Sigma model BPS lumps on a torus

Abstract

We study doubly periodic Bogomol'nyi-Prasad-Sommerfield lumps in supersymmetric CP NÀ1 nonlinear sigma models on a torus T 2 . Following the philosophy of the Harrington-Shepard construction of calorons in Yang-Mills theory, we obtain the n-lump solutions on compact spaces by suitably arranging the n lumps on R 2 at equal intervals. We examine the modular invariance of the solutions and find that there are no modular invariant solutions for n ¼ 1, 2 in this construction.

Winding Hopfions on R2×S1

“…In particular, flat spaces with one or more directions compactified as circles are useful in T-duality between topological solitons in different dimensions. For instance, Yang-Mills instantons on R 3 × S 1 and T 4 , known as Carolons, are related to monopoles, while lumps on R×S 1 [18] and T 2 [19] and vortices on R × S 1 [20] and T 2 [21] are related to domain walls. Hopfions on different geometry have not been studied much except for some outstanding works.…”