Recent Developments in Discrete Torsion

TL;DR

The paper reframes discrete torsion as the choice of orbifold group action on the $B$ field, providing a purely mathematical basis via cohomology. It shows that twisted-sector phases, D-brane projective actions, and related phenomena across Type II and heterotic string theories all arise from this $B$-field orbifold action, encoded by $H^2( abla rightarrow Gamma, U(1))$ data. The work also extends the framework to $C$ fields via $H^3( abla rightarrow Gamma, U(1))$ and discusses implications for moduli lifting in Vafa-Witten scenarios. Overall, the approach unifies disparate observations about discrete torsion and clarifies its role in higher-form gauge data and D-brane physics. This has broad implications for understanding orbifold consistency and the geometry of fluxes in string theory.

Abstract

In this short note we briefly review some recent developments in understanding discrete torsion. Specifically, we give a short overview of the highlights of a group of recent papers which give the basic understanding of discrete torsion. Briefly, those papers observe that discrete torsion can be completely understood simply as the choice of action of the orbifold group on the B field. We summarize the main points of that work.

Figures (2)

• Figure 1: Lift of closed loop to covering space.
• Figure 2: A twisted sector contribution to the one-loop partition function.