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Title:
Loop Condensation in Three Dimensional Twisted Gauge Theories
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Abstract:
Recent discoveries of novel 3D gapped topological phases raises the question of how to drive phase transitions between them. For 2D topological phases, phase transition can be driven by the condensation of bosonic anyons. In 3D, besides point like anyons, topological excitations also come in the form of loops whose condensation can also lead to phase transition. What is the counterpart of the ‘bosonic’ condition on the loops so that they can be condensed? This question becomes especially interesting in the context of twisted gauge theories, where loops can have nontrivial braiding statistics among themselves. I will address this issue in this talk. We find that, when the loop braiding statistics is nontrivial, the condensation of loops must be accompanied by the condensation of some quasi-particles to result in a gapped trivial phase. We enumerate all possible particle / loop condensation possibilities to drive such transitions. Moreover, just like in the 2D case, a correspondence exist between bulk condensation and gapped boundary conditions of topological phases. We investigate the dependence of ground state degeneracy on the boundary condition which provides a way to distinguish different gauge theories.
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