Abstract
We consider a vector gauge theory in 2 + 1 dimensions of the type recently proposed by Radzihovsky and Hermele [1] to describe fracton phases of matter. The theory has U(1)XU(1) vector gauge fields coupled to an additional vector field with a non conventional gauge symmetry. We added to the theory scalar matter in order to break the gauge symmetry. We analyze non trivial configurations by reducing the field equations to first order self dual (BPS) equations which we solved numerically. We have found vortex solutions for the gauge fields which in turn generate for the extra vector field non-trivial configurations that can be associated to magnetic dipoles.
Highlights
The study of non-trivial solutions in quantum field theories has historically played an essential role in describing non-perturbative phenomena usually linked to topological properties of theses theories, both in High Energy applications [2] and in condensed matter systems [3]
A connection in the low energy limit between fracton phases and tensor gauge theories was studied in ref
Interest in the subject grew in various directions of condensed matter and quantum field theories physics including studies on gravity and elasticity areas
Summary
The study of non-trivial solutions in quantum field theories has historically played an essential role in describing non-perturbative phenomena usually linked to topological properties of theses theories, both in High Energy applications [2] and in condensed matter systems [3]. In this work we will consider a theory where the U (1) × U (1) vector gauge fields in the RH model are minimally coupled to scalar matter implementing the Higgs mechanism.
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