SusyPy (short for Supersymmetry Python) is a symbolic algebra system, built on top of Cadabra2, for performing intricate tensor arithmetic in supersymmetry.

• LaTeX-like inputs for tensor expressions.
• Complete compatibility with Cadabra2's existing library, Ex/ExNode objects, and tree structure.
• Complete simplification of tensor expressions in a canonical way.
• Spinor-index canonicalization.
• Two- and four-index Fierz expansions.
• Symbolic Fourier and inverse Fourier transforms.
• Evaluation of tensor traces.
• Handling of Feynman propagators.
• Supersymmetry multiplet solvers.
• SUSY-invariant action solver.
• Calculation of a multiplet's holoraumy.

To install, you will need the SusyPy wheel file, which has the name susypy-1.0.0-py3-none-any.whl. Now, if you are using pip, go to your terminal and run the command

pip install susypy-1.0.0-py3-none-any.whl

Once installed, to use SusyPy, you simply need to write in any Python file

import susypy

⚠️ WARNING: SusyPy will only run on Python 3.8 or newer, so make sure to update your version of Python.

TIP: To make sure that you are installing SusyPy into the right version of Python, use pip3.8 instead of pip in the installation command.

Input into SusyPy is given as LaTeX strings into Ex() wrappers. All expressions, whether vectorial or spinorial, are evaluated with the evaluate() function. Below is a simple example of evaluating a product of gamma matrices and the spinor metric. Notice that the algorithm enforces NW-SE convention.

>>> ex = Ex(r'(\Gamma_{a})_{\alpha \beta} (\Gamma^{b})^{\beta \gamma} C_{\gamma \eta}')
>>> evaluate(ex)
'-\indexbracket(Γ_{a}^{b})_{α η}-C_{α η} δ_{a}^{b}'

In order to generate the Fierz expansion of an expression, one can input the expression, the basis, and the desired spinor indices of the factors in the expansion into fierz_expand(). For example, the following code generates (A.24) in Gates2019.

>>> ex = Ex(r'\delta_{\alpha}^{\eta} \delta_{\beta}^{\gamma} + \delta_{\beta}^{\eta} \delta_{\alpha}^{\gamma}')
>>> basis = [Ex(r'C_{\alpha \beta}'), Ex(r'(\Gamma^{a})_{\alpha \beta}'), Ex(r'(\Gamma^{a b})_{\alpha \beta}'), Ex(r'(\Gamma^{a b c})_{\alpha \beta}'), Ex(r'(\Gamma^{a b c d})_{\alpha \beta}'), Ex(r'(\Gamma^{a b c d e})_{\alpha \beta}')]
>>> commuted = [r'_{\alpha}', r'_{\beta}']
>>> uncommuted = [r'_{\eta}', r'_{\gamma}']
>>> fierz_expand(ex, basis, commuted, uncommuted)

(To do: use this subsection to demonstrate the other algorithms.)