Abstract
We make a connection between quantum phase transitions in condensed matter systems, and supersymmetric gauge theories that are of interest in the particle physics literature. In particular, we point out interesting effects of the supersymmetric quantum electrodynamics upon the critical behavior of the Ginzburg-Landau model. It is shown that supersymmetry fixes the critical exponents, as well as the Landau-Ginzburg para- meter, and that the model resides in the type II regime of superconductivity.
Highlights
A very well studied model in the condensed matter literature is the Ginzburg-Landau (GL) model [1], described by the lagrangian of an Abelian Higgs model = D 2 m2 F 2 (1)where is a complex scalar field charged under the abelian gauge field A, with the gauge covariant derivative and field strength D = ieA (2)F = A A (3)When m2 > 0, the gauge symmetry is exact, and the model describes a massive complex scalar particle that interacts with a massless photon
In this article we point out that the generalization of the Ginzburg-Landau model to a supersymmetric one necessarily introduces fermions both in the matter and gauge supermultiplets, and that the restrictions imposed by the symmetries of the model unambigiously determine the critical exponents and the Landau-Ginzburg parameter, which is found to be in the type II regime of superconductivity
We conclude that supersymmetry provides the kind of lagrangian studied in [4], and that the values of the Ginzburg parameter and of the critical exponents are similar to the ones obtained in [4], without a second coupling constant for the scalar quartic self-interaction, and without many fermions
Summary
A very well studied model in the condensed matter literature is the Ginzburg-Landau (GL) model [1], described by the lagrangian of an Abelian Higgs model. When m2 > 0 , the gauge symmetry is exact, and the model describes a massive complex scalar particle that interacts with a massless photon. On the other hand, when m2 < 0 the gauge symmetry is spontaneously broken, and in this Higgs phase the model describes a massive gauge boson and a massive real scalar field. In this article we point out that the generalization of the Ginzburg-Landau model to a supersymmetric one necessarily introduces fermions both in the matter and gauge supermultiplets, and that the restrictions imposed by the symmetries of the model unambigiously determine the critical exponents and the Landau-Ginzburg parameter, which is found to be in the type II regime of superconductivity
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