Lowest dimension gauge-invariant operators in SU(N) Yang-Mills theories.
We look at operators of the form
$$\mathcal{L}{\mathrm{int}} \supset \frac{1}{\Lambda^{k}} X Q{i} G^{\otimes k}_{N},$$
where
The code is very simple to install. Simply clone this repository and navigate to the root directory and do
pip install .
The code is a simple collection of functions, all located in tesselation/functions.py
. An example of their use is in Tesselation.ipynb
. There are four primary functions of interest to the user:
l_pair(p, i)
Pair of l that results in the optimal irreducible representation in tensor product of X times Q_i.
Parameters:
p : array_like
Dynkin label of X.
i : int
Index of only nonzero Dynkin coefficient in Q_i.Returns:
l1, l2 : int, int
Pair of l such that p[l1] !=0, p[l2] != 0, l1 is largest l such that l <= N - i, and is smallest l such that l > l1.
Nality(p)
N-ality of irreducible representation X. The number of boxes in the Young tableau for X mod N.
Parameters:
p : array_like
Dynkin label of X.Returns:
t : int
The number of boxes in the Young tableau for X mod N.
fj(p)
Optimum irreducible representation in the tensor product of X times Q_i.
Parameters:
p : array_like
Dynkin label of X.Returns:
fj : array_like
Resulting Dynkin label for optimal irreducible representation.
kmin(p)
Minimum number of copies of the adjoint such that tensor product X Q_i G_N ... G_N contains a trivial subspace.
Parameters:
p : array_like
Dynkin label of irreducible representation X.Returns:
kmin : int
Minimum number of copies of the adjoint representation such that the operator is gauge invariant.