Nahm transform for periodic monopoles and N = 2 super Yang-Mills theory

Sergey Cherkis, Anton Kapustin

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

We study Bogomolny equations on ℝ2 × double-struck S sign11. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperkähler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of N = 2 super Yang-Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.

Original languageEnglish (US)
Pages (from-to)333-371
Number of pages39
JournalCommunications in Mathematical Physics
Volume218
Issue number2
StatePublished - Apr 2001
Externally publishedYes

Fingerprint

Monopole
Yang-Mills Theory
Yang-Mills theory
monopoles
Transform
Higgs
Moduli Space
infinity
Infinity
Gauge Group
String Theory
Quantum Theory
One to one correspondence
Energy
Gauge Theory
string theory
gauge theory
Periodic Solution
Circle
Exact Solution

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Nahm transform for periodic monopoles and N = 2 super Yang-Mills theory. / Cherkis, Sergey; Kapustin, Anton.

In: Communications in Mathematical Physics, Vol. 218, No. 2, 04.2001, p. 333-371.

Research output: Contribution to journalArticle

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