# Comments on the Random Thirring Model

## TL;DR

This paper analyzes a random-coupling Thirring model in 1+1 dimensions, computing its two-point function and RG flow, revealing that randomness makes the couplings marginally irrelevant, contrasting with the standard model.

## Contribution

It provides the first detailed large N analysis of the random Thirring model, including two-point functions and RG flow, highlighting the impact of randomness on marginal operators.

## Key findings

- Two-point function computed at large distances for any coupling strength.
- Random couplings are statistically marginally irrelevant in the large N limit.
- Leading quadratic term in the beta function vanishes, cubic term matches RG flow.

## Abstract

The Thirring model with random couplings is a translationally invariant generalisation of the SYK model to 1+1 dimensions, which is tractable in the large N limit. We compute its two point function, at large distances, for any strength of the random coupling. For a given realisation, the couplings contain both irrelevant and relevant marginal operators, but statistically, in the large N limit, the random couplings are overall always marginally irrelevant, in sharp distinction to the usual Thirring model. We show the leading term to the $\beta$ function in conformal perturbation theory, which is quadratic in the couplings, vanishes, while its usually subleading cubic term matches our RG flow.