arXiv subjects

Simone Giacomelli

Publications and source records attributed to Simone Giacomelli.

At least 19 recordsLinked to original sources

arXiv2025

Breaking bad theories of class $\mathcal S$

We study weakly-coupled descriptions/channel decompositions of the 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ of type $\mathfrak{su}(N)$, from the perspective of the 3d $\mathcal{N}=4$ mirror duals of their circle compactifications. This is a delicate problem when the channel decomposition produces pathological, or bad, 4d configurations that correspond to spheres with non-maximal punctures. The star-shaped quivers, describing the 3d mirrors associated with such bad 4d configurations, are bad 3d $\mathcal{N}=4$ theories. Leveraging recent results regarding 3d bad theories, we identify a new and interesting family of bad theories, which we coin \textit{broken} theories, that naturally arise in this context. Using these broken theories, we develop a systematic and analytic method that determines the generically non-Lagrangian matter sectors and the weakly-coupled gauge groups in such channel decompositions. We understand these weakly-coupled descriptions as emerging dynamically via Higgs mechanisms triggered by operators acquiring vacuum expectation values.

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arXiv2025

From Regular to Irregular: A Unified Origin for Argyres-Douglas Theories

We propose that Argyres-Douglas theories of type $D_p(\mathrm{SU}(N))$ and $(A_{p-1}, A_{N-1})$ - both realizable as Type A class $\mathcal{S}$ theories with irregular punctures - can be obtained via a sequence of mass deformations from a common ancestor: a class $\mathcal{S}$ theory with only regular punctures. Building on our previous work, this result establishes that these theories ultimately originate from 6d $\mathcal{N}=(1,0)$ orbi-instanton theories compactified on a torus. The requisite 4d mass deformations are realized as tractable Fayet-Iliopoulos deformations on the 3d mirror quiver. The core of our method is a constructive procedure that utilizes the Euclidean algorithm to define a chain of deformations connecting different $D_p(\mathrm{SU}(N))$ theories. By reversing this chain, we recursively build a "parent" star-shaped quiver for any given $(N,p)$. This quiver is the 3d mirror theory of the required class $\mathcal{S}$ ancestor. We substantiate our general claims with several detailed examples that explicitly illustrate the deformation procedure.

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arXiv2024

All Class $\mathcal{S}$ Theories of Type-$A$ Originate from Orbi-instantons

A surprising relation between 4d $\mathcal{N}=2$ class $\mathcal{S}$ superconformal field theories of Type-$A$ and 6d $\mathcal{N}=(1,0)$ orbi-instanton theories is investigated. We find that all of the theories in the former class can be obtained by a series of deformations of the 4d theories arising from compactifying the latter on a torus. This is demonstrated by examining Fayet--Iliopoulos (FI) deformations of the $E_8$-shaped magnetic quivers of the orbi-instanton theories whose body fits into the affine $E_8$ Dynkin diagram with a tail attached. Turning on FI parameters at the appropriate gauge groups leads, in stages, to $E_7$-shaped, $E_6$-shaped, and general star-shaped quivers, where the latter are magnetic quivers for the class $\mathcal{S}$ theory of Type-$A$ on a sphere with punctures. Deforming a suitable star-shaped quiver, one obtains a magnetic quiver of the Type-$A$ class $\mathcal{S}$ theory with general genus and an arbitrary number of punctures. Given such a theory, we also propose the inverse algorithm, thereby determining a parent orbi-instanton theory. This is achieved by uplifting the corresponding magnetic quiver step by step to the star-shaped, $E_6$-shaped, $E_7$-shaped, and $E_8$-shaped quivers, where at each step all of the underbalanced nodes, possessing non-zero FI parameters, are dualized. The latter $E_8$-shaped quiver then characterizes the 6d orbi-instanton theory from which the class $\mathcal{S}$ theory in question originates.

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arXiv2024

$\mathcal{N} = 2$ Orbi-S-Folds

We introduce a new class of non-compact backgrounds of Type IIB string theory preserving eight supercharges by combining S-folds and non-perturbative 7-branes wrapping orbifolds, and study the four-dimensional superconformal field theories arising at low energy on $D3$-branes probing them. We draw a precise correspondence between this setup and the torus compactification of six-dimensional orbi-instanton theories with a Stiefel-Whitney twist, and use it to determine the main features of such strongly-coupled systems, like central charges, spectra of Coulomb-branch operators, networks of Higgs-branch flows. Finally, with the aim to improve our understanding of the landscape of $\mathcal{N}=2$ superconformal field theories, and possibly to extend their classification beyond rank two, we provide a detailed catalogue of all the rank-three theories that our framework gives access to.

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arXiv2024

Discrete Global Symmetries: Gauging and Twisted Compactification

Discrete global symmetries of 4d $\mathcal{N}=2$ SCFTs are studied via two operations: gauging and twisted compactification. We consider gauging of discrete symmetries in several well-known 4d $\mathcal{N}=2$ SCFTs, including $\mathrm{SU}(n)$ SQCD with $2n$ flavors, theories of class $\mathcal{S}$ of type $A_{2n-1}$, and Argyres--Douglas theories of type $(A_N, A_N)$, as well as propose new 4d SCFTs as a result. The wreathing technique, which involves gauging a subgroup of the automorphism group of the quiver diagram of the corresponding 3d mirror theory, is exploited. This allows us to understand several properties of discretely gauged theories, including moduli spaces and how discrete gauging affects the mixed 't Hooft anomaly between the 1-form symmetry and the 0-form flavor symmetry. Many examples are viewed through the lens of the Argyres--Seiberg duality and its generalization. We also examine discrete gauging of $\mathrm{SU}(2)$ SQCD with 4 flavors by various $\mathbb{Z}_2$ and $\mathbb{Z}_2 \times \mathbb{Z}_2$ subgroups of the permutation group $S_4$ using the superconformal index. Regarding compactification, we propose a magnetic quiver for 4d $\mathcal{N}=2$ $\mathrm{SU}(n)$ SQCD with $2n$ flavors compactified on a circle with a $\mathbb{Z}_2$ twist. The twisted compactification by non-invertible symmetries of the 4d $\mathcal{N}=4$ SYM theory with gauge group $\mathrm{SU}(N)$ is revisited. The non-invertible symmetry naturally gives rise to a $\mathbb{Z}_k$ action on the scalar fields parametrizing the moduli space. Upon examining the $\mathbb{Z}_k$ invariant chiral ring of the Higgs branch, we find that, in addition to the largest branch of the moduli space that is expected to be captured by the ABJ(M) theory, there exist in general nilpotent operators that lead to a branch of the moduli space which is a radical ideal.

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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

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

N=1 SCFTs from F-theory on Orbifolds

We study four-dimensional superconformal field theories living on the worldvolume of $D3$ branes probing minimally-supersymmetric F-theory backgrounds, focusing on the case of orbi-orientifold setups with and without 7-branes. We observe that these theories are closely related to compactifications of six-dimensional $\mathcal{N}=(1,0)$ theories on a torus with flux, where the flux quanta is mapped in Type IIB to the defining data of the orbifold group. We analyze the cases of class $\mathcal{S}_k$ theories as well as of compactifications of the E-string and of orbi-instanton theories. We also classify $\mathcal{S}$-fold configurations in F-theory preserving minimal supersymmetry in four dimensions and their mass deformations.

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arXiv2023

Comments on Non-invertible Symmetries in Argyres-Douglas Theories

We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories. This class of theories arises from diagonal gauging of the flavor symmetry of a collection of multiple copies of $D_p(\mathrm{SU}(N))$ theories. The same set of theories that we study can also be realized from 6d $\mathcal{N}=(1,0)$ compactification on a torus. The main example in this class is the $(A_2, D_4)$ theory. We show in detail that this specific theory bears the same structures of non-invertible duality and triality defects as those of $\mathcal{N}=4$ super Yang-Mills with gauge algebra $\mathfrak{su}(2)$. We extend this result to infinitely many other Argyres-Douglas theories in the same family, including those with central charges $a=c$ whose conformal manifold is one dimensional, and those with $a\neq c$ whose conformal manifold has dimension larger than one. Our result is supported by examining certain special cases that can be realized in terms of theories of class $\mathcal{S}$.

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arXiv2023

FI-flows of 3d N=4 Theories

We study the 3d $\mathcal{N}=4$ RG-flows triggered by Fayet-Iliopoulos deformations in unitary quiver theories. These deformations can be implemented by a new quiver algorithm which contains at its heart a problem at the intersection of linear algebra and graph theory. When interpreted as magnetic quivers for SQFTs in various dimensions, our results provide a systematic way to explore RG-flows triggered by mass deformations and generalizations thereof. This is illustrated by case studies of SQCD theories and low rank 4d $\mathcal{N}=2$ SCFTs. A delightful by-product of our work is the discovery of an interesting new 3d mirror pair.

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arXiv2022

Hierarchies of RG flows in 6d $(1,0)$ massive E-strings

We extend the analysis of arXiv:2208.11703 to the 6d $(1,0)$ SCFTs known as massive E-string theories, which can be engineered in massive Type IIA with $8-n_0<8$ D8-branes close to an O8$^-$ (or O8$^*$ if $n_0=8,9$). For each choice of $n_0=1,\ldots,9$ the massive $E_{1+(8-n_0)}$-strings (including the more exotic $\tilde{E}_1$ and $E_0$) are classified by constrained $E_8$ Kac labels, i.e. a subset of $\text{Hom}(\mathbb{Z}_k,E_8)$, from which one can read off the flavor subalgebra of $E_{1+(8-n_0)}$ of each SCFT. We construct hierarchies for two types of Higgs branch RG flows: flows between massive theories defined by the same $n_0$ but different labels; flows between massive theories with different $n_0$. These latter flows are triggered by T-brane vev's for the right $\mathrm{SU}$ factor of the SCFT global symmetry, whose rank is a function of both $k$ and $n_0$, a situation which has so far remained vastly unexplored.

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arXiv2022

A tale of 2-groups: D$_p$(USp(2N)) theories

A 1-form symmetry and a 0-form symmetry may combine to form an extension known as the 2-group symmetry. We find the presence of the latter in a class of Argyres-Douglas theories, called $D_p($USp$(2N))$, which can be realized by $\mathbb{Z}_2$-twisted compactification of the 6d $\mathcal{N}=(2,0)$ of the $D$-type on a sphere with an irregular twisted puncture and a regular twisted full puncture. We propose the $3$d mirror theories of general $D_p($USp$(2N))$ theories that serve as an important tool to study their flavor symmetry and Higgs branch. Yet another important result is presented: We elucidate a technique, dubbed ''bootstrap'', which generates an infinite family of $D^b_p(G)$ theories, where for a given arbitrary group $G$ and a parameter $b$, each theory in the same family has the same number of mass parameters, same number of marginal deformations, same $1$-form symmetry, and same $2$-group structure. This technique is utilized to establish the presence or absence of the 2-group symmetries in several classes of $D^b_p(G)$ theories. In this regard, we find that the $D_p($USp$(2N))$ theories constitute a special class of Argyres-Douglas theories that have a 2-group symmetry.

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arXiv2022

Probing 7-branes on Orbifolds

D3 branes in the vicinity of an E6, E7, or E8 stack of 7-branes in flat space are known to host at low energy a famous class of strongly-coupled N = 2 superconformal field theories featuring exceptional global symmetry. What if, instead, the 7-branes wrap an orbifold? We give a systematic characterization of such theories in the case of C2/Zn, and determine their main properties, like global symmetries, spectra of Coulomb-branch operators, and patterns of Higgs-branch flows. We put forward a set of rules to construct their magnetic quivers, which directly generalize what happens in the perturbative case, and later derive them using the duality with M5 branes probing M9 walls.

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arXiv2022

Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories

Higher-form symmetries have proved useful in constraining the dynamics of a number of quantum field theories. In the context of the Argyres-Douglas (AD) theories of the $(G,G')$ type, we find that the 1-form symmetries are invariant under the Higgs branch flow, and that they are captured by the non-Higgsable sector at a generic point on the Higgs branch of the AD theory in question. As a consequence, dimensional reduction of an AD theory with a non-trivial 1-form symmetry to 3d leads to a free sector. We utilize these observations, along with other results, to propose systematically the mirror theories for the AD theories of the $(A_n, E_m)$ type. As a by-product of these findings, we discover many important results: the Flip-Flip duality for all $T[G]$ theories with simply-laced group $G$, including the exceptional ones; the class $\mathcal{S}$ descriptions of exceptional affine Dynkin diagram such that all gauge groups are special unitary; the universality of the mirror theories for $D_{h^\vee_G}(G)$ with $h^\vee_G$ the dual Coxeter number of $G$; and the triviality of the 2-group structure in the $(A_n, E_m)$ theories.

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arXiv2021

Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S

A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are 6d N=(2,0) theories that are boundary conditions of 7d TQFTs, with the defect group arising from surface defects. In this paper, we study codimension-two defects in 6d N=(2,0) theories, and find that the line defects living inside these codimension-two defects are mutually non-local and hence also form a defect group. Thus, codimension-two defects in a 6d N=(2,0) theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the 7d bulk TQFT. A codimension-two defect carrying a non-trivial defect group acts as an irregular puncture when used in the construction of 4d N=2 Class S theories. The defect group associated to such an irregular puncture provides extra "trapped" contributions to the 1-form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and non-conformal irregular punctures. Along the way, we discover many new classes of irregular punctures. A key role in the analysis of defect groups is played by two different geometric descriptions of the punctures in Type IIB string theory: one provided by isolated hypersurface singularities in Calabi-Yau threefolds, and the other provided by ALE fibrations with monodromies.

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arXiv2021

Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories

The Argyres-Douglas (AD) theories of type $(D_n,D_m)$, realized by type IIB geometrical engineering on a single hypersurface singularity, are studied. We analyze their conformal manifolds and propose the 3d mirror theories of all theories in this class upon reduction on a circle. A subclass of the AD theories in question that admits marginal couplings is found to be $\mathrm{SO}$ or $\mathrm{USp}$ gaugings of certain $D_p(\mathrm{SO}(2N))$ and $D_p(\mathrm{USp}(2N))$ theories. For such theories, we develop a method to derive this weakly-coupled description from the Newton polygon associated to the singularity. We further find that the presence of crepant resolutions of the geometry is reflected in the presence of a (non-abelian) symplectic-type gauge node in the quiver description of the 3d mirror theory. The other important results include the 3d mirrors of all $D_p(\mathrm{SO}(2N))$ theories, as well as certain properties of the $D_p(\mathrm{USp}(2N))$ theories that admit Lagrangian descriptions.

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arXiv2021

Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations

We describe how the geometry of the Higgs branch of 5d superconformal field theories is transformed under movement along the extended Coulomb branch. Working directly with the (unitary) magnetic quiver, we demonstrate a correspondence between Fayet-Iliopoulos deformations in 3d and 5d mass deformations. When the Higgs branch has multiple cones, characterised by a collection of magnetic quivers, the mirror map is not globally well-defined, however we are able to utilize the correspondence to establish a local version of mirror symmetry. We give several detailed examples of deformations, including decouplings and weak-coupling limits, in $(D_n,D_n)$ conformal matter theories, $T_N$ theory and its parent $P_N$, for which we find new Lagrangian descriptions given by quiver gauge theories with fundamental and anti-symmetric matter.

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arXiv2021

Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories

Argyres-Douglas theories constitute an important class of superconformal field theories in $4$d. The main focus of this paper is on two infinite families of such theories, known as $D^b_p(\mathrm{SO}(2N))$ and $(A_m, D_n)$. We analyze in depth their conformal manifolds. In doing so we encounter several theories of class $\mathcal{S}$ of twisted $A_{\text{odd}}$, twisted $A_{\text{even}}$ and twisted $D$ types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include $D_p(G)$ theories, with $G$ non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the $3$d mirror theories, also known as the magnetic quivers, for the $D^b_p(\mathrm{SO}(2N))$ theories, with $p \geq b$, and the $(A_m, D_n)$ theories, with arbitrary $m$ and $n$. We also discuss the $3$d reduction and mirror theories of certain $D^b_p(\mathrm{SO}(2N))$ theories, with $p < b$, where the former arises from gauging topological symmetries of some $T^\sigma_\rho[\mathrm{SO}(2M)]$ theories that are not manifest in the Lagrangian description of the latter.

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