The algorithm is based on the Verlinde formula [3] applied to a modular transformation matrix S. The latter is computed using the Kac-Peterson formula [1], combined with the orbit Lie algebra formalism developed in collaboration with J. Fuchs and C. Schweigert (building on earlier work with S. Yankielowicz [4]).

Some additional features:

- Computation of spectra of WZW-models (or untwisted affine Lie
algebras) and of all their simple current invariants;
- Computation of "spectra" for twisted affine Lie
algebras;
- C=1 orbifold and N=0,1,2 minimal model spectra;
- 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
- Boundaries and crosscaps for some exceptional
invariants;
- Computation of Annulus, Moebius and Klein bottle
coefficients;
- Computation of open and closed string spectra, including
tadpole cancellation;
- Computation of spectra for twisted affine Lie
algebras;
- Partial computation of modular invariant partition functions
using Galois
and Quasi-Galois
symmetries of S;
- 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 Xl.characters in the directory ~/Library/Kac (X=A,...,G and l is the rank of the algebra).

Boundary CFT features are available as of version 6.0

Please report any problems to Bert Schellekens.

The program is written in C and presently three compiled versions are available: a terminal interface for NeXTSTEP (Motorola/Intel), as well as for SUN and linux, and a graphical interface version only for NeXTSTEP (Motorola/Intel) (the latter is only available for version 4):

The graphical version has an extensive HELP system, the terminal versions have a built-in help system, and there is also an example file and a file with a description of the syntax. The terminal version is fully programmable, and admits indefintely nested loops and procedures. The graphical version has the same functionality, but non-interactively: a programme file with an extension .kac can be run by double-clicking, and output can be directed to a file (try example.kac, but remove the "Quit" statement).

This program was written for private use, but it is freely available to anyone interested in it. However, I would appreciate an e-mail notification to the address t58@nikhef.nl, just to have an idea of who is using it, and to inform users of new versions. Feedback is always welcome. If you need a version for another kind of computer, please let me know.

Latest version (6.1): 24-04-03.

Linux version (intel processors): The 'save preferences' command writes certain settings to disk, to a file '.Defaults/Kac' in your home directory. On SUN and NeXT machines the directory '.Defaults' is created if it didn't exist; on linux machines this directory must first be created by hand.

Windows version (4.0): Runs in an MS-DOS window under Windows 98/95. Not very well tested. Some file options may not work, and the CPU-time indication is approximate

Version 4

- NeXT graphical interface version
- NeXT terminal version
- SUN terminal version
- linux terminal version
- windows version

Version 6

- Version 6.1 for linux (tested on RedHat 7.3 and 8.0)
- Version 6.2 for linux (tested on RedHat 9)
- Version 6.0 for next

This is a manual for version 6.0 (still under construction)

- Manual
- Example file for terminal versions
- Syntax file for terminal versions
- Index files for exceptional algebras

Version 7

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

This version requires "readline" and has command line completion and history

Basic command line version

This version requires "readline" and has command line completion and history

Basic command line version

Basic command line version

Manual for version 7.0 (still under construction)

Last update: 2 august 2006