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Principal Chiral Field at Large N

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arxiv hep-th/9403099 v1 pith:QC53IEDW submitted 1994-03-17 hep-th

V.A.Fateev , V.A.Kazakov , P.B.Wiegmann This is my paper · ORCID
classification hep-th
keywords fieldlargechiralenergyexactfoundgroundperturbative
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We present the exact and explicit solution of the principal chiral field in two dimensions for an infinitely large rank group manifold. The energy of the ground state is explicitly found for the external Noether's fields of an arbitrary magnitude. The exact Gell-Mann - Low function exhibits the asymptotic freedom behaviour at large value of the field in agreement with perturbative calculations. Coefficients of the perturbative expansion in the renormalized charge are calculated. They grow factorially with the order showing the presence of renormalons. At small field we found an inverse logarithmic singularity in the ground state energy at the mass gap which indicates that at $N=\infty$ the spectrum of the theory contains extended objects rather then pointlike particles.

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Cited by 3 Pith papers

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  1. Maximal Transcendentality of the Double-Scaled PCM

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    Proves maximal transcendentality to all orders for the vacuum-energy expansion of the double-scaled large-N PCM, with coefficients as rational polynomials in odd zeta values after a natural coupling shift.

  2. The complete trans-series for conserved charges in integrable field theories

    hep-th 2025-01 conditional novelty 7.0 of 10

    A unified Wiener-Hopf construction gives all-order trans-series for conserved charges in O(N), SU(N), Lieb-Liniger, Gaudin-Yang and capacitor models, with numerically checked Borel resummation.

  3. (Un)solvable Matrix Models for BPS Correlators

    hep-th 2025-08 unverdicted novelty 6.0 of 10

    Proposes complex matrix models for BPS correlators in N=4 SYM, relating eigenvalue distributions to LLM droplet shapes and enabling computations of one-point functions and three-point correlators via reductions to kno...

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