Periodic Euclidean solutions and the finite-temperature Yang-Mills gas

Calorons on the lattice - a new perspective

“…When non-trivial, it resolves the fact that a caloron is built from constituent monopoles, their mass ratios directly determined by the holonomy [1,2]. These solutions differ from the (deformed) instantons described by the Harrington-Shepard solution [3], for which the holonomy is trivial. What we find by (improved [4]) cooling on a finite lattice, to relatively high accuracy, is SU(2) configurations that fit these infinite volume caloron solutions for arbitrary constituent monopole mass ratios.…”

“…Up to now only the maximal mass, 8π 2 /β, of such a BPS monopole was considered. It arises in terms of the caloron with trivial holonomy, described by the Harrington-Shepard solution [3]. Rossi [17] showed that at high temperature, equivalent to a large scale parameter, this solution indeed becomes a BPS monopole [7].…”

Instantons and magnetic monopoles on R3×S1 with arbitrary simple gauge groups

“…In recent years there has been some interest in the connection between magnetic monopoles and instantons in theories with partially compactified space [1,2,3]. Especially by employing the Tduality on D-branes, we have shown that a single instanton in the theory with SU n gauge group on space R 3 × S 1 can be interpreted as a composite of n distinct fundamental monopoles [1].…”

“…The number of zero modes 4c 2 (G) around a single instanton can be interpreted as a sum of five modes for the position and scale and the rest for the global gauge modes which changes the embedded solution. On R 3 × S 1 , one find a periodic instanton solution, which turns out to be a special limit where the gauge symmetry is partially restored [1,9,3]. We expect the number of zero modes to be identical to the R 4 case.…”

Existence of hyperbolic calorons

“…As in the situation of zero-temperature instantons, finite-action t-periodic gauge field solutions can be stratified [3] by homotopy classes defined by maps from S 2 × S 1 into S 3 and such finite-temperature instantons have been explicitly constructed by Harrington & Shepard [4], and called calorons, which approach the zero-temperature instantons in the limit β → ∞ so that the asymmetry between the spatial and temporal coordinates, x and t, in the partition function (1.2) disappears. Motivated by the work on hyperbolic monopoles [5][6][7] in the extreme curvature limit [8] in connection to the Euclidean monopoles, Harland [9] carried out a study of hyperbolic calorons and showed that, within Witten's SO(3)-symmetric dimensionally reduced ansatz [10], hyperbolic calorons may be obtained through constructing multiple vortex solutions of an Abelian Higgs Bogomol'nyi system over a cylindrical stripe.…”