The program Kac

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The main purpose of "Kac" is to compute fusion rules for Wess-Zumino-Witten models based 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 [8] (except the so-called "Mavericks" [10].)

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):

Kac interface

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

Version 6

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

Version 7
The "basic commandline versions" should work on any system with the correct CPU, as indicated. The other versions require the "readline" library.