Mathematics

Lattice Gauge theories (LGT) are, among other things, a very useful tool to construct or understand Topological phases of matter such as the Spin Liquids. In this talk, I will explain first how to formalize the construction of a LGT with either a compact Lie group or a finite group, trying to underline the most important features as the absence of symmetry breaking (Elitzur's theorem) and the choice of extended order parameters. In the second part, I will consider the specific case of a Z_2 LGT commonly known as Ising Gauge, sketching the phase diagram with a particular attention to the deconfined phase.