# Expansion for the solutions of the Bogomolny equations on the torus

@article{GonzlezArroyo2004ExpansionFT, title={Expansion for the solutions of the Bogomolny equations on the torus}, author={Antonio Gonz{\'a}lez-Arroyo and Alberto Ramos}, journal={Journal of High Energy Physics}, year={2004}, volume={2004}, pages={008-008} }

We show that the solutions of the Bogomolny equations for the abelian Higgs model on a two-dimensional torus, can be expanded in powers of a quantity measuring the departure of the area from the critical area. This allows a precise determination of the shape of the solutions for all magnetic fluxes and arbitrary position of the Higgs field zeroes. The expansion is carried out to 51 orders for a couple of representative cases, including the unit flux case. We analyse the behaviour of the…

## 14 Citations

### Dynamics of critical vortices on the torus and on the plane

- Mathematics, Physics
- 2007

We use the Bradlow parameter expansion to construct the metric tensor in the space of solutions of the Bogomolny equations for the Abelian Higgs model on a two-dimensional torus. Using this metric we…

### Bogomolny equations for vortices in the noncommutative torus

- Mathematics
- 2005

We derive Bogomolny-type equations for the abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary…

### Small winding-number expansion: vortex solutions at critical coupling

- Physics
- 2015

A bstractWe study an axially symmetric solution of a vortex in the Abelian-Higgs model at critical coupling in detail. Here we propose a new idea for a perturbative expansion of a solution, where the…

### Vortex solutions in the noncommutative torus

- Mathematics
- 2006

Vortex configurations in the two-dimensional torus are considered in noncommutative space. We analyze the BPS equations of the Abelian Higgs model. Numerical solutions are constructed for the…

### Phenomenology of symmetry breaking from extra dimensions

- Physics
- 2007

Motivated by the electroweak hierarchy problem, we consider theories with two extra dimensions in which the four-dimensional scalar fields are components of gauge boson in full space. We explore the…

### Integrability in theories with local U(1) gauge symmetry

- Mathematics
- 2007

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown…

### Constructing SU(N) fractional instantons

- MathematicsJournal of High Energy Physics
- 2020

Abstract
We study self-dual SU(N) gauge field configurations on the 4 torus with twisted boundary conditions, known as fractional instantons. Focusing on the minimum non-zero action case, we…

### The gaugino condensate from asymmetric four-torus with twists

- Physics, Mathematics
- 2022

We calculate the gaugino condensate in SU(2) super Yang-Mills theory on an asymmetric four-torus T with ’t Hooft’s twisted boundary conditions. The T asymmetry is controlled by a dimensionless…

### Non-abelian vortices on the torus

- Mathematics
- 2007

We study periodic arrays of non-Abelian vortices in an SU(N) × U(1) gauge theory with Nf flavors of fundamental matter multiplets. We carefully discuss the corresponding twisted boundary conditions…

### Non-Abelian vortices on a cylinder: Duality between vortices and walls

- Physics, Mathematics
- 2006

We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a…

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