Susyno is a Mathematica package which calculates the 2-loop renormalisation group equations of generic supersymmetric models, based on any gauge group (the only exception being multiple U(1) groups) and with any field content.

As input Susyno only requires the gauge group, the representations, the number of flavours and the abelian discrete symmetries of the model. Susyno then automatically generates the superpotential and the soft SUSY breaking Lagrangian, as well as other relevant group theoretical quantities. These are then used to calculate the 2-loop beta functions for all the parameters of the model.

With no special relation to supersymmetry nor renormalisation group equations, Susyno also contains several group theoretical functions which can be used on their own. Baring time and memory constraints, these are valid for any Lie/gauge group and for any representation(s) — see for example, in the built-in documentation, the functions Casimir, ConjugateIrrep, DynkinIndex, DimR, Invariants, PermutationSymmetryOfInvariants, ReduceRepProduct, RepMatrices, RepName, RepsUpToDimN, TriangularAnomalyValue. There are additional functions which are related to symmetry breaking: DecomposeReps, RegularSubgroupProjectionMatrix, SubgroupEmbbedingCoefficients. There are also some functions related to the permutation group $S_n$: DecomposeSnProduct, HookContentFormula, SnClassCharacter, SnClassOrder, SnIrrepDim, SnIrrepGenerators. A tutorial on using the program for group theory computations can be found here .

Sym2Int is a Mathematica package which is related to Susyno (see here for more details ).

Author: Renato Fonseca

Getting started

Susyno works with Mathematica 7 or newer. The latest version is available here for download:

(Susyno 3.7)

Decompressing the downloaded zip file will generate a folder Susyno. This folder should be placed in a directory visible to Mathematica (typing $Path in Mathematica shows a list of the possible locations). A good choice is to place it (the whole Susyno folder and not just its contents!) in

(Mathematica base directory)/AddOns/Applications
Linux, Mac OS
(Mathematica base directory)\AddOns\Applications

Once this is done the package is installed. To load Susyno, type in the front end



The program's manual (version 1) has been published in the journal Computer Physics Communications. The reference is "Renato M. Fonseca, Calculating the renormalisation group equations of a SUSY model with Susyno, Computer Physics Communications 183 (2012) 2298" (the arXiv version is available here ).

Susyno also includes a detailed, up-to-date built-in documentation. Once the package is installed, these files are automatically integrated into the Mathematica help system.

Results for the RGEs of specific models

The output of the program has been compared with several results in the literature. In particular, the following models have been considered: Susyno agrees with these published results.

Renato Fonseca


Last updated
08 April 2020