Classical and quantum solitons in the symmetric space sine-Gordon theories

We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1 + 1-dimensions which are associated to a symmetric space F / G , and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We...

Full description

Saved in:
Bibliographic Details
Published in:The journal of high energy physics 2011-04, Vol.2011 (4), Article 119
Main Authors: Hollowood, Timothy J., Luis Miramontes, J.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Elementary Particles
High energy physics
Orbital mechanics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum mechanics
Quantum Physics
Relativity Theory
Solitary waves
String Theory
Subgroups
Symmetry
Tensors
Time dependence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1 + 1-dimensions which are associated to a symmetric space F / G , and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal moduli space that can be identified with a particular co-adjoint orbit of the unbroken subgroup H ⊂ G . Classically the solitons come in a continuous spectrum which encompasses the perturbative fluctuations of the theory as the kink charge becomes small. We show that the solitons can be quantized by allowing the collective coordinates to be time-dependent to yield a form of quantum mechanics on the co-adjoint orbit. The quantum states correspond to symmetric tensor representations of the symmetry group H and have the interpretation of a fuzzy geometric version of the co-adjoint orbit. The quantized finite tower of soliton states includes the perturbative modes at the base.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2011)119