arXiv subjects

Noppadol Mekareeya

Publications and source records attributed to Noppadol Mekareeya.

At least 19 recordsLinked to original sources

arXiv2026

Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations

Five-dimensional $\mathcal{N}=1$ superconformal field theories admit a rich variety of generalised global symmetries, including higher-form and 2-group symmetries and their 't$~$Hooft anomalies. We show that this data can be extracted directly from the blow-up equations governing the instanton partition functions of such theories on the $Ω$-background. The central object is the classical prefactor $\exp(-V_n)$ weighting each magnetic flux on the blown-up geometry: evaluated on a background for the electric 1-form symmetry, the fractional parts of its exponents encode the cubic self-anomaly of the 1-form symmetry and its mixed anomalies with the instanton, flavour, gravitational, and $\mathrm{SU}(2)_R$ symmetries. Combined with the faithful continuous global symmetry of the ultraviolet fixed point, determined from the superconformal index, the same data decides whether the theory possesses a 2-group symmetry or a mixed 't$~$Hooft anomaly. We illustrate the method in gauge theories, including $\mathrm{SU}(4)$ and $\mathrm{USp}(4)$ with antisymmetric hypermultiplets and $\mathrm{Spin}(7)$ and $\mathrm{Spin}(8)$ with vector hypermultiplets, as well as in several families of non-Lagrangian theories. New results include the effective prepotentials of the $B_N$ and $B_N^{(1,2,3)}$ families, the cubic 1-form anomalies of the rank-two theories $\mathbb{P}^2\cup\mathbb{F}_3$ and $\mathbb{P}^2\cup\mathbb{F}_6$, and several mixed 1-form--flavour and 1-form--$\mathrm{SU}(2)_R$ anomalies.

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arXiv2026

Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D

We investigate the landscape of 6d $\mathcal{N}=(1,0)$ D-type orbi-instanton superconformal field theories (SCFTs) and their torus compactifications to four-dimensional class $\mathcal{S}$ theories. By analysing a general class of 6d F-theory constructions via generalised quivers, we demonstrate that -- in contrast to the well-characterised A-type series -- the dimensional reductions that admit a 4d class $\mathcal{S}$ description on a Riemann sphere with three untwisted D-type punctures constitute only a subset of the full orbi-instanton landscape. For this subclass, we show that the punctures can be effectively characterised by two sets of integers: the $s$-labels and the $m$-labels. The $s$-labels, or ``Kac-type labels'', serve as the D-type analogues to the Kac labels used in A-type theories; we establish their correspondence with ``modified excess numbers'' in the associated 3d mirror theories (magnetic quivers). The $m$-labels are further introduced to streamline the mapping from 6d generalised quivers to their class $\mathcal{S}$ descriptions. Furthermore, we analyse physical distinctions arising from 6d $θ$ angles and explore the hierarchy of Higgs branch flows. In doing so, we uncover instances of ``hidden Higgsings'' -- renormalization group flows present in the 6d parent theories that are not manifest in the puncture closures of the corresponding class $\mathcal{S}$ descriptions.

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arXiv2026

Orthosymplectic Quivers: Indices, Hilbert Series, and Generalised Symmetries

We investigate generalised global symmetries in 3d $\mathcal{N}=4$ orthosymplectic quiver gauge theories. Using the superconformal index, we identify a $D_8$ categorical symmetry web in a class of theories featuring $\mathfrak{so}(2N) \times \mathfrak{usp}(2N)$ gauge algebra (at zero Chern-Simons levels) and $n$ bifundamental half-hypermultiplets, analogous to ABJ-type models. As a distinct contribution, we improve the prescription, previously studied in the literature, for computing Coulomb branch Hilbert series of $\mathrm{SO}(N)$ gauge theories with $N_f$ vector hypermultiplets. Our improved prescription extends these methods by incorporating fugacities for discrete zero-form symmetries - specifically charge conjugation and magnetic symmetries - and properly treating background magnetic fluxes for the flavour symmetry. This refinement enables calculations for various global forms ($\mathrm{O}(N)^\pm, \mathrm{Spin}(N), \mathrm{Pin}(N)$) and ensures consistency with the Coulomb branch limit of the superconformal index and known dualities. The proper treatment of fluxes is particularly essential for analysing orthosymplectic quivers where such a flavour symmetry is gauged. We verify our methods through several examples, including an analysis of the mapping of discrete symmetries under mirror symmetry for $T[\mathrm{SO}(N)]$ and $T[\mathrm{USp}(2N)]$ theories. The analysis also readily generalises to the $T_ρ[\mathrm{SO}(N)]$ and $T_ρ[\mathrm{USp}(2N)]$ theories associated with partition $ρ$.

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arXiv2026

Interplay of Generalised Symmetries and Moduli Spaces in 3d $\mathcal{N}=5$ SCFTs

The moduli space and generalised global symmetries of 3d $\mathcal{N} = 5$ superconformal field theories are investigated, with a focus on the orthosymplectic ABJ theories and their discrete gauging variants. We extend the known classification of $\mathcal{N}=5$ moduli spaces as orbifolds $\mathbb{H}^{2N}/Γ$, where $Γ$ is a quaternionic reflection group, to theories incorporating $\mathrm{Spin}$, $\mathrm{O}^-$, and $\mathrm{Pin}$-type gauge groups. In these cases, we find that the moduli space is governed not by $Γ$ itself, but by a $\mathbb{Z}_2$ central extension thereof, for which we explicitly describe the generators. We provide a systematic method to construct the group $Γ'$ governing the moduli space of a theory $\mathcal{T}'$ obtained by gauging a $\mathbb{Z}_2$ zero-form symmetry of an original theory $\mathcal{T}$. This is achieved by identifying the specific generator that must be added to $Γ$. We compute the Hilbert series for these moduli spaces and verify them against the corresponding limits of the superconformal index, finding perfect agreement. We also discuss how 't Hooft anomalies for the zero-form symmetries manifest in the superconformal index and the moduli space. Furthermore, we revisit the symmetry category of the $\mathfrak{so}(2N)_{2k} \times \mathfrak{usp}(2N)_{-k}$ theories. Building on previous work that identified the symmetry category for all parities of $N$ and $k$, we provide the explicit symmetry webs for the opposite parity $D_8$ case. We find that the details of these webs differ from the previously studied $D_8$ webs corresponding to the both even parity case. Finally, we analyse theories with unequal ranks, those containing the $\mathfrak{so}(2N+1)$ gauge algebra, and the two SCFT variants based on the $F(4)$ superalgebra.

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arXiv2026

Limits of the Superconformal Index and the Moduli Space of 3d $\mathcal{N}=3$ Theories

We compute the Hilbert series of three-dimensional $\mathcal{N}=3$ quiver gauge theories by taking a specific limit of the superconformal index. Our approach introduces auxiliary fugacities associated with symmetries which, while not present in the full theory, arise as effective symmetries on specific branches of the moduli space. By evaluating the index in a limit governed by these parameters, we successfully isolate the Hilbert series of the desired branches. We validate our results against the literature and provide several new extensions. We focus primarily on linear and circular quivers with unitary gauge groups, which originate from Type IIB brane configurations involving generic $(p,q)$ fivebranes. We further generalise this approach to star-shaped and orthosymplectic $\mathcal{N}=3$ quivers. Finally, we investigate the geometric branches of affine Dynkin quivers, demonstrating agreement with known results, while offering new predictions for unexplored cases.

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arXiv2025

New punctures for six-dimensional compactifications

Six-dimensional superconformal field theories (SCFTs) give rise to four-dimensional (4d) ones when compactified on Riemann surfaces. In the $\mathcal{N}=(2,0)$ case, this yields the famous class S family. For $\mathcal{N}=(1,0)$ theories that arise from linear unitary quivers, the holographic duals of the 4d theories are known in massive IIA supergravity, but only without punctures. Working in the probe approximation, we identify all possible BPS punctures in these models and characterize them by computing their defect Weyl anomalies. For class S, our results reproduce the known expressions in the appropriate limit. In the more general $\mathcal{N}=(1,0)$ case, they predict new 4d SCFTs and their large-$N$ anomaly coefficients.

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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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arXiv2025

Generalised-Edged Quivers and Global Forms

Non-simply laced quivers, despite the lack of complete Lagrangian descriptions, play an important role in characterising moduli spaces of supersymmetric field theories. Notably, the moduli space of instantons in non-simply laced gauge groups can be understood by means of such quivers. We generalise the notion of non-simply laced unitary quivers to those whose edges carry two labels $(p,q)$, dubbed $(p,q)$-edged quivers. The special case of $(p,1)$ corresponds to a conventional non-simply laced edge studied in the literature. In the case of unframed $(p,q)$-edged quivers, we show how to parametrise the lattice of magnetic fluxes upon ungauging the decoupled $\mathrm{U}(1)$, and how one can pick sublattices thereof corresponding to different global forms of the quiver related by discrete gauging. This form of discrete gauging can be applied to any unframed unitary quivers, not just ones with generalised edges. We utilise both the Hilbert series and the superconformal index to study moduli spaces and 't Hooft anomalies. In particular, we study mixed 't Hooft anomalies between a one-form symmetry and a zero-form continuous topological symmetry in various $(p,q)$-edged quivers. We also provide an alternative realisation of the moduli space of $\mathfrak{so}(2n+1)$ instantons via gauging discrete symmetries in supersymmetric QCD with a symplectic gauge group and a large number of flavours.

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arXiv2025

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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arXiv2025

Wreathing, Discrete Gauging, and Non-invertible Symmetries

't Hooft anomalies of discrete global symmetries and gaugings thereof have rich mathematical structures and far-reaching physical consequences. We examine each subgroup $G$, up to automorphisms, of the permutation group $S_4$ that acts on the four legs of the affine $D_4$ quiver diagram, which is mirror dual to the 3d $\mathcal{N}=4$ $\mathrm{SU}(2)$ gauge theory with four flavours. These actions are studied in terms of how each permutation cycle acts on the superconformal index of the theory in question. We present a prescription for refining the index with respect to the fugacities associated with the Abelian discrete symmetries that are subgroups of $G$. This allows us to study sequential gauging of various subgroups of $G$ and construct symmetry webs. We study the effects of 't Hooft anomalies and non-invertible symmetries that arise from discrete gauging on the index. When the whole symmetry $G$ is gauged, our results are in perfect agreement with a type of discrete operations on the quiver, known as wreathing, discussed in the literature. We provide a general prescription for computing the index for any wreathed quivers that contain unitary or special unitary gauge groups. We demonstrate this in an example of the 3d $\mathcal{N}=4$ $\mathrm{U}(N)$ gauge theory with $n$ flavours and compare the results with gauging the charge conjugation symmetry associated with the flavour symmetry of such a theory.

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arXiv2024

Superconformal anomalies for string defects in six-dimensional $\mathcal{N} = (1,0)$ SCFTs

We study the anomalies of two-dimensional BPS defects in six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories. Using a holographic description of these defects furnished by probe D4-branes in AdS${}_7$ solutions of ten-dimensional type IIA supergravity, we compute the two independent defect Weyl anomalies from the on-shell action for a spherical defect and defect sphere entanglement entropy. We find agreement between the holographic prediction for the defect A-type anomaly coming from the defect sphere free energy and the leading large $N$ contribution to the defect `t Hooft anomaly found using anomaly inflow. We also find agreement between the holographic computation of the expectation value of a surface operator wrapping a torus and the supersymmetric localization computation for a circular Wilson loop in $\mathcal{N}=1$ super Yang-Mills theory on $S^5$. Lastly, we holographically compute the defect gravitational anomaly from the Wess-Zumino action of the probe D4-brane, which provides a subleading large $N$ correction to the defect A-type anomaly.

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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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arXiv2023

Chern-Simons-Trinion Theories: One-form Symmetries and Superconformal Indices

We study 3d theories containing $\mathcal{N}=3$ Chern-Simons vector multiplets coupled to the $\mathrm{SU}(N)^3$ flavour symmetry of 3d $T_N$ theories with Chern-Simons level $k_1$, $k_2$ and $k_3$. It was formerly pointed out that these theories flow to infrared SCFTs with enhanced $\mathcal{N}=4$ supersymmetry when $1/k_1+1/k_2+1/k_3=0$. We examine superconformal indices of these theories which reveal that supersymmetry of the infrared SCFTs may get enhanced to $4 \leq \mathcal{N} \leq 6$ if such a condition is satisfied. Moreover, even if the Chern-Simons levels do not obey the aforementioned condition, we find that there is still an infinite family of theories that flows to infrared SCFTs with $\mathcal{N}=4$ supersymmetry. The 't Hooft anomalies of the one-form symmetries of these theories are analysed. As a by-product, we observe that there is generally a decoupled topological sector in the infrared. When the infrared SCFTs have $\mathcal{N} \geq 4$ supersymmetry, we also study the Higgs and Coulomb branch limits of the indices which provide geometric information of the moduli space of the theories in question in terms of the Hilbert series.

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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

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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arXiv2023

The ABCDEFG of Instantons and W-algebras

For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N=2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.

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arXiv2023

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

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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