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Matteo Sacchi

Publications and source records attributed to Matteo Sacchi.

At least 19 recordsLinked to original sources
arXiv2026

$G_2$-Manifolds from 4d $\mathcal{N}=1$ Quivers

Inspired by quantum field-theoretic constructions of 4d $\mathcal{N}=1$ quiver gauge theories that flow to superconformal field theories (SCFTs), we construct 7d manifolds of $G_2$-holonomy, which geometrically engineer these quivers in M-theory. Field theoretically, the 4d quivers are obtained by flux torus compactifications of 6d $\mathcal{N}=(1,0)$ SCFTs. The 6d theory compactified on a circle gives rise to a 5d KK-theory, which has a geometric realization as M-theory on a non-compact elliptically fibered Calabi-Yau threefold. Following the field-theoretical prescription, these local geometries are fibered over a circle to realize (topological) $G_2$-holonomy manifolds. We carry this out concretely in the case of the rank 1 E-string theory and its 4d quivers and construct new families of $G_2$-holonomy spaces.

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arXiv2026

Mirror symmetry on a circle

We investigate the small circle, or high temperature, limit of the supersymmetric index identities for the three-dimensional abelian mirror symmetry of SQED. There exist two possible limits, depending on how the parameters of the theory are scaled with the radius of the circle. In both cases the result is qualitatively similar. One side always reduces to the sphere partition function of a two-dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model (GLSM). The opposite side has a two-fold interpretation, either as the sphere partition function of the Landau--Ginzburg (LG) model that is Hori--Vafa dual to the GLSM, or as a Coulomb gas integral for a correlation function of Liouville or Toda CFT. This approach thus provides a systematic way to generate integral identities between partition functions of GLSMs on the one hand, and partition functions of LG models or CFT Coulomb gas integrals on the other. The latter perspective finds useful applications in the recently proposed 2d/2d correspondence, which relates sphere partition functions of unitary 2d $\mathcal{N}=(2,2)$ theories and correlation functions of non-unitary 2d CFTs that both descend from compactifications of a unitary 4d $\mathcal{N}=2$ SCFT. We present an example based on the $(A_{k-1},A_{N-1})$ Argyres--Douglas theories, where the CFT is a non-unitary minimal model. We also give a purely two-dimensional derivation of the identities obtained in the small circle limit which is inspired by the Kapustin--Strassler piecewise derivation of 3d abelian mirror symmetry.

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arXiv2025

$2+2=4$

Motivated by the observation that $2+2=4$, we consider four-dimensional $\mathcal{N}=2$ superconformal field theories on $S^2\times\Sigma$, turning on a suitable rigid supergravity background. On the one hand, reduction of a four-dimensional theory ${T}$ on a Riemann surface $\Sigma$ leads to a family $\mathscr{F}[{T}, \Sigma]$ of two-dimensional $(2,2)$ unitary SCFTs, a two-dimensional analog of the four-dimensional theories of class $\mathscr{S}$. On the other hand, reduction on $S^2$ yields a non-unitary two-dimensional CFT $\mathscr{C}[{T}]$ whose chiral algebra is the same as the one associated to ${T}$ by the standard SCFT/VOA correspondence. This construction upgrades the vertex operator algebra to a full-fledged two-dimensional CFT. What's more, it leads to a novel 2d/2d correspondence, a "$2+2 = 4$" analog of the "$4+2=6$" AGT correspondence: the $S^2$ partition function of $\mathscr{F}[{T}; \Sigma]$ is computed by correlation functions of $\mathscr{C}[{T}]$ on $\Sigma$. The elliptic genus of $\mathscr{F}[{T}; \Sigma]$ is instead computed by a topological QFT $\mathscr{E}[T]$ on $\Sigma$. A central question is whether one can give a purely two-dimensional presentation of the family $\mathscr{F}[{T}; \Sigma]$ of $(2, 2)$ theories. We propose an algorithm to realize the $(2, 2)$ theories as gauged linear sigma models when ${T}$ is an Argyres-Douglas theory of type $(A_1, A_{2k})$ and $\Sigma$ an $n$-punctured sphere. We perform stringent checks of our conjecture for $k=1$ and $k=2$.

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arXiv2025

Schur Connections: Chord Counting, Line Operators, and Indices

Recently, an intriguing correspondence was conjectured in arXiv:2409.11551 between Schur half-indices of pure 4d $SU(2)$ $\mathcal{N}=2$ supersymmetric Yang-Mills (SYM) theory with line operator insertions and partition functions of the double scaling limit of the Sachdev-Ye-Kitaev model (DSSYK). Motivated by this, we explore a generalization to $SU(N)$ $\mathcal{N}=2$ SYM theories. We begin by deriving the algebra of line operators, $\mathcal{A}_{\text{Schur}}$, representing it both in terms of the $\mathfrak{q}$-Weyl algebra and $\mathfrak{q}$-deformed harmonic oscillators, respectively. In the latter framework, the half-index admits a natural description as an expectation value in the Fock space of the oscillators. This $\mathfrak{q}$-oscillator perspective further suggests an interpretation in terms of generalized colored chord counting, and maps the half-index to a purely combinatorial quantity. Finally, we establish a connection with the quantum Toda chain, which is an integrable model whose commuting Hamiltonians can be identified with the Wilson lines of the $SU(N)$ SYM, and their eigenfunctions correspond to the function basis appearing in the half-index.

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arXiv2024

3d SUSY enhancement and non-semisimple TQFTs from four dimensions

It has been recently shown that the celebrated SCFT$_4$/VOA$_2$ correspondence can be bridged via three-dimensional field theories arising from a specific R-symmetry twisted circle reduction. We apply this twisted reduction to the $(A_1,A_{n})$ and $(A_1,D_{n})$ families of 4d $\mathcal{N}=2$ Argyres-Douglas SCFTs using their $\mathcal{N}=1$ Agarwal-Maruyoshi-Song Lagrangians. From $(A_1,A_{2n})$ we derive the Gang-Kim-Stubbs family of 3d $\mathcal{N}=2$ gauge theories with SUSY enhancement to $\mathcal{N}=4$ in the infrared, generalizing a recent derivation made in the special cases $n=1,2$. Topological twists of these theories are known to yield $semisimple$ TQFTs supporting $rational$ VOAs on holomorphic boundaries. From $(A_1,A_{2n-1})$, $(A_1,D_{2n+1})$, and $(A_1,D_{2n})$, we obtain three new infinite families of 3d $\mathcal{N}=2$ abelian gauge theories, all with monopole superpotentials, flowing to $\mathcal{N}=4$ SCFTs without Coulomb branch, but with the same non-trivial Higgs branch as the four-dimensional parent. Their topological A-twist yields $non$-$semisimple$ TQFTs related to $logarithmic$ VOAs such as $\widehat{\mathfrak{su}}(2)_{-4/3}$.

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arXiv2024

Deconfinements, Kutasov-Schwimmer dualities and $D_p[SU(N)]$ theories

Kutasov-Schwimmer (KS) dualities involve a rank-$2$ field with a polynomial superpotential. We derive KS-like dualities via deconfinement, that is assuming only Seiberg-like dualities, which instead just involve fundamental matter. Our derivation is split into two main steps. The first step is the construction of two families of linear quivers with $p\!-\!1$ nodes that confine into a rank-$2$ chiral field with degree-$(p\!+\!1)$ superpotential. Such chiral field is an $U(N)$ adjoint in 3d and an $USp(2N)$ antisymmetric in 4d. In the second step we use these linear quivers to derive, via deconfinement, in a relatively straightforward fashion, two classes of KS-like dualities: the Kim-Park duality for $U(N)$ with adjoint in 3d and the Intriligator duality for $USp(2N)$ with antisymmetric in 4d. We also discuss the close relation of our 3d family of confining unitary quivers to the 4d $\mathcal{N}\!=\!2$ $D_p[SU(N)]$ SCFTs by circle compactification and various deformations.

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arXiv2024

Dimensionally Reducing Generalized Symmetries from (3+1)-Dimensions

Recently there has been an increasing interest in the study of generalized symmetries in dimensions higher than two. This has lead to the discovery of various manifestations of generalized symmetries, notably higher-group and non-invertible symmetries, in four dimensions. In this paper we shall examine what happens to this structure when the 4d theory is compactified to lower dimensions, specifically to 3d and 2d, where we shall be mainly interested in generalized symmetry structures whose origin can be linked to mixed flavor-gauge anomalies. We discuss several aspects of the compactification, and in particular argue that under certain conditions the discussed generalized symmetry structure may trivialize in the infrared. Nevertheless, we show that even when this happens the presence of the 4d generalized symmetry structure may still leave an imprint on the low-energy theory in terms of additional 't Hooft anomalies or by breaking part of the symmetry. We apply and illustrate this using known examples of compactifications from four dimensions, particularly, the reduction of 4d $\mathcal{N}=1$ $U(N_c)$ SQCD on a circle to 3d and on a sphere to 2d.

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arXiv2024

Probing bad theories with the dualization algorithm II

We continue our analysis of bad theories, focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver.

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arXiv2023

Simplifying the Type $A$ Argyres-Douglas Landscape

A well-established organisational principle for Argyres--Douglas-type $\mathcal{N}=2$ superconformal field theories in four dimensions is to characterise such theories by the data defining a(n irregular) Hitchin system on $\mathbb{CP}^1$. The dictionary between Hitchin system data and various features of the corresponding SCFT has been studied extensively, but the overall structure of the resulting space of SCFTs still appears quite complicated. In this work, we systematically delineate a variety of simplifications that arise within this class of constructions due to several large classes of isomorphisms between SCFTs associated with inequivalent Hitchin system data (and their exactly marginal gaugings). We restrict to the most studied class of theories, namely the type $A$ theories without outer automorphism twists.

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arXiv2023

Probing bad theories with the dualization algorithm I

Recently an algorithm to build $SL(2,\mathbb{Z})$ duals, including mirror duals, of 3d $\mathcal{N}=4$ quiver theories and their 4d $\mathcal{N}=1$ uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with $U(N_c)$ gauge group in 3d and $USp(2N_c)$ in 4d, while in an upcoming paper we will consider linear quivers which, in the 3d case, have both unitary and special unitary bad nodes.

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arXiv2023

S-confining gauge theories and supersymmetry enhancements

We propose new classes of $4d$ $\mathcal{N}\!=\!1$ S-confining gauge theories, with a simple gauge group, rank-two matter and cubic superpotentials. The gauge group can be symplectic, orthogonal or special unitary. In some cases we derive the dualities via the deconfinement technique that uses iteratively known, more fundamental, dualities. In the symplectic case we discuss the $3d$ reduction to a confining unitary gauge theory with monopole superpotential. This $3d$ S-confinement provides an understanding of a recently proposed $4d$ $\mathcal{N}\!=\!1$ theory that flows to the conformal manifold of $\mathcal{N}\!=\!4$ SYM with $SU(2n+1)$ gauge group. The $3d$ perspective allows us to generalize this construction to another similar flow with supersymmetry enhancement: a $4d$ $\mathcal{N}\!=\!1$ theory that flows to the conformal manifold of a $4d$ $\mathcal{N}\!=\!2$ necklace theory with $SU(2n+1)^3$ gauge group.

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arXiv2023

5d to 3d compactifications and discrete anomalies

Much insight into the dynamics of quantum field theories can be gained by studying the relationship between field theories in different dimensions. An interesting observation is that when two theories are related by dimensional reduction on a compact surface, their 't Hooft anomalies corresponding to continuous symmetries are also related: the anomaly polynomial of the lower-dimensional theory can be obtained by integrating that of the higher-dimensional one on the compact surface. Naturally, this relation only holds if both theories are even dimensional. This raises the question of whether similar relations can also hold for the case of anomalies in discrete symmetries, which might be true even in odd dimensions. The natural generalization to discrete symmetries is that the anomaly theories, associated with the lower and higher dimensional theories, would be related by reduction on the compact surface. We explore this idea for compactifications of 5d superconformal field theories (SCFTs) to 3d on Riemann surfaces with global-symmetry fluxes. In this context, it can be used both as a check for these compactification constructions and for discovering new anomalies in the 5d SCFTs. This opens the way to applying the same idea of dimensional reduction of the anomaly theory to more general types of compactifications.

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arXiv2023

$G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls

We propose new $G_2$-holonomy manifolds, which geometrize the Gaiotto-Kim 4d N=1 duality domain walls of 5d N=1 theories. These domain walls interpolate between different extended Coulomb branch phases of a given 5d superconformal field theory. Our starting point is the geometric realization of such a 5d superconformal field theory and its extended Coulomb branch in terms of M-theory on a non-compact singular Calabi-Yau three-fold and its K\"ahler cone. We construct the 7-manifold that realizes the domain wall in M-theory by fibering the Calabi-Yau three-fold over a real line, whilst varying its K\"ahler parameters as prescribed by the domain wall construction. In particular this requires the Calabi-Yau fiber to pass through a canonical singularity at the locus of the domain wall. Due to the 4d N=1 supersymmetry that is preserved on the domain wall, we expect the resulting 7-manifold to have holonomy $G_2$. Indeed, for simple domain wall theories, this construction results in 7-manifolds, which are known to admit torsion-free $G_2$-holonomy metrics. We develop several generalizations to new 7-manifolds, which realize domain walls in 5d SQCD theories and walls between 5d theories which are UV-dual.

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arXiv2023

Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs

Many interesting phenomena in quantum field theory such as dualities and symmetry enhancements can be understood using higher dimensional constructions. In this paper, we study compactifications of the rank $1$ $5d$ Seiberg $E_{N_f+1}$ SCFTs to $3d$ on Riemann surfaces of genus $g>1$. We rely on the recent progress in the study of compactifications of $6d$ SCFTs to $4d$ and torus compactifications of $5d$ SCFTs to conjecture $3d$ $\mathcal{N}=2$ theories corresponding to the reduction of said $5d$ SCFTs on three punctured spheres. These can then be used to build $3d$ $\mathcal{N}=2$ models corresponding to compactifications on more general surfaces. The conjectured theories are tested by comparing their properties against those expected from the compactification picture.

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arXiv2022

The $SL(2,\mathbb{Z})$ dualization algorithm at work

Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for $3d$ $\mathcal{N}=4$ linear quivers and for their $4d$ $\mathcal{N}=1$ uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the $3d$ theories, where mirror symmetry is realized as $S$-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of $S$-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is $SL(2,\mathbb{Z})$ in $3d$ and $PSL(2,\mathbb{Z})$ in $4d$. This also produces dualities for $3d$ $\mathcal{N}=3$ theories with Chern--Simons couplings, some of which have enhanced $\mathcal{N}=4$ supersymmetry, and their new $4d$ $\mathcal{N}=1$ counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany--Witten move in field theory.

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arXiv2022

Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices

Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete zero-form global symmetries, and possibly a one-form symmetry, in 3d $\mathcal{N} \geq 3$ gauge theories using the superconformal index. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, such as the $\mathrm{U}(1)_k$ gauge theory with hypermultiplets of diverse charges, the $T(\mathrm{SU}(N))$ theory of Gaiotto-Witten, the theories with $\mathfrak{so}(2N)_{2k}$ gauge algebra and hypermultiplets in the vector representation, and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries of some of these models, we obtain various interesting theories with non-invertible symmetries or two-group structures.

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arXiv2022

A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs

Compactifying 6d superconformal field theories (SCFTs) to 4d $\mathcal{N}=1$ theories on two-punctured spheres (tubes) and tori with flux is realized using duality domain walls in 5d $\mathcal{N}=1$ Kaluza-Klein (KK) theories, which are usually denoted by $flux$ $domain$ $walls$. We revisit this construction and study it in detail from the 5d perspective, specifically rephrasing it using the box graph description of the extended Coulomb branch phases of 5d theories. This perspective could be helpful in understanding how to equivalently realize the 4d $\mathcal{N}=1$ models from geometric engineering in M-theory. Along the way, we show how to recover various properties of the 4d theories from the 5d perspective, such as the flux associated to the domain wall configurations and the presence of a $\mathfrak{u}(1)$ global symmetry in the 4d theory descending from the KK symmetry on the tube, which is broken to a discrete subgroup on a flux torus. We demonstrate all of these ideas using the rank 1 E-string theory.

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arXiv2022

Higgs, Coulomb, and Hall-Littlewood

The Higgs branch of 4d $\mathcal{N}=2$ SCFTs can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class $\mathcal{S}$ theory with four or more $\mathbb{Z}_2$-twisted punctures, they do not match. We construct 3d mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4d theory. We further construct $a=c$ theories in class $\mathcal{S}$ using the twisted punctures, and these theories, which includes the $\hat{D}_4(SU(2n+1))$ theories, have Hall--Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all $a=c$ theories with non-empty Higgs branch, including $\mathcal{N}\ge 3$ SCFTs.

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