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

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

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

  4. BulletComputation 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. BulletBoundaries and crosscaps for some exceptional invariants;

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

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

  8. BulletComputation of spectra for twisted affine Lie algebras;

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

  10. BulletComputation 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. BulletVersion 7.0 for linux (basic commandline version)

  2. BulletVersion 7.0 for Mac (G4, G5)

  3. BulletVersion 7.0 for Mac (Universal binary)

  4. BulletVersion 7.4x for linux CSL 5.2

Version 8

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

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

Manual (still under construction)


Kac is an acronym that stands for “Komputations with Algebras and Currents”.

The main purpose of "Kac" is to compute fusion rules for Rational Conformal Field Theories based on affine Lie Algebras and their simple current extensions.

This includes most coset CFT’s and their tensor products.

It also computes annulus, Moebius and Klein bottle coefficients for open/unoriented CFT’s.

Here is brief account of the history of Kac