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CritPt / Challenge_65_main / Consider a fermion field ψ that is in the adjoint representations of a…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

code template

Code

import sympy as sp

psi = sp.symbols('psi')
tr = sp.Function('tr')

def answer(psi, tr):
    r"""
    Return expressions of the indecomposable gauge invariant operators in Sympy format.

    Inputs
    ----------
    psi: sympy.Symbol, the fermion field, $\psi$
    tr: sympy.Function, the trace function, $\text{tr}$

    Outputs
    ----------
    operators: set[sympy.Expr], a set of all the indecomposable gauge invariant operators with charge smaller or equal to 5 in the rank 2 theory.
    """

    # ------------------ FILL IN YOUR RESULTS BELOW ------------------
    operators = ... # a SymPy expression of inputs
    # ---------------------------------------------------------------

    return operators

problem description

# Problem setup: Consider a fermion field

\psi

that is in the adjoint representations of a

U(N)

gauge group and carries a global

U(1)

charge 1. Please use the following notation: denote the fermion field by

\psi

and the trace of the gauge group representation by

\text{tr}

. So, for example, a charge

1

single trace field should be written as

\text{tr} (\psi)

. If two orderings of field define the same operator up to a sign, always write smaller charge fields on the left whenever possible. # Main problem: In the rank 2 theory, write down all the indecomposable gauge-invariant operators with charge smaller or equal to 5.

Plain-text mathematical notation (without MathML)

# Problem setup:
Consider a fermion field ψ that is in the adjoint representations of a U(N) gauge group and carries a global U(1) charge 1. Please use the following notation: denote the fermion field by ψ and the trace of the gauge group representation by tr. So, for example, a charge 1 single trace field should be written as tr(ψ). If two orderings of field define the same operator up to a sign, always write smaller charge fields on the left whenever possible.

# Main problem:
In the rank 2 theory, write down all the indecomposable gauge-invariant operators with charge smaller or equal to 5.

Original LaTeX notation

# Problem setup:
Consider a fermion field $\psi$ that is in the adjoint representations of a $U(N)$ gauge group and carries a global $U(1)$ charge 1. Please use the following notation: denote the fermion field by $\psi$ and the trace of the gauge group representation by $\text{tr}$. So, for example, a charge $1$ single trace field should be written as $\text{tr} (\psi)$. If two orderings of field define the same operator up to a sign, always write smaller charge fields on the left whenever possible.

# Main problem:
In the rank 2 theory, write down all the indecomposable gauge-invariant operators with charge smaller or equal to 5.

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Source and history

upstream_id / Original problem ID: Challenge_65_main
task_id: 327718c8-3fba-5242-bcad-f9fcccd8114a
task_key: train--Challenge~5f65~5fmain
task_revision_id: 1
config / split: / train

Official source

initial import