### Abstract

We study the Bogomol'nyi-Prasad-Sommerfeld (BPS) vortices in the (1+1)- dimensional N = (2, 2) supersymmetric U(1) gauged double strok C Sign P ^{1} nonlinear sigma model.We use the moduli matrix approach to analytically construct the moduli space of solutions and solve numerically the BPS equations. We identify two topologically inequivalent types of magnetic vortices, which we call S and N vortices. Moreover, we discuss their relation to instantons (lumps) present in the ungauged case. In particular, we describe how a lump is split into a couple of component S-N vortices after gauging. We extend this analysis to the case of the extended Abelian Higgs model with two flavors, which is known to admit semi-local vortices. After gauging the relative phase between fields, semi-local vortices are also split into component vortices. We discuss interesting applications of this simple set-up. Firstly, the gauging of nonlinear sigma models reveals a semiclassical 'partonic' nature of instantons in 1+1 dimensions. Secondly, weak gauging provides for a new interesting regularization of the metric of semi-local vortices.

Original language | English |
---|---|

Article number | 175401 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 45 |

Issue number | 17 |

DOIs | |

Publication status | Published - 2012 May 4 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*45*(17), [175401]. https://doi.org/10.1088/1751-8113/45/17/175401

**Decomposing instantons in two dimensions.** / Nitta, Muneto; Vinci, Walter.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 45, no. 17, 175401. https://doi.org/10.1088/1751-8113/45/17/175401

}

TY - JOUR

T1 - Decomposing instantons in two dimensions

AU - Nitta, Muneto

AU - Vinci, Walter

PY - 2012/5/4

Y1 - 2012/5/4

N2 - We study the Bogomol'nyi-Prasad-Sommerfeld (BPS) vortices in the (1+1)- dimensional N = (2, 2) supersymmetric U(1) gauged double strok C Sign P 1 nonlinear sigma model.We use the moduli matrix approach to analytically construct the moduli space of solutions and solve numerically the BPS equations. We identify two topologically inequivalent types of magnetic vortices, which we call S and N vortices. Moreover, we discuss their relation to instantons (lumps) present in the ungauged case. In particular, we describe how a lump is split into a couple of component S-N vortices after gauging. We extend this analysis to the case of the extended Abelian Higgs model with two flavors, which is known to admit semi-local vortices. After gauging the relative phase between fields, semi-local vortices are also split into component vortices. We discuss interesting applications of this simple set-up. Firstly, the gauging of nonlinear sigma models reveals a semiclassical 'partonic' nature of instantons in 1+1 dimensions. Secondly, weak gauging provides for a new interesting regularization of the metric of semi-local vortices.

AB - We study the Bogomol'nyi-Prasad-Sommerfeld (BPS) vortices in the (1+1)- dimensional N = (2, 2) supersymmetric U(1) gauged double strok C Sign P 1 nonlinear sigma model.We use the moduli matrix approach to analytically construct the moduli space of solutions and solve numerically the BPS equations. We identify two topologically inequivalent types of magnetic vortices, which we call S and N vortices. Moreover, we discuss their relation to instantons (lumps) present in the ungauged case. In particular, we describe how a lump is split into a couple of component S-N vortices after gauging. We extend this analysis to the case of the extended Abelian Higgs model with two flavors, which is known to admit semi-local vortices. After gauging the relative phase between fields, semi-local vortices are also split into component vortices. We discuss interesting applications of this simple set-up. Firstly, the gauging of nonlinear sigma models reveals a semiclassical 'partonic' nature of instantons in 1+1 dimensions. Secondly, weak gauging provides for a new interesting regularization of the metric of semi-local vortices.

UR - http://www.scopus.com/inward/record.url?scp=84859811199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859811199&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/45/17/175401

DO - 10.1088/1751-8113/45/17/175401

M3 - Article

AN - SCOPUS:84859811199

VL - 45

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 17

M1 - 175401

ER -