Instanton Moduli for T**3xR
Pierre van Baal (Instituut-Lorentz, University of Leiden)
TL;DR
This paper reviews instanton moduli on a torus, discusses the Nahm transformation's implications, and explores solutions on T**3xR, highlighting open problems and new applications of the transformation.
Contribution
It introduces an explicit application of the Nahm transformation to selfdual solutions on T**4 and discusses properties relevant to instantons on T**3xR.
Findings
No exact charge one instanton on T**4 exists.
Vacuum tunnelling solutions exist as one dimension tends to infinity.
Open problem: detailed description of the moduli space for T**3xR.
Abstract
We review the specific problems that arise when studying instantons on a torus. We discuss how the Nahm transformation shows that no exact charge one instanton on T**4 can exist. However, taking one of the directions (the time) to infinity, it can be shown that vacuum to vacuum tunnelling solutions exist. A precise description of the moduli space for T**3xR, studied numerically using lattice techniques, remains an interesting open problem. New is an explicit application of the Nahm transformation to (anti-)selfdual constant curvature solutions on T**4 and a discussion of its properties relevant to instantons on T**3xR.
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