Double-Scaling Limit in Principal Chiral Model: a New Non-Critical String?

Abstract

We initiate a systematic, non-perturbative study of the large-$N$ expansion in the two-dimensional $\text{SU}(N)\times \text{SU}(N)$ Principal Chiral Model (PCM). Starting with the known infinite-$N$ solution for the ground state at fixed chemical potential \cite{Fateev:1994dp,Fateev:1994ai}, we devise an iterative procedure to solve the Bethe ansatz equations order by order in $1/N$. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-$N$ expansion. The resulting double-scaling limit bears striking similarities to the $c=1$ non-critical string theory and suggests that the double-scaled PCM is dual to a non-critical string with a $(2+1)$-dimensional target space where an additional dimension emerges dynamically from the $\text{SU}(N)$ Dynkin diagram.

arXiv comment6 pages, 1 figure, v2: typos fixed, minor corrections

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Cited by in corpus (8)

• Resurgence in the O(4) sigma model
• New renormalons from analytic trans-series
• From perturbative to non-perturbative in the O(4) sigma model
• Testing the Bethe ansatz with large N renormalons
• Quantization of Harer-Zagier formulas
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Three roads to the energy gap
• Resurgence and $1/N$ Expansion in Integrable Field Theories