Derive a non-asymptotic modular S-transform for chiral deformations

Develop an exact, non-perturbative derivation of the modular S-transformation for the generalized partition function ⟨exp(λ W_0)⟩ of a two-dimensional conformal field theory deformed by a holomorphic local field W(z), avoiding an order-by-order expansion in the fugacities and establishing the transformation without relying on asymptotic series.

Background

The paper proves a universal recursive description of the modular S-transform for generalized partition functions of chiral deformations in an asymptotic expansion in the fugacities. This establishes the modular behavior order by order and generalizes previous conjectures.

However, an exact (non-asymptotic) S-transform is known only in special, essentially free, models (e.g., Ising and symplectic fermions). Extending the result beyond asymptotics would provide a complete modular characterization of chiral deformations in general conformal field theories.

References

It is also important to remember that our results are obtained in an asymptotic expansion in the fugacities. A broader understanding of how to derive the modular transformation of the deformed conformal field theory, without working term by term in the asymptotic expansion, remains an outstanding problem.

— Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations  (2603.28244 - Ashok et al., 30 Mar 2026) in Section 6: Discussion, Outlook