Sebastian Novak | Searcharxiv

arXiv2015

Spin from defects in two-dimensional quantum field theory

We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in terms of a triangulation equipped with extra data. The amplitude for the spin surfaces is defined to be the amplitude for the underlying oriented surface together with a defect network dual to the triangulation. Independence of the triangulation and of the other choices follows if the line defect and junctions are obtained from a Delta-separable Frobenius algebra with involutive Nakayama automorphism in the monoidal category of topological defects. For rational conformal field theory we can give a more explicit description of the defect category, and we work out two examples related to free fermions in detail: the Ising model and the so(n) WZW model at level 1.

hep-th↗

arXiv2014

State sum construction of two-dimensional topological quantum field theories on spin surfaces

We provide a combinatorial model for spin surfaces. Given a triangulation of an oriented surface, a spin structure is encoded by assigning to each triangle a preferred edge, and to each edge an orientation and a sign, subject to certain admissibility conditions. The behaviour of this data under Pachner moves is then used to define a state sum topological field theory on spin surfaces. The algebraic data is a Delta-separable Frobenius algebra whose Nakayama automorphism is an involution. We find that a simple extra condition on the algebra guarantees that the amplitude is zero unless the combinatorial data satisfies the admissibility condition required for the reconstruction of the spin structure.

math.QA↗