Periodic monopoles with singularities and N = 2 super-QCD

Sergey Cherkis, Anton Kapustin

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We study solutions of the Bogomolny equation on ℝ2 × S1 with prescribed singularities. We show that the Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperkähler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain N = 2 d = 4 supersymmetric gauge theories on ℝ3 × S1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on ℝ2 × S1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane.

Original languageEnglish (US)
Pages (from-to)1-35
Number of pages35
JournalCommunications in Mathematical Physics
Volume234
Issue number1
DOIs
StatePublished - Mar 2003
Externally publishedYes

Fingerprint

Monopole
monopoles
M-Theory
quantum chromodynamics
Singularity
Branch
Spectral Curve
Metric
One to one correspondence
Higgs
Gauge Theory
Moduli Space
curves
Infinity
Transform
infinity
Eigenvalue
gauge theory
Curve
eigenvalues

ASJC Scopus subject areas

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

Cite this

Periodic monopoles with singularities and N = 2 super-QCD. / Cherkis, Sergey; Kapustin, Anton.

In: Communications in Mathematical Physics, Vol. 234, No. 1, 03.2003, p. 1-35.

Research output: Contribution to journalArticle

@article{d3c1a73cfe4646c598d97da4d62bde4c,
title = "Periodic monopoles with singularities and N = 2 super-QCD",
abstract = "We study solutions of the Bogomolny equation on ℝ2 × S1 with prescribed singularities. We show that the Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperk{\"a}hler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain N = 2 d = 4 supersymmetric gauge theories on ℝ3 × S1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on ℝ2 × S1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane.",
author = "Sergey Cherkis and Anton Kapustin",
year = "2003",
month = "3",
doi = "10.1007/s00220-002-0786-0",
language = "English (US)",
volume = "234",
pages = "1--35",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Periodic monopoles with singularities and N = 2 super-QCD

AU - Cherkis, Sergey

AU - Kapustin, Anton

PY - 2003/3

Y1 - 2003/3

N2 - We study solutions of the Bogomolny equation on ℝ2 × S1 with prescribed singularities. We show that the Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperkähler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain N = 2 d = 4 supersymmetric gauge theories on ℝ3 × S1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on ℝ2 × S1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane.

AB - We study solutions of the Bogomolny equation on ℝ2 × S1 with prescribed singularities. We show that the Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperkähler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain N = 2 d = 4 supersymmetric gauge theories on ℝ3 × S1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on ℝ2 × S1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane.

UR - http://www.scopus.com/inward/record.url?scp=0037346860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037346860&partnerID=8YFLogxK

U2 - 10.1007/s00220-002-0786-0

DO - 10.1007/s00220-002-0786-0

M3 - Article

VL - 234

SP - 1

EP - 35

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -