arXiv subjects

Alessandro Pini

Publications and source records attributed to Alessandro Pini.

At least 19 recordsLinked to original sources

arXiv2026

Non-perturbative corrections to line defect integrated correlators in $Sp(N)$ SCFTs

We consider the $\mathcal{N}=4$ SYM theory with gauge group $Sp(N)$ and the $\mathcal{N}=2$ superconformal field theory consisting of four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-two antisymmetric representation of the $Sp(N)$ gauge group. Building on previous results obtained via supersymmetric localization and a Toda equation, we determine the leading non-perturbative corrections at strong coupling to the integrated correlator between a Wilson line and two Higgs-branch moment map operators. In the case of the $\mathcal{N}=2$ SCFT, the presence of truncated asymptotic expansions led us to develop a resurgent method complementary to Cheshire cat resurgence. This approach has the advantage of yielding an exact expression for the correlator in terms of an analytic function, which can subsequently be expanded in the strong-coupling regime.

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arXiv2025

Integrated correlators of coincident Wilson lines in $SU(N)$ gauge theories at strong coupling

We consider two four-dimensional gauge theories with gauge group $SU(N)$: the $\mathcal{N}=4$ Super Yang-Mills (SYM) theory and the $\mathcal{N}=2$ quiver gauge theory obtained as a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ SYM. In this context, we study a novel class of integrated correlators, namely those involving $n$-coincident Wilson lines and two moment map operators of conformal dimension two. By exploiting supersymmetric localization, we obtain exact expressions for these observables valid in the large-$N$ limit. Furthermore, using a combination of analytical and numerical methods, we derive their strong coupling expansions.

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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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arXiv2025

Integrated line-defect correlators in $Sp(N)$ SCFTs at strong coupling

We consider two four-dimensional SCFTs with gauge group $Sp(N)$: the $\mathcal{N}=4$ SYM theory and the $\mathcal{N}=2$ theory with four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-2 antisymmetric representation of the gauge group. Using supersymmetric localization and by exploiting a Toda equation, we compute the integrated correlator between a half-BPS Wilson line and two moment map operators of conformal dimension 2. We obtain exact expressions for this observable, valid for any value of the 't Hooft coupling in the large $N$-limit of the theory and we derive the corresponding strong coupling expansions.

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arXiv2024

Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling

We consider the four-dimensional $\mathcal{N}=2$ quiver gauge theory arising from a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills with gauge group $SU(2N)$. We study the integrated correlator between a half-BPS Wilson line and two Higgs branch operators of conformal dimension 2. Using supersymmetric localization, we resum the perturbative series for this observable and obtain exact expressions for both the planar and next-to-planar terms of its large $N$ expansion, valid for arbitrary values of the 't Hooft coupling. Finally, through a combination of analytical and numerical methods, we determine the leading terms of the corresponding strong-coupling expansions.

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arXiv2024

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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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 Pad\'e resummation of the perturbative series.

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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 Pad\'e resummations of the perturbative series.

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arXiv2021

Discrete gauging and Hasse diagrams

We analyse the Higgs branch of 4d $\mathcal{N}=2$ SQCD gauge theories with non-connected gauge groups $\widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2$ whose study was initiated in arXiv:1804.01108. We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d $\mathcal{N}=4$ magnetic quivers for the Higgs branches in the type $I$ discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.

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arXiv2021

The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class $\mathcal{S}_k$

Even though for generic $\mathcal{N}=1$ theories it is not possible to separate distinct branches of supersymmetric vacua, in this paper we study a special class of $\mathcal{N}=1$ SCFTs, these of Class $\mathcal{S}_k$ for which it is possible to define Coulomb and Higgs branches precisely as for the $\mathcal{N}=2$ theories of Class $\mathcal{S}$ from which they descend. We study the BPS operators that parameterise these branches of vacua using the different limits of the superconformal index as well as the Coulomb and Higgs branch Hilbert Series. Finally, with the tools we have developed, we provide a check that six dimensional $(1,1)$ Little String theory can be deconstructed from a toroidal quiver in class $\mathcal{S}_k$

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arXiv2020

4d $\mathcal{N}=3$ indices via discrete gauging

A class of 4d $\mathcal{N}=3$ SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of $\mathcal{N}=4$ Super Yang-Mills theory. This discrete subgroup contains elements of both the $SU(4)$ R-symmetry group and the $SL(2,\mathbb{Z})$ S-duality group of $\mathcal{N}=4$ SYM. We give a prescription for how to perform the discrete gauging at the level of the superconformal index and Higgs branch Hilbert series. We interpret and match the information encoded in these indices to known results for rank one $\mathcal{N}=3$ theories. Our prescription is easily generalised for the Coloumb branch and the Higgs branch indices of higher rank theories, allowing us to make new predictions for these theories. Most strikingly we find that the Coulomb branches of higher rank theories are generically not-freely generated.

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arXiv2020

(Mis-)Matching Type-B Anomalies on the Higgs Branch

Building on arXiv:1911.05827, we uncover new properties of type-B conformal anomalies for Coulomb-branch operators in continuous families of 4D $\mathcal{N}=2$ SCFTs. We study a large class of such anomalies on the Higgs branch, where conformal symmetry is spontaneously broken, and compare them with their counterpart in the CFT phase. In Lagrangian theories, the non-perturbative matching of the anomalies can be determined with a weak coupling Feynman diagram computation involving massive multi-loop banana integrals. We extract the part corresponding to the anomalies of interest. Our calculations support the general conjecture that the Coulomb-branch type-B conformal anomalies always match on the Higgs branch. On the other hand, we argue that the potential mismatch of anomalies implies the existence of a second covariantly constant metric on the conformal manifold (other than the Zamolodchikov metric), which would impose restrictions on its holonomy group.

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arXiv2020

Discrete gauge theories of charge conjugation

We define gauge theories whose gauge group includes charge conjugation as well as standard $\mathrm{SU}(N)$ transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For $N$ even, we show that there are exactly two possible such groups which we dub $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$. We construct the transformation rules for the fundamental and adjoint representations, allowing us to explicitly build four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories based on $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$ and understand from first principles their global symmetry. We compute the Haar measure on the groups, which allows us to quantitatively study the operator content in protected sectors by means of the superconformal index. In particular, we find that both types of $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$ groups lead to non-freely generated Coulomb branches.

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arXiv2019

Non-Connected Gauge Groups and the Plethystic Program

We present in the context of supersymmetric gauge theories an extension of the Weyl integration formula, first discovered by Robert Wendt, which applies to a class of non-connected Lie groups. This allows to count in a systematic way gauge-invariant chiral operators for these non-connected gauge groups. Applying this technique to $\mathrm{O}(n)$, we obtain, via the ADHM construction, the Hilbert series for certain instanton moduli spaces. We validate our general method and check our results via a Coulomb branch computation, using three-dimensional mirror symmetry.

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arXiv2019

Gauge theories from principally extended disconnected gauge groups

We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions. Although in this work we focus on 4d theories with N=2 SUSY, such construction is independent of spacetime dimensions and supersymmetry. These groups implement in a consistent way the discrete gauging of charge conjugation, for arbitrary rank. Focusing on the principal extension of SU(N), we explain how many of the exact methods for theories with 8 supercharges can be put into practice in that context. We then explore the physical consequences of having a disconnected gauge group: we find that the Coulomb branch is generically non-freely generated, and the global symmetry of the Higgs branch is modified in a non-trivial way.

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arXiv2017

Towards Deconstruction of the Type D (2,0) Theory

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional $(2,0)$ theory of type $D_k$. This 4d theory is defined by a necklace quiver with alternating gauge nodes $\mathrm{O}(2k)$ and $\mathrm{Sp}(k)$. We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of $\mathrm{O}$ versus $\mathrm{SO}$ gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.

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arXiv2017

HWG for Coulomb branch of $3d$ Sicilian theory mirrors

Certain star shaped quivers exhibit a pattern of symmetry enhancement on the Coulomb branch of $3d$ $\mathcal{N}=4$ supersymmetric gauge theories. This paper studies a subclass of theories where such global symmetry enhancement occurs through a computation of the Highest Weight Generating Function (HWG) and of the corresponding Hilbert Series (HS), providing a further test of the Coulomb branch formula. This special subclass has a feature in which the HWG takes a particularly simple form, as a simple rational function which is either a product of simple poles (termed freely generated) or a simple PE (termed complete intersection). Out of all possible star shaped quivers, this is a particularly simple subclass. The present study motivates a further study of identifying all star shaped quivers for which their HWG is of this simple form.

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arXiv2017

Large $N$ correlation functions in $\mathcal{N}=2$ superconformal quivers

Using supersymmetric localization, we consider four-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained from $\mathbb{Z}_n$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory in the large $N$ limit at weak coupling. In particular, we show that: 1) The partition function for arbitrary couplings can be constructed in terms of universal building blocks. 2) It can be computed in perturbation series, which converges uniformly for $|λ_I|<π^2$, where $λ_I$ are the 't Hooft coupling of the gauge groups. 3) The perturbation series for two-point functions can be explicitly computed to arbitrary orders. There is no universal effective coupling by which one can express them in terms of correlators of the $\mathcal{N}=4$ theory. 4) One can define twisted and untwisted sector operators. At the perturbative orbifold point, when all the couplings are the same, the correlators of untwisted sector operators coincide with those of $\mathcal{N}=4$ Super Yang-Mills theory. In the twisted sector, we find remarkable cancellations of a certain number of planar loops, determined by the conformal dimension of the operator.

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