Publications

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In this paper we propose infinitely many RG flows between the diagonal minimal models of the WN algebras. These are higher spin extended algebras that contains the stress energy tensor together with conserved currents of increasingly higher spin.

The flows that we find take the remarkable N-independent form WN(p,q)-> WN(p, kp-q), and generalize the ones recently found for Virasoro.

Short letter prepared as a contribution to the proceedings of the conference "Non-perturbative Methods in QFT" at Kyushu University (March 10-14, 2025).

We summarize our work on translational invariant defects in 2d deformed CFTs.

We prove the analytic Langlands conjecture for parabolic bundles of genus 0 and rank 1, employing the Separation of Variables method: a technique of the theory of integrable models.

We derive a condition for defects in deformed 2D CFT to commute with the perturbed Hamitonian. Such defects fail to be topological, but are still conserved and lead to infinitely many non-local conserved charges. We apply this construction to Virasoro Minimal models, where.

We illustrate the existence of infinitely non-local charges associated to deformations that were not known to be integrable.

We develop a general formalism to describe the Renormalization Group Flow of Schur indices and fusion algebras of BPS line defects in four-dimensional N=2 Supersymmetric Quantum Field Theories. The formalism includes and extends known results about the Seiberg-Witten description of these structures. Another application of the formalism is to describe the spectrum of BPS particles of N=2 gauge theories with matter in terms of the spectrum of pure N=2 gauge theories. Applications to the theory of quantum groups and to the quantization of cluster varieties are also discussed.

We investigate of RG flows between Virasoro minimal models that are protected by non invertible symmetries. We introduce a family of non-linear integral equations that appear to encode the exact finite-size, ground-state energies of these flows, including non-integrable cases, such as the recently proposed M(kq + I,q) → M(kq − I,q). Our family of NLIEs generalises the integrable flows known in the literature: ϕ(1,3), ϕ(1,5), ϕ(1,2) and ϕ(2,1). This work uncovers a new interplay between exact solvability and non-invertible symmetries.

We extend the study of integrable structures and analyticity of the spectrum in large

Nc QCD2 to a broad class of theories called the generalized QCD, which are given by the Lagrangian L ∝ trB∧F−trV(B) coupled to quarks in the fundamental representation. We recast the Bethe-Salpeter equation for the meson spectrum into a TQ-Baxter equation and determine a transfer matrix in a closed form for any given polynomial V(B). From there we derive various properity of the mesons' spectra. Lastly, we illustrate that this structure persists in the large-representation limit of the generalized QCD with the SU(2) gauge group.

We explore new aspects of fermionic p-form symmetries, present in physical fermionic systems. We propose a novel procedure to gauge these global symmetries. We also discuss fermionic symmetries whose charged objects are disorder operators, and dualization procedures for fermionic tensor-spinor fields.

We study integrable structure of mesons in 2d QCD in the large N limit. By recasting the 't Hooft equation into a TQ-Baxter equation, we access various analytical properties of the spectrum. Among those we produce a convergent series expansion spectral sums and asymototic expansion for the mesons' wavefunctions. In addiction, we study a intereseting multi-sheeted structure of the mesons' masses as function of the quark mass.

Picture in the background: lonely lighthouse in the Ustica island, Palermo, Sicily

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