Exact generalized partition function of 2D CFTs at large central charge

TL;DR

This work addresses the generalized partition function of 2d CFTs decorated by higher qKdV charges in the large central charge limit. It proposes that the qKdV charges factorize into an auxiliary non-interacting boson description, enabling a non-perturbative expression for the generalized free energy via an explicit boson spectrum inferred from thermal averages. The authors verify the proposed eigenvalue structure for the first seven charges, derive a closed-form expression for the boson-spectrum coefficients $\xi_k^p$, and conjecture the full spectrum to obtain an exact $Z$ as a function of an infinite tower of chemical potentials, valid at leading orders in $1/c$. The approach extends thermal one-point function data to the full generalized partition function, with the main technical result being the explicit formula for the subleading free-energy term $f_1(t)$, expressed through the boson energies $M_r$ and saddle-point data; this has potential implications for generalized Gibbs ensembles and holographic interpretations in large-$c$ CFTs.

Abstract

We discuss generalized partition function of 2d CFTs decorated by higher qKdV charges on thermal cylinder. We propose that in the large central charge limit qKdV charges factorize such that generalized partition function can be rewritten in terms of auxiliary non-interacting bosons. The explicit expression for the generalized free energy is readily available in terms of the boson spectrum, which can be deduced from the conventional thermal expectation values of qKdV charges. In other words, the picture of the auxiliary non-interacting bosons allows extending thermal one-point functions to the full non-perturbative generalized partition function. We verify this conjecture for the first seven qKdV charges using recently obtained pertrubative results and find corresponding contributions to the auxiliary boson masses. We further extend these results by conjecturing the full spectrum of bosons and find an exact expression for the generalized partition function as a function of infinite tower of chemical potentials in the limit of large central charge.