3,127 research outputs found
Equivariant Crossed Modules and Cohomology of Groups with Operators
In this paper we study equivariant crossed modules in its link with strict
graded categorical groups. The resulting Schreier theory for equivariant group
extensions of the type of an equivariant crossed module generalizes both the
theory of group extensions of the type of a crossed module and the one of
equivariant group extensions.Comment: 20 pag
Categorical aspects of bivariant K-theory
This survey article on bivariant Kasparov theory and E-theory is mainly
intended for readers with a background in homotopical algebra and category
theory. We approach both bivariant K-theories via their universal properties
and equip them with extra structure such as a tensor product and a triangulated
category structure. We discuss the construction of the Baum-Connes assembly map
via localisation of categories and explain how this is related to the purely
topological construction by Davis and Lueck
Spontaneous symmetry breaking from anyon condensation
In a physical system undergoing a continuous quantum phase transition,
spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian
fail to be preserved in the ground state. In the traditional Landau theory, a
symmetry group can break down to any subgroup. However, this no longer holds
across a continuous phase transition driven by anyon condensation in symmetry
enriched topological orders (SETOs). For a SETO described by a -crossed
braided extension , we show that
physical considerations require that a connected \'etale algebra admit a -equivariant algebra structure for symmetry to be
preserved under condensation of . Given any categorical action
such that for all , we show there is a short exact
sequence whose splittings correspond to -equivariant algebra structures. The
non-splitting of this sequence forces spontaneous symmetry breaking under
condensation of . Furthermore, we show that if symmetry is preserved, there
is a canonically associated SETO of , and
gauging this symmetry commutes with anyon condensation.Comment: 35 pages, comments welcome. To appear in Journal of High Energy
Physic
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