Perturbative study of large $N$ principal chiral model with twisted reduction

TL;DR

This study computes perturbative coefficients of the internal energy in the twisted reduced principal chiral model using NSPT, confirming large N equivalence with the ordinary PCM and analyzing finite-N corrections and computational feasibility.

Contribution

It provides the first four perturbative coefficients for TRPCM's internal energy and verifies their agreement with PCM results at large N, demonstrating the model's consistency.

Findings

First four perturbative coefficients computed and verified against PCM.

Finite-N corrections are smaller in TRPCM than in PCM.

Feasibility of extending calculations to higher orders analyzed.

Abstract

We compute the first four perturbative coefficients of the internal energy for the twisted reduced principal chiral model (TRPCM) using numerical stochastic perturbation theory (NSPT). This matrix model has the same large $N$ limit as the ordinary principal chiral model (PCM) at infinite volume. Indeed, we verify that the first three coefficients match the analytic result for the PCM coefficients at large $N$ with a precision of three to four significant digits. The fourth coefficient also matches our own NSPT calculation of the corresponding PCM coefficient at large $N$. The finite-$N$ corrections to all coefficients beyond the leading order are smaller for TRPCM than for PCM. We analyze the variance to determine the feasibility of extending the calculations to higher orders.