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CritPt / Challenge_13_main / Consider a (1+1)-D CFT on a torus that consists of right- and left-moving edges…

Problem

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problem description

# Problem setup: Consider a (1+1)-D CFT on a torus that consists of right- and left-moving edges of a Moore-Read state at filling fraction

\nu=1/k

. The primary fields are labeled by

(j_L,n_L,j_R,n_R)

, where

j_{L/R}=0,1/2,1

n_{L/R}\in Z_{2k}

and the electron operators in the theory are

(1,2k,0,0)

and

(0,0,1,2k)

. # Main problem: Given

k=2

, find the expectation values of Verlinde lines assuming the identity operator has expectation value 1. Return your answer as a tuple

(j_L,n_L,j_R,n_R,\lambda_{(j_L,n_L,j_R,n_R)})

, where

\lambda_{(j_L,n_L,j_R,n_R)}

is the expectation value.

Plain-text mathematical notation (without MathML)

# Problem setup:
Consider a (1+1)-D CFT on a torus that consists of right- and left-moving edges of a Moore-Read state at filling fraction ν=1/k. The primary fields are labeled by (j_(L),n_(L),j_(R),n_(R)), where j_(L/R)=0,1/2,1, n_(L/R)∈Z_(2k)  and the electron operators in the theory are (1,2k,0,0) and (0,0,1,2k).

# Main problem:
Given k=2, find the expectation values of Verlinde lines assuming the identity operator has expectation value 1. Return your answer as a tuple (j_(L),n_(L),j_(R),n_(R),λ_((j_(L),n_(L),j_(R),n_(R)))), where λ_((j_(L),n_(L),j_(R),n_(R))) is the expectation value.

Original LaTeX notation

# Problem setup:
Consider a (1+1)-D CFT on a torus that consists of right- and left-moving edges of a Moore-Read state at filling fraction $\nu=1/k$. The primary fields are labeled by $(j_L,n_L,j_R,n_R)$, where $j_{L/R}=0,1/2,1$, $n_{L/R}\in Z_{2k}$  and the electron operators in the theory are $(1,2k,0,0)$ and $(0,0,1,2k)$.

# Main problem:
Given $k=2$, find the expectation values of Verlinde lines assuming the identity operator has expectation value 1. Return your answer as a tuple $(j_L,n_L,j_R,n_R,\lambda_{(j_L,n_L,j_R,n_R)})$, where $\lambda_{(j_L,n_L,j_R,n_R)}$ is the expectation value.

code template

Code

import sympy as sp

def answer():
    r"""
    Return the expectation values of Verlinde lines and corresponding labels.

    Inputs
    ----------
    None

    Outputs
    ----------
    values: set[tuple[float, int, float, int, complex]], a set of tuples $(j_L,n_L,j_R,n_R,\lambda_{(j_L,n_L,j_R,n_R)})$
        where $\lambda_{(j_L,n_L,j_R,n_R)}$ is the expectation value of the Verlinde line operator.
    """

    # ------------------ FILL IN YOUR RESULTS BELOW ------------------
    values = ...
    # ---------------------------------------------------------------

    return values

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Source and history

upstream_id / Original problem ID: Challenge_13_main
task_id: f5aef08f-3cf1-51cb-a156-01306d31122a
task_key: train--Challenge~5f13~5fmain
task_revision_id: 3
config / split: / train

Official source

initial import