default.
- W4384111578 modified "2023-09-27" @default.
- W4384111578 title "Multi-fractional instantons in $SU(N)$ Yang-Mills theory on the twisted $mathbb T^4$" @default.
- W4384111578 doi "https://doi.org/10.48550/arxiv.2307.04795" @default.
- W4384111578 hasPublicationYear "2023" @default.
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