Self-dual sectors for scalar field theories in (1 + 1) dimensions

Ferreira, L. (0000 0004 1937 0722, Instituto de Física de São Carlos, IFSC/USP, Universidade de São Paulo, Caixa Postal 369, CEP 13560-970, São Carlos, SP, Brazil) ; Klimas, P. (0000 0001 2188 7235, Universidade Federal de Santa Catarina, Trindade, CEP 88040-900, Florianópolis, SC, Brazil) ; Zakrzewski, Wojtek (0000 0000 8700 0572, Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE, U.K.)

04 January 2019

Abstract: We use ideas of generalized self-duality conditions to construct real scalar field theories in (1 + 1)-dimensions with exact self dual sectors. The approach is based on a pre-potential U that defines the topological charge and the potential energy of these theories. In our algebraic method to construct the required pre-potentials we use the representation theory of Lie groups. This approach leads naturally to an infinite set of degenerate vacua and so to topologically non-trivial self-dual solutions of these models. We present explicit examples for the groups SU(2), SU(3) and SO(5) and discuss some properties of these solutions.

Published in: JHEP 1901 (2019) 020
Published by: Springer/SISSA
DOI: 10.1007/JHEP01(2019)020
arXiv: 1808.10052
License: CC-BY-4.0

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