The main purpose of "Kac" is to compute fusion rules for RCFT’s related to Wess-Zumino-Witten models on arbitrary group manifolds. This includes semi-simple groups and non-simply connected group manifolds. The latter are described algebraically in terms of Simple Currents. The program can also compute fusion rules for most coset conformal field theories.

The algorithm is based on the Verlinde formula applied to a modular transformation matrix S. The latter is computed using the Kac-Peterson formula, combined with the orbit Lie algebra formalism developed in collaboration with J. Fuchs and C. Schweigert (building on earlier work with S. Yankielowicz).

Some additional features:

1. Computation of spectra of WZW-models (or untwisted affine Lie algebras) and of all their simple current invariants;
   

2. Computation of "spectra" for twisted affine Lie algebras;
   

3. C=1 orbifold and N=0,1,2 minimal model spectra;
   

4. Computation of boundary and crosscap formulas for simple current invariants, using the formulas developed in collaboration with J. Fuchs, C. Schweigert, L. Huiszoon and J. Walcher
   

5. Boundaries and crosscaps for some exceptional invariants;
   

6. Computation of annulus, Moebius and Klein bottle coefficients;
   

7. Computation of open and closed string spectra, including tadpole cancellation;
   

8. Computation of spectra for twisted affine Lie algebras;
   

9. Partial computation of modular invariant partition functions using Galois and Quasi-Galois symmetries of S;
   

10. Computation of higher indices of all representations of all simple Lie-algebras (For the exceptional algebras Index files are needed as input). Put them in a directory ~/Library/Kac. In combination with FORM the program can be used to compute characters of Lie-algebra representations. For this purpose Kac generates FORM input file named Xr.characters in the directory ~/Library/Kac (X=A,...,G and r is the rank of the algebra).
    

Please report any problems to Bert Schellekens.

The "basic commandline versions" should work on any system with the correct CPU, as indicated. The other versions require the "readline" library.

Version 7

1. Version 7.0 for linux (basic commandline version)
   

2. Version 7.0 for Mac (G4, G5)
   

3. Version 7.0 for Mac (Universal binary)
   

4. Version 7.4x for linux CSL 5.2
   

Version 8

1. Version 8.08578 for Mac (intel, Apple Silicon)
   

2. Version 8.08067 for linux (Compiled on Scientific Linux 6.8)
   

Manual (still under construction)