Excitation basis for (3+1)d topological phases

Clement Delcamp

doi:10.1007/jhep12(2017)128

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arXiv · 1709.04924

Excitation basis for (3+1)d topological phases

Clement Delcamp

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Abstract

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev's quantum double model. The corresponding lattice Hamiltonian yields excitations located at torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu's tube algebra. This defines an algebraic structure extending the Drinfel'd double. Its irreducible representations, labeled by two fluxes and one charge, characterize the torus-excitations. The tensor product of such representations is introduced in order to construct a basis for (3+1)d gauge models which relies upon the fusion of the defect excitations. This basis is defined on manifolds of the form $\Sigma \times \mathbb{S}_1$, with $\Sigma$ a two-dimensional Riemann surface. As such, our construction is closely related to dimensional reduction from (3+1)d to (2+1)d topological orders.

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Clement Delcamp. 2017-09-14. Excitation basis for (3+1)d topological phases. https://doi.org/10.1007/jhep12(2017)128

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