arXiv subjects

Paolo Vallarino

Publications and source records attributed to Paolo Vallarino.

7 recordsLinked to original sources

arXiv2026

Bremsstrahlung function in $\mathcal{N}=2$ SCFTs far beyond the supergravity limit

We study the Bremsstrahlung function in two four-dimensional $\mathcal{N}=2$ superconformal gauge theories: the E-theory, with hypermultiplets in the symmetric and antisymmetric representations, and the D-theory, with antisymmetric and fundamental matter. Using matrix model techniques, we derive exact results at arbitrary coupling for the first few orders in the large-$N$ expansion. At leading order, both theories are shown to be planar equivalent to $\mathcal{N}=4$ Super Yang-Mills, while beyond the planar limit their behavior differs significantly. For the E-theory, we prove that the subleading correction is exactly given by a derivative of the free energy with respect to the coupling. This relation enables us to determine the complete strong-coupling expansion for the Bremsstrahlung function, including non-perturbative contributions, by exploiting known results for the free energy. For the D-theory, the exact expressions have a more intricate structure. We perform a detailed analysis of the strong-coupling regime of the subleading large-$N$ corrections, showing that, in this case, there are expansions in inverse powers of the coupling which truncate after finitely many terms. We further analyze the non-perturbative effects at strong coupling and derive closed-form expressions also for these contributions. These results provide precise predictions for the holographic duals of both theories beyond the supergravity approximation, probing higher orders in the large-$N$ expansion and the full subleading corrections at strong coupling.

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arXiv2026

One-point functions of the Lagrangian in $\mathcal{N}=4$ SYM with boundaries, defects and interfaces

We obtain one-point functions of the ambient Lagrangian $\mathcal{O}_{\mathcal{L}}$ in $\mathcal{N}=4$ SYM with $\frac{1}{2}$-BPS boundaries, defects and interfaces classified by Gaiotto and Witten, which include maximally supersymmetric Janus interfaces and BCFTs relevant for double holography, as well as for Janus interfaces with reduced supersymmetry. For Janus interfaces we extend recent results capturing $\langle \mathcal{O}_{\mathcal{L}}\rangle$ in certain limits to exact dependence on $N$ and $λ$, and confirm a non-renormalization conjecture. We also clarify recent results for Janus variants preserving less supersymmetry. For general $\frac{1}{2}$-BPS Gaiotto-Witten theories with genuine defect degrees of freedom we derive one-point functions using supersymmetric localization, confirm that the results agree with holographic predictions in the appropriate limits, and show that the one-point functions in general exhibit non-trivial coupling dependence.

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arXiv2025

Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM

We consider the $4d$ $\mathcal{N}=2$ superconformal quiver gauge theory obtained by a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills (SYM). By exploiting supersymmetric localization, we study the integrated correlator of two Coulomb branch and two moment map operators and the integrated correlator of four moment map operators, determining exact expressions valid for any value of the 't Hooft coupling in the planar limit. Additionally, for the second correlator, we obtain an exact expression also for the next-to-planar contribution. Then, we derive the leading terms of their strong-coupling expansions and outline the differences with respect to the $\mathcal{N}=4$ SYM theory.

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arXiv2025

Analytical and numerical routes to strong coupling in $\mathcal{N}=2$ SCFTs

We consider the $\mathcal{N}=2$ quiver gauge theory arising from a $\mathbb{Z}_M$ orbifold of $\mathcal{N}=4$ Super Yang-Mills theory. Over the years, exploiting supersymmetric localization, exact expressions for several observables have been derived in the planar limit of this theory. In particular, some of these can be expressed as Fredholm determinants of semi-infinite matrices and their strong coupling expansions in inverse powers of the 't Hooft coupling have been calculated analytically to any desired order. On the other hand, there are also observables that cannot be rewritten in such a closed form, therefore extracting information at strong coupling is more complicated and almost no results are known beyond the leading order. In this work we focus on two observables of this type: the correlators of $n$ coincident Wilson loops and the integrated correlators of two Higgs branch operators in the presence of a Wilson line. We introduce an analytic method to evaluate the first terms of their strong coupling expansions. We also outline a numerical algorithm that serves as an independent check of the analytical results and provides predictions in cases where analytical techniques are currently not known.

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arXiv2023

Wilson loop correlators at strong coupling in $\mathcal{N}=2$ quiver gauge theories

We consider 4-dimensional $\mathcal{N} = 2$ superconformal quiver theories with $SU(N)^M$ gauge group and bi-fundamental matter and we evaluate correlation functions of $n$ coincident Wilson loops in the planar limit of the theory. Exploiting specific untwisted/twisted combinations of these operators and using supersymmetric localization, we are able to resum the whole perturbative expansion and find exact expressions for these correlators that are valid for all values of the 't Hooft coupling. Moreover, we analytically derive the leading strong coupling behaviour of the correlators, showing that they obey a remarkable simple rule. Our analysis is complemented by numerical checks based on a Padé resummation of the perturbative series.

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arXiv2023

Exceptionally simple integrated correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

Supersymmetric localisation has led to several modern developments in the study of integrated correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory. In particular, exact results have been derived for certain integrated four-point functions of superconformal primary operators in the stress tensor multiplet valid for all classical gauge groups, $SU(N)$, $SO(N)$, and $USp(2N)$, and for all values of the complex coupling, $τ=θ/(2π)+4πi/g^2_{_{YM}}$. In this work we extend this analysis and provide a unified two-dimensional lattice sum representation for all simple gauge groups, in particular for the exceptional series $E_r$ (with $r=6,7,8$), $F_4$ and $G_2$. These expressions are manifestly covariant under Goddard-Nuyts-Olive duality which for $F_4$ and $G_2$ is given by particular Fuchsian groups. We show that the perturbation expansion of these integrated correlators is universal in the sense that it can be written as a single function of three parameters, called Vogel parameters, and a suitable 't Hooft-like coupling. To obtain the perturbative expansion for the integrated correlator with a given gauge group we simply need substituting in this universal expression specific values for the Vogel parameters. At the non-perturbative level we conjecture a formula for the one-instanton Nekrasov partition function with simple gauge group and general $Ω$-deformation background. We check that our expression reduces in various limits to known results and that it produces, via supersymmetric localisation, the same one-instanton contribution to the integrated correlator as the one derived from the lattice sum. Finally, we consider the action of the hyperbolic Laplace operator in $τ$ on the integrated correlators with exceptional gauge groups and derive inhomogeneous Laplace equations very similar to the ones previously obtained for classical gauge groups.

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arXiv2023

Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling

We study the correlation function between one single-trace scalar operator and a circular Wilson loop in the $4d$ $\mathcal{N}=2$ superconformal field theory with gauge group $SU(N)$ and matter transforming in the symmetric and anti-symmetric representations. By exploiting supersymmetric localization, we resum the perturbative expansion of this correlator in the large-$N$ 't Hooft limit. Furthermore, using both analytical and numerical techniques, we provide a prediction for the leading term of its strong coupling expansion and we compare this prediction to numerical Padé resummations of the perturbative series.

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