Tube algebras, excitations statistics and compactification in gauge models of topological phases
Abstract
We consider lattice Hamiltonian realizations of (d+1)dimensional Dijkgraaf Witten theory. In (2+1) d, it is wellknown that the Hamiltonian yields pointlike excita tions classified by irreducible representations of the twisted quantum double. This can be confirmed using a tube algebra approach. In this paper, we propose a generalisation of this strategy that is valid in any dimensions. We then apply this generalisation to derive the algebraic structure of looplike excitations in (3+1) d, namely the twisted quantum triple. The irreducible representations of the twisted quantum triple algebra correspond to the simple looplike excitations of the model. Similarly to its (2+1) d counterpart, the twisted quantum triple comes equipped with a compatible comultiplication map and an Rmatrix that encode the fusion and the braiding statistics of the looplike excitations, respectively. Moreover, we explain using the language of loopgroupoids how a model defined on a man ifold that is ntimes compactified can be expressed in terms of another model in nlower dimensions. This can in turn be used to recast higherdimensional tube algebras in terms of lower dimensional analogues.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2019
 DOI:
 10.1007/JHEP10(2019)216
 arXiv:
 arXiv:1905.08673
 Bibcode:
 2019JHEP...10..216B
 Keywords:

 Topological States of Matter;
 Anyons;
 Gauge Symmetry;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 71 pages