TL;DR
This paper investigates BPS lump solutions in supersymmetric CP^{N-1} sigma models on a torus, exploring their construction, modular invariance, and limitations for small lump numbers.
Contribution
It introduces a method to construct doubly periodic BPS lumps on a torus inspired by caloron constructions, analyzing their modular properties and invariance.
Findings
No modular invariant solutions for n=1,2 lumps.
Constructed n-lump solutions with equal spacing on R^2.
Analyzed modular invariance properties of the solutions.
Abstract
We study doubly periodic Bogomol'nyi-Prasad-Sommerfield (BPS) lumps in supersymmetric CP^{N-1} non-linear 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=1,2 in this construction.
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