### Abstract

Existence and uniqueness of the solution are proved for the 'master equation' derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N
_{F} charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N
_{C}) gauge theory with N
_{F} hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N
_{C}) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.

Original language | English (US) |
---|---|

Pages (from-to) | 783-800 |

Number of pages | 18 |

Journal | Communications in Mathematical Physics |

Volume | 267 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2006 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*267*(3), 783-800. https://doi.org/10.1007/s00220-006-0083-4

**Moduli space of BPS walls in supersymmetric gauge theories.** / Sakai, Norisuke; Yang, Yisong.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 267, no. 3, pp. 783-800. https://doi.org/10.1007/s00220-006-0083-4

}

TY - JOUR

T1 - Moduli space of BPS walls in supersymmetric gauge theories

AU - Sakai, Norisuke

AU - Yang, Yisong

PY - 2006/11

Y1 - 2006/11

N2 - Existence and uniqueness of the solution are proved for the 'master equation' derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N F charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N C) gauge theory with N F hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N C) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.

AB - Existence and uniqueness of the solution are proved for the 'master equation' derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N F charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N C) gauge theory with N F hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N C) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.

UR - http://www.scopus.com/inward/record.url?scp=33748540479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748540479&partnerID=8YFLogxK

U2 - 10.1007/s00220-006-0083-4

DO - 10.1007/s00220-006-0083-4

M3 - Article

AN - SCOPUS:33748540479

VL - 267

SP - 783

EP - 800

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -