Argyres-Douglas Theories Research Articles

Modularity in Argyres-Douglas theories with a = c

We consider a family of Argyres-Douglas theories, which are 4D N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 strongly coupled superconformal field theories (SCFTs) but share many features with 4D N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super-Yang-Mills theories. In particular, the two central charges of these theories are the same, namely a = c. We derive a simple and illuminating formula for the Schur index of these theories, which factorizes into the product of a Casimir term and a term referred to as the Schur partition function. While the former is controlled by the anomaly, the latter is identified with the vacuum character of the corresponding chiral algebra and is expected to satisfy the modular linear differential equation. Our simple expression for the Schur partition function, which can be regarded as the generalization of MacMahon’s generalized sum-of-divisor function, allows one to numerically compute the series expansions efficiently, and furthermore find the corresponding modular linear differential equation. In a special case where the chiral algebra is known, we are able to derive the corresponding modular linear differential equation using Zhu’s recursion relation. We further study the solutions to the modular linear differential equations and discuss their modular transformations. As an application, we study the high temperature limit or the Cardy-like limit of the Schur index using its simple expression and modular properties, thus shedding light on the 1/4-BPS microstates of genuine N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs with a = c and their dual quantum gravity via the AdS/CFT correspondence.

Liouville irregular states of half-integer ranks

We conjecture a set of differential equations that characterizes the Liouville irregular states of half-integer ranks, which extends the generalized AGT correspondence to all the (A1, Aeven) and (A1, Dodd) types Argyres-Douglas theories. For lower half-integer ranks, our conjecture is verified by deriving it as a suitable limit of a similar set of differential equations for integer ranks. This limit is interpreted as the 2D counterpart of a 4D RG-flow from (A1, D2n) to (A1, D2n−1). For rank 3/2, we solve the conjectured differential equations and find a power series expression for the irregular state |I(3/2)〉. For rank 5/2, our conjecture is consistent with the differential equations recently discovered by H. Poghosyan and R. Poghossian.

A note on rank 5/2 Liouville irregular block, Painlevé I and the H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}0 Argyres-Douglas theory

We study 4d type H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}0 Argyres-Douglas theory in Ω-background by constructing Liouville irregular state of rank 5/2. The results are compared with generalized Holomorphic anomaly approach, which provides order by order expansion in Ω-background parameters ϵ1,2. Another crucial test of our results provides comparison with respect to Painlevé I τ-function, which was expected to be hold in self-dual case ϵ1 = −ϵ2. We also discuss Nekrasov-Shatashvili limit ϵ1 = 0, accessible either by means of deformed Seiberg-Witten curve, or WKB methods.

Dualities of adjoint SQCD and supersymmetry enhancement

We propose a new dual description of four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 SU(N) gauge theory with one adjoint (X) and Nf fundamental matters with a superpotential W = TrXp+1. The dual theory consists of the D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{D} $$\\end{document}p[SU(N)] Argyres-Douglas theory coupled to SU(N) gauge theory and Nf fundamentals with a superpotential deformation. We study renormalization group fixed points of the Argyres-Douglas dual theories with and without superpotential deformations, and identify the conditions for them to be dual to the fixed points of adjoint SQCD. We check our proposal via matching central charges, chiral operators and superconformal indices. We find that when Nf = 2N and p = 2, the dual theory flows to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SU(N) superconformal QCD with 2N flavors upon suitable superpotential deformation, exhibiting supersymmetry enhancement.

A toolkit for ortho-symplectic dualities

We propose new confining dualities in 3dN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 gauge theories with orthogonal gauge groups, with and without monopole superpotentials. Deriving some of those dualities requires a sequence of gauging and Higgsing for a ℤ2 symmetry. This prevents the gauge theory from developing a smooth quantum moduli space and affects the global structure of the gauge group, muting it from SO to O+.The confining dualities provide tools to deconfine fields transforming in the symmetric rank-2 representation of classical gauge groups. As an application, we propose and derive S-confining dualities for SO(N) (Sp(N)) gauge theories with an adjoint and 1 (2) fundamentals, respectively. From these S-confining dualities, we readily obtain various duality appetizers and the 3d mirror of A2N Argyres-Douglas theories.

On irregular states and Argyres-Douglas theories

Conformal theories of the Argyres-Douglas type are notoriously hard to study given that they are isolated and strongly coupled thus lacking a lagrangian description. In flat space, an exact description is provided by the Seiberg-Witten theory. Turning on a Ω-background makes the geometry “quantum” and tractable only in the weak curvature limit. In this paper we use the AGT correspondence to derive Ω-exact formulae for the partition function, in the nearby of monopole points where the dynamics is described by irregular conformal blocks of the CFT. The results are checked against those obtained by the recursion relations coming from a conformal anomaly in the region where the two approaches overlap. The Nekrasov-Shatashvili limit is also discussed. Finally, we comment on the existence of black holes in De Sitter space whose low energy dynamics is described by an Argyres-Douglas theory.

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 Dp(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 (A2, D4) 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 \U0001d530\U0001d532(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 ≠ 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 \U0001d4ae.

A tale of 2-groups: Dp(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 Dp(USp(2N)), which can be realized by ℤ2-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 3d mirror theories of general Dp(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}_p^b(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}_p^b(G) theories. In this regard, we find that the Dp(USp(2N)) theories constitute a special class of Argyres-Douglas theories that have a 2-group symmetry.

Operator spectroscopy for 4D SCFTs with a=c

We study a rich set of four-dimensional superconformal field theories with both central charges identical: $a=c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type ${\mathcal{D}}_{p}(G)$, with or without adjoint chiral multiplets, in 2106.12579 and 2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting superconformal field theories with $a=c$ in the infrared.

Higgs branches of Argyres-Douglas theories as quiver varieties

We present a general prescription for constructing 3d mathcal{N} = 4 Lagrangians for the IR SCFTs that arise from the circle reduction of a large class of Argyres-Douglas theories. The resultant Lagrangian gives a realization of the Higgs branch of the 4d SCFT as a quiver variety, up to a set of decoupled interacting SCFTs with empty Higgs branches. As representative examples, we focus on the families (Ap−N−1, AN−1) and Dp(SU(N)). The Lagrangian in question is generically a non-ADE-type quiver gauge theory involving only unitary gauge nodes with fundamental and bifundamental hypermultiplets, as well as hypermultiplets which are only charged under the U(1) subgroups of certain gauge nodes. Our starting point is the Lagrangian 3d mirror of the circle-reduced Argyres-Douglas theory, which can be read off from the class mathcal{S} construction. Using the toolkit of the S-type operations, developed in [1], we show that the mirror of the 3d mirror for any Argyres-Douglas theory in the aforementioned families is guaranteed to be a Lagrangian theory of the above type, up to some decoupled free sectors. We comment on the extension of this procedure to other families of Argyres-Douglas theories. In addition, for the case of Dp(SU(N)) theories, we compare these 3d Lagrangians to the ones found in [2] and propose that the two are related by an IR duality. We check the proposed IR duality at the level of the three-sphere partition function for specific examples. In contrast to the 3d Lagrangians in [2], which are linear chains involving unitary-special unitary nodes, we observe that the Coulomb branch global symmetries are manifest in the 3d Lagrangians that we find.

Argyres-Douglas avatars of Coulomb branch physics

We study ultraviolet (UV) incarnations of deep infrared (IR) physics on the Coulomb branch of the simplest interacting 4D mathcal{N} = 2 superconformal field theory: the minimal Argyres-Douglas (MAD) theory. One of the most basic properties of the Coulomb branch is an emergent infinite-dimensional higher-spin symmetry. While the MAD theory is interacting and therefore does not have such a symmetry, we find UV operators that encode the emergent complex higher-spin symmetry on the Coulomb branch. Moreover, we show that cousins of these UV operators give rise to cousins of the IR higher-spin multiplets. In terms of superconformal representation theory, we are led to a conjecture on the exact spectrum of {overline{mathcal{C}}}_{R,rleft(j,overline{j}right)} multiplets in the MAD theory for all R, r, j, and overline{j} satisfying R+overline{j}-j+1=0 , thereby making progress towards a full characterization of the protected spectrum. Along the way, we give a geometrical interpretation of these operators and include them in an extension of the Coulomb branch / mathcal{N} = 2 chiral operator correspondence.

Line defects in three dimensional mirror symmetry beyond ADE quivers

Understanding the map of line defects in a Quantum Field Theory under a given duality is generically a difficult problem. This paper is the second in a series which aims to address this question in the context of 3d mathcal{N} = 4 mirror symmetry. A general prescription for constructing vortex defects and their mirror maps in quiver gauge theories beyond the A-type was presented by the author in an earlier paper [1], where specific examples involving D-type and affine D-type quivers were discussed. In this paper, we apply the aforementioned prescription to construct a family of vortex defects as coupled 3d-1d systems in quiver gauge theories beyond the ADE-type, and study their mirror maps. Specifically, we focus on a class of quiver gauge theories involving unitary gauge nodes with edge multiplicity greater than 1, i.e. two gauge nodes in these theories may be connected by multiple bifundamental hypermultiplets. Quiver gauge theories of this type arise as 3d mirrors of certain Argyres-Douglas theories compactified on a circle. Some of these quiver gauge theories are known to have a pair of 3d mirrors, which are themselves related by an IR duality, discussed recently in [2]. For a concrete example where a pair of 3d mirrors do exist, we study how the vortex defects constructed using our prescription map to Wilson defects in each mirror theory.

On the protected spectrum of the minimal Argyres-Douglas theory

Despite the power of supersymmetry, finding exact closed-form expressions for the protected operator spectra of interacting superconformal field theories (SCFTs) is difficult. In this paper, we take a step towards a solution for the “simplest” interacting 4D mathcal{N} = 2 SCFT: the minimal Argyres-Douglas (MAD) theory. We present two results that go beyond the well-understood Coulomb branch and Schur sectors. First, we find the exact closed-form spectrum of multiplets containing operators that are chiral with respect to any mathcal{N} = 1 ⊂ mathcal{N} = 2 superconformal subalgebra. We argue that this “full” chiral sector (FCS) is as simple as allowed by unitarity for a theory with a Coulomb branch and that, up to a rescaling of U(1)r quantum numbers and the vanishing of a finite number of states, the MAD FCS is isospectral to the FCS of the free mathcal{N} = 2 Abelian gauge theory. In the language of superconformal representation theory, this leaves only the spectrum of the poorly understood {overline{mathcal{C}}}_{R,{r}_{left(j,overline{j}right)}} multiplets to be determined. Our second result sheds light on these observables: we find an exact closed-form answer for the number of {overline{mathcal{C}}}_{0,{r}_{left(j,0right)}} multiplets, for any r and j, in the MAD theory. We argue that this sub-sector is also as simple as allowed by unitarity for a theory with a Coulomb branch and that there is a natural map to the corresponding sector of the free mathcal{N} = 2 Abelian gauge theory. These results motivate a conjecture on the full local operator algebra of the MAD theory.

Holographic duals of M5-branes on an irregularly punctured sphere

We provide explicit holographic duals of M5-branes wrapped on a sphere with one irregular puncture and one regular puncture of arbitrary type. The solutions generalise the solutions corresponding to M5-branes wrapped on a disc recently constructed by Bah-Bonetti-Minasian-Nardoni by allowing for a general choice of regular puncture. We show that the central charges, flavour central charges and conformal dimensions of BPS operators match with a class of Argyres-Douglas theory.

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 (An, Em) 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_G^{vee }} (G) with {h}_G^{vee } the dual Coxeter number of G; and the triviality of the 2-group structure in the (An, Em) theories.

OPE coefficients in Argyres-Douglas theories

The calculation of physical quantities in certain quantum field theories such as those of the Argyres-Douglas type is notoriously hard, due to the lack of a Lagrangian description. Here we tackle this problem following two alternative approaches. On the one hand, we use localization on the four-sphere to compute two-correlators and OPE coefficients in Argyres-Douglas superconformal theories. On the other hand, we use the conformal bootstrap machinery to put stringent bounds on such coefficients, only relying on the knowledge of central charge and conformal dimension of the operators. We compare the results obtained with these two methods and find good agreement for all rank-one cases and for the rank-two Argyres-Douglas theories (A1, A4) and (A1, A5), in the moduli space of pure SU(5) and SU(6) super Yang-Mills. We also apply our results from localization to obtain bounds on the dimensions of the lightest neutral unprotected operators of the CFTs.

Argyres-Douglas theories in class S without irregularity

We make a preliminary investigation into twisted A_{2n}A2n theories of class \mathcal S𝒮. Contrary to a common piece of folklore, we establish that theories of this type realise a variety of models of Argyres-Douglas type while utilising only regular punctures. We present an in-depth analysis of all twisted A_2A2 trinion theories, analyse their interrelations via partial Higgsing, and discuss some of their generalised SS-dualities.

Spin thresholds, RG flows, and minimality in 4D N=2 QFT

Long ago, Argyres and Douglas discovered a particularly simple interacting 4D $\mathcal{N}=2$ superconformal field theory (SCFT) on the Coulomb branch of $SU(3)$ $\mathcal{N}=2$ super Yang-Mills. Further hints of the theory's simplicity arise due to the fact that it has the smallest possible value of the $c$ central charge among unitary interacting $\mathcal{N}=2$ SCFTs. The main purpose of this paper is to uncover additional aspects of this minimal Argyres-Douglas (MAD) theory's simplicity. In particular, we argue that: (1) the MAD theory shares an infinite set of large spin thresholds in part of its operator spectrum with the free $\mathcal{N}=2$ Maxwell theory (this data is therefore invariant under generic $\mathcal{N}=2$-preserving renormalization group flows to the IR), and (2) the MAD theory has, at every order in the natural grading, the smallest number of ``Schur'' operators of any unitary $\mathcal{N}=2$ theory (interacting or free). We then show that property (1) has a suitable generalization for all $({A}_{1},{A}_{2k})$ cousins of the MAD theory. In particular, the corresponding large spin thresholds encode generic renormalization group flows within this class. This construction therefore gives a different handle on these flows from the one provided by the Seiberg-Witten description. To emphasize the importance of these spin thresholds, we abstractly study theories with ``enough matter'' to form Higgs branches and argue that infinitely many spin thresholds are small or vanishing.

Wall-crossing of TBA equations and WKB periods for the third order ODE

We study the WKB periods for the third order ordinary differential equation (ODE) with polynomial potential, which is obtained by the Nekrasov-Shatashvili limit of (A2,AN) Argyres-Douglas theory in the Omega background. In the minimal chamber of the moduli space, we derive the Y-system and the thermodynamic Bethe ansatz (TBA) equations by using the ODE/IM correspondence. The exact WKB periods are identified with the Y-functions. Varying the moduli parameters of the potential, the wall-crossing of the TBA equations occurs. We study the process of the wall-crossing from the minimal chamber to the maximal chamber for (A2,A2) and (A2,A3). When the potential is a monomial type, we show the TBA equations obtained from the (A2,A2) and (A2,A3)-type ODE lead to the D4 and E6-type TBA equations respectively.

Mathcal{N} = 4 SYM, Argyres-Douglas theories, and an exact graded vector space isomorphism

In this first of two papers, we explain in detail the simplest example of a broader set of relations between apparently very different theories. Our example relates mathfrak{su}(2) mathcal{N} = 4 super Yang-Mills (SYM) to a theory we call “(3, 2)”. This latter theory is an exactly marginal diagonal SU(2) gauging of three D3(SU(2)) Argyres-Douglas (AD) theories. We begin by observing that the Schur indices of these two theories are related by an algebraic transformation that is surprisingly reminiscent of index transformations describing spontaneous symmetry breaking on the Higgs branch. However, this transformation breaks half the supersymmetry of the SYM theory as well as its full mathcal{N} = 2 SU(2)F flavor symmetry. Moreover, it does so in an interesting way when viewed through the lens of the corresponding 2D vertex operator algebras (VOAs): affine currents of the small mathcal{N} = 4 super-Virasoro algebra at c = −9 get mapped to the mathcal{A}(6) stress tensor and some of its conformal descendants, while the extra supersymmetry currents on the mathcal{N} = 4 side get mapped to higher-dimensional fermionic currents and their descendants on the mathcal{A}(6) side. We prove these relations are facets of an exact graded vector space isomorphism (GVSI) between these two VOAs. This GVSI respects the U(1)r charge of the parent 4D theories. We briefly sketch how more general mathfrak{su}(N) mathcal{N} = 4 SYM theories are related to an infinite class of AD theories via generalizations of our example. We conclude by showing that, in this class of theories, the mathcal{A}(6) VOA saturates a new inequality on the number of strong generators.