### Abstract

We obtain exact analytical solutions for a class of SO(l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = (p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects (p = 0, 1, 2,.. ; l = 1), vortex-like defects (p = 1, 2, 3; l = 2), and the ’t Hooft-Polyakov monopole (p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

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

Article number | 12 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2018 |

### Fingerprint

### Keywords

- Field Theories in Higher Dimensions
- Field Theories in Lower Dimensions
- Solitons Monopoles and Instantons

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2018*(3), [12]. https://doi.org/10.1007/JHEP03(2018)012

**Some exact solutions for maximally symmetric topological defects in Anti de Sitter space.** / Alvarez, Orlando; Haddad, Matthew.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2018, no. 3, 12. https://doi.org/10.1007/JHEP03(2018)012

}

TY - JOUR

T1 - Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

AU - Alvarez, Orlando

AU - Haddad, Matthew

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We obtain exact analytical solutions for a class of SO(l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = (p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects (p = 0, 1, 2,.. ; l = 1), vortex-like defects (p = 1, 2, 3; l = 2), and the ’t Hooft-Polyakov monopole (p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

AB - We obtain exact analytical solutions for a class of SO(l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = (p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects (p = 0, 1, 2,.. ; l = 1), vortex-like defects (p = 1, 2, 3; l = 2), and the ’t Hooft-Polyakov monopole (p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

KW - Field Theories in Higher Dimensions

KW - Field Theories in Lower Dimensions

KW - Solitons Monopoles and Instantons

UR - http://www.scopus.com/inward/record.url?scp=85043289835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043289835&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2018)012

DO - 10.1007/JHEP03(2018)012

M3 - Article

AN - SCOPUS:85043289835

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 12

ER -