Non BPS noncommutative vortices

GUSTAVO S LOZANO

Caxambu

Conferencia; XXV Encontro Nacional de Pariculas e Campos, Caxambu, Brasil, 2004; 2004

Sociedade Brasilera de Fisica

The study of noncommutative solitons and instantons -finite energy or finite action solutions to the classical equations of motion of noncommutative field theories- has been a field of intense activity after the revival of interest in these theories in connection with strings and brane dynamics. In fact, the first explicit instanton solutions that were constructed in four dimensional Yang-Mills theory strongly influenced developments in string quantization. Concerning solitons, not only the noncommutative counterparts of vortex, monopoles and other localized solutions in ordinary space were constructed but regular stable solutions which become singular in the commutative limit were also discovered. Most of these solitons correspond to selfdual/antiselfdual (BPS) solutions which are more simple to obtain than those arising from the Euler Lagrange (EL) equations of motion. Moreover, in even dimensional spaces, calculations can be simplified by exploiting the connection between noncommutative Moyal product in configuration space and a Hilbert space representation which realizes noncommutativity in terms of creation and annihilation operators acting on a Fock space. Among the BPS soliton solutions that have been obtained in this way, particular interest has attracted the construction of noncommutative BPS vortices - static solutions of the noncommutative version of the Abelian Higgs model, both when the gauge field dynamics is governed by Maxwell and/or Chern-Simons actions. The moduli space of these BPS vortices has been studied in detail showing an interesting phase diagram with a critical point at some value of the dimensionless parameter resulting from the combination of the gauge coupling constant, the scalar expectation value and the noncommutative parameter. In thepresent work we construct exact vortex solutions to the equations of motion of the Abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point. We show that our solutions behave as smooth deformations of vortices in ordinary space time except for parity symmetry breaking effects induced by the non commutative parameter.