E. Sobko

The principle of maximal transcendentality is proved to all orders for the vacuum energy of a strongly interacting quantum field theory.

Maximal transcendentality is a powerful but poorly understood organising principle in quantum field theory, predicting that only the most complex terms remain in observables. We prove it to all orders for the strongly coupled large-N Principal Chiral Model in a double-scaling regime. The vacuum-energy coefficients are polynomials in odd zeta values, and the first 35 orders reveal further number-theoretic structures. 

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.

Transcendentality proof

Maximal transcendentality of the double-scaled PCM