Fully extended r-spin topological field theories
Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
Final Report Abstract
The topic of this project was the investigation of certain types of topological quantum field theories (TQFTs) in two dimensions, which depend on particular tangential structures called r-spin structures, generalisations of ordinary spin structures associated to the r-fold cover of the rotational group, a speciality to dimension two. The motivation of the study of these was twofold. TQFTs with these tangential structure are non-trivial, but still not too complicated to study and they provide good testing ground for the so-called cobordism hypothesis. The second motivation was to obtain examples of such TQFTs beyond the already known more or less trivial ones. Both of these goals have been achieved. Together with my hosting researcher Nils Carqueville we have proved the two-dimensional cobordism hypothesis with r-spin structures and provided a new class of fully extended r-spin TQFTs from two-categories of Landau–Ginzburg models. Together with Nils Carqueville and Ehud Meir we have furthermore provided a rich family of non-extended TQFTs with a complete set of invariants for any value of r. Moving beyond the primary goals of the project together with Ingo Runkel and Gerard M. T. Watts we have given a construction of two-dimensional spin conformal field theories and a new class of examples these based on Bershadsky–Polyakov models. This paves the ground for further mathematical study of conformal field theories and supersymmetric theories.
Publications
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Fully extended r-spin TQFTs. Quantum Topology, 14(3), 467-532.
Carqueville, Nils & Szegedy, Lóránt
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Parity and spin CFT with boundaries and defects. SciPost Physics, 15(5).
Runkel, Ingo; Szegedy, Lóránt & Watts, Gérard M. T.
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Invariants of r-spin TQFTs and non-semisimplicity. Journal of Algebra, 664, 101-128.
Carqueville, Nils; Meir, Ehud & Szegedy, Lóránt
