Comments on the random Thirring model
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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 β function in conformal perturbation theory, which is quadratic in the couplings, vanishes, while its usually subleading cubic term matches our RG flow.
Keywords1/N Expansion Gauge-gravity correspondence
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- A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev/, University of California, Santa Barbara U.S.A., 7 April 2015.
- A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/, University of California, Santa Barbara U.S.A., 27 May 2015.
- I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, seventh edition, Elsevier/Academic Press, Amsterdam The Netherlands, (2007).Google Scholar
- J.L. Cardy, Conformal invariance and statistical mechanics, Les Houches France, (1988) [INSPIRE].
- M. Abramowitz and I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, ninth Dover printing, tenth GPO printing ed., Dover, New York U.S.A., (1964).Google Scholar
- P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York U.S.A., (1997) [INSPIRE].