Generalised twisted partition functions

TL;DR

This paper studies a broad class of twisted partition functions in 2D conformal field theories, providing a classification framework, interpreting algebraic structures physically, and suggesting new avenues for CFT analysis.

Contribution

It introduces a general classification of twist operators in 2D CFTs, extending previous results and linking algebraic and physical perspectives.

Findings

Derived a classification equation for compatible twist operators

Solved the classification in specific cases

Connected algebraic structures to physical interpretations

Abstract

We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.