SusyPy

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

Features:

• 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.

Installation:

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.

User Guide:

Getting Started:

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.)