arXiv subjects

Giovanni Ravazzini

Publications and source records attributed to Giovanni Ravazzini.

3 recordsLinked to original sources

arXiv2026

Higher-Rank Mathieu Opers, Toda Chain, and Analytic Langlands Correspondence

We study the Riemann-Hilbert problem associated to flat sections of oper connections of arbitrary rank on the twice-punctured Riemann sphere with irregular singularities of the mildest type. We construct the solutions in terms of the solutions to a single non-linear integral equation. It follows from this construction that the generating function of the submanifold of opers coincides with the Yang-Yang function of the quantum Toda chain, proving a conjecture by Nekrasov, Rosly and Shatashvili. In this way we may furthermore reformulate the quantization conditions of the Toda chain in terms of the connection problem, for which we also provide a solution. We finally interpret our results as a variant of the Analytic Langlands Correspondence for the real version of the Hitchin system corresponding to the Toda chain.

math-ph↗

arXiv2026

Higher-Rank Connections and Deformed Schrödinger Operators

We study the connection problem for a class of linear differential equations of order $N$ closely related to the Baxter equation of the quantum Toda chain. The space of solutions is $N$-dimensional and several linearly independent solutions decay at each singularity, leading to a rich structure of boundary value problems. We derive the weakest quantization conditions compatible with decaying behavior at both singularities, and formulate these conditions in terms of the associated monodromy data. In doing so, we prove the quantization conditions predicted by the topological string/spectral theory duality for a family of deformed Schrödinger equations. More generally, our results point to a hierarchy of spectral problems interpolating between the minimal conditions studied here and the maximally decaying boundary conditions of the $N$-particle quantum Toda chain.

math-ph↗

arXiv2024

Taming non-analyticities of QFT observables

Many observables in quantum field theories are involved non-analytic functions of the parameters of the theory. However, it is expected that they are not arbitrarily wild, but rather have only a finite amount of geometric complexity. This expectation has been recently formalized by a tameness principle: physical observables should be definable in o-minimal structures and their sharp refinements. In this work, we show that a broad class of non-analytic partition and correlation functions are tame functions in the o-minimal structure known as $\mathbb{R}_{\mathscr{G}}$ - the structure defining Gevrey functions. Using a perturbative approach, we expand the observables in asymptotic series in powers of a small coupling constant. Although these series are often divergent, they can be Borel-resummed in the absence of Stokes phenomena to yield the full partition and correlation functions. We show that this makes them definable in $\mathbb{R}_{\mathscr{G}}$ and provide a number of motivating examples. These include certain 0-dimensional quantum field theories and a set of higher-dimensional quantum field theories that can be analyzed using constructive field theory. Finally, we discuss how the eigenvalues of certain Hamiltonians in quantum mechanics are also definable in $\mathbb{R}_{\mathscr{G}}$.

hep-th↗