Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 2

Towards super Teichmuller spin TQFT

Pages: 245 – 294



Nezhla Aghaei (Centre for Quantum Mathematics, University of Southern Denmark, Odense, Denmark; Max Planck Institut für Mathematik, Bonn, Germany; and Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Switzerland)

M. K. Pawelkiewicz (Institut de Physique Theorique, CEA Saclay, Gif Sur Yvette, France)

Masahito Yamazaki (Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, University of Tokyo, Kashiwa, Chiba, Japan)


The quantization of the Teichmüller theory has led to the formulation of the so-called Teichmüller TQFT for $3$‑manifolds. In this paper we initiate the study of “supersymmetrization” of the Teichmüller TQFT, which we call the super Teichmüller spin TQFT. We obtain concrete expressions for the partition functions of the super Teichmüller spin TQFT for a class of spin $3$‑manifold geometries, by taking advantage of the recent results on the quantization of the super Teichmüller theory. We then compute the perturbative expansions of the partition functions, to obtain perturbative invariants of spin $3$‑manifolds. We also comment on the relations of the super Teichmüller spin TQFT to $3$‑dimensional Chern–Simons theories with complex gauge groups, and to a class of 3d $\mathcal{N}=2$ theories arising from the compactifications of the M5‑branes.

Published 27 December 2022