Comments on the Random Thirring Model

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.