Modular Transformations and Invariants in the Context of Fractional Level Affine sl(2|1;C)

TL;DR

This paper investigates the modular transformation properties of admissible characters of the affine superalgebra sl(2|1;C) at fractional levels, explicitly calculating modular invariants for specific cases and identifying series of invariants.

Contribution

It provides a detailed analysis of modular transformations and invariants for fractional level affine superalgebras, including explicit calculations for key cases.

Findings

Explicit modular invariants for u=2 and u=3 cases.

Identification of A-series and D-series modular invariants.

Characterization of modular transformation properties at fractional levels.

Abstract

The modular transformation properties of admissible characters of the affine superalgebra sl(2|1;C) at fractional level k=1/u-1, u=2,3,... are presented. All modular invariants for u=2 and u=3 are calculated explicitly and an A-series and D-series of modular invariants emerge.