Maximal Transcendentality of the Double-Scaled PCM

Evgeny Sobko

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arXiv · 2606.09972

Maximal Transcendentality of the Double-Scaled PCM

Evgeny Sobko

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Abstract

We prove, to all orders, maximal transcendentality of the strongly coupled large-N Principal Chiral Model in the double-scaling regime introduced in our earlier work. We also prove that, after a natural shift of the coupling constant, the coefficients of the vacuum-energy expansion are expressed purely as polynomials in odd zeta values with rational coefficients. The first 35 explicitly computed orders reveal further number-theoretic regularities, pointing to hidden structure beyond maximal transcendentality.

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Evgeny Sobko. 2026-06-08. Maximal Transcendentality of the Double-Scaled PCM. https://arxiv.org/abs/2606.09972

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