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.

27 pages. Minor changes

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• Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
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• Conformality of $1/N$ corrections in SYK-like models
• Generalized conformal structure, dilaton gravity and SYK
• Chiral Algebras of Two-Dimensional SYK Models
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• The onset of quantum chaos in disordered CFTs
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• The chiral SYK model in three-dimensional holography
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• Quasiparticle tunnelling in two coupled chiral SYK model