We discuss a novel UV completion of a class of Argyres-Douglas (AD) theories in the Ω-background by its embedding into the renormalisation group flow from five dimensional $$ \mathcal{N}=1 $$ superconformal field theories (SCFT) on $\textit{S}$ . This is obtained via analysing these theories in the light of ($\textit{q}$-)Painlevé/gauge theory correspondence, which allows to compute the five dimensional BPS partition functions as an expansion in the Wilson loop vev with integer $\textit{q}$-polynomials coefficients. These are derived formulating the gauge theory on a blown-up geometry and using a five-dimensional lift of (topological) operator/state correspondence. We discuss in detail the phase diagram of the four dimensional limits, pinpointing the special AD loci. Explicit computations are reported for $$ {\overset{\sim }{E}}_1 $$ SCFT and its limit to H = ($\textit{A}$ $\textit{, A}$ ) AD theory.

Italy

Giulio Bonelli

Pavlo Gavrylenko

Ideal Majtara

Alessandro Tanzini

On a 5D UV completion of Argyres-Douglas theories

The one-loop gravitational path integral around Euclidean de Sitter space $\textit{S}$ has a complex phase that casts doubt on a state counting interpretation. Recently, it was proposed to cancel this phase by including an observer. We explore this proposal in the case where the observer is a charged black hole in equilibrium with the de Sitter horizon. We compute the phase of the one-loop determinant within a two-dimensional dilaton gravity reduction, using both numerical and analytical methods. Our results interpolate between previous studies of a probe geodesic observer and the Nariai solution. We also revisit the prescription for going from the Euclidean path integral to the state-counting partition function, finding a positive sign in the final density of states.

United States

Yiming Chen

Douglas Stanford

Haifeng Tang

China

Zhenbin Yang

On the phase of the de Sitter density of states

We propose an $$ \mathcal{N}=2 $$ preserving deformation that leads to the confining phase of the 3d reduction of the $\textit{D}$ [SU($\textit{N}$)] Argyres-Douglas theories, referred to as 𝔻 [SU($\textit{N}$)]. This deformation incorporates monopole superpotential terms, which have recently played interesting roles in exploring possible RG fixed points of 3d supersymmetric gauge theories. Employing this confining phenomenon in 3d 𝔻 [SU($\textit{N}$)] theories, we also propose a deconfined version of the Kim-Park duality, an IR duality for 3d $$ \mathcal{N}=2 $$ adjoint SQCDs, where an adjoint matter field is replaced by a linear quiver tail of 𝔻 [SU($\textit{N}$)]. Surprisingly, both the confinement of deformed 𝔻 [SU($\textit{N}$)] and the deconfined Kim-Park duality can be proven only assuming some basic 3d $$ \mathcal{N}=2 $$ IR dualities. Finally, we propose a variant of the Kim-Park duality deformed by a single monopole superpotential term, which can also be derived using the same method.

Chiung Hwang

South Korea

Sungjoon Kim

S-confinement of 3d Argyres-Douglas theories and the Seiberg-like duality with an adjoint matter

We study the bosonic VOA associated with the 3D $$ \mathcal{N}=4 $$ abelian linear quiver gauge theories arising from compactifying 4D $$ \mathcal{N}=2 $$ Argyres-Douglas theories of ($\textit{A}$ $\textit{, A}$ ) and ($\textit{A}$ $\textit{, D}$ ) types. These VOAs are obtained by canceling the gauge anomaly of the H-twisted 3D theory on the half-space by Heisenberg algebras on the boundary. We particularly conjecture a complete set of strong generators of these bosonic VOAs, which contains more than the Virasoro stress tensor and those arising from Higgs branch operators. We also find that these bosonic VOAs contain copies of the $\textit{W}$ vertex algebra at $\textit{c}$ = −2 as sub vertex algebras.

Japan

Takahiro Nishinaka

Hikaru Sasaki

On bosonic vertex algebras associated with 3D reductions of Argyres-Douglas theories

A well-established organisational principle for Argyres-Douglas-type 𝒩 = 2 superconformal field theories in four dimensions is to characterise such theories by the data defining a(n irregular) Hitchin system on ℂℙ . 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 $\textit{A}$ theories without outer automorphism twists.

United Kingdom

Christopher Beem

Mario Martone

Matteo Sacchi

Palash Singh

Jake Stedman

Simplifying the type $\textit{A}$ Argyres-Douglas landscape

We propose that Argyres-Douglas theories of type $\textit{D}$ (SU($\textit{N}$)) and ($\textit{A}$ $\textit{, A}$ ) — 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 $\textit{D}$ (SU($\textit{N}$)) theories. By reversing this chain, we recursively build a “parent” star-shaped quiver for any given ($\textit{N, p}$). 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.

Simone Giacomelli

William Harding

Thailand

Noppadol Mekareeya

Alessandro Mininno

From regular to irregular: a unified origin for Argyres-Douglas theories

Vertex operator algebras (VOAs) arise in protected subsectors of supersymmetric quantum field theories, notably in 4d $$ \mathcal{N} $$ = 2 superconformal field theories (SCFT) via the Schur sector and in twisted 3d $$ \mathcal{N} $$ = 4 theories via boundary algebras. These constructions are connected through twisted circle compactifications, which can be best understood from the dynamics of BPS particles in the Coulomb branch of the 4d SCFT. This data is encoded in an operator $$ \hat{\Phi} $$ acting on the Hilbert space of an auxiliary quantum mechanics of BPS particles, whose trace yields the partition functions of a 3d topological field theory (TFT) bounding the VOA. We generalize this trace formula by considering higher powers of $$ \hat{\Phi} $$ , leading to a finite family of VOAs associated with a given 4d SCFT. Applying this framework to Argyres-Douglas theories labeled by ($\textit{A}$ , $\textit{G}$), where $\textit{G}$ is an ADE-type group of rank up to 8, we extract the modular data of the family of boundary VOAs via TFT partition function calculations on Seifert manifolds. Our results suggest that the modular data obtained from different powers of $$ \hat{\Phi} $$ are related by Galois transformations.

Byeonggi Go

Qiang Jia

Heeyeon Kim

From BPS spectra of Argyres-Douglas theories to families of 3d TFTs

A correction to this paper has been published: https://doi.org/10.1007/JHEP11(2023)198

Armenia

Hasmik Poghosyan

Rubik Poghossian

Erratum to: A note on rank 5/2 Liouville irregular block, Painlevé I and the $$ {\mathcal{H}}_0 $$ Argyres-Douglas theory

We construct TBA equations for D-type Argyres-Douglas theories with an SU(2) flavor symmetry based on their spectral networks. We show that the solutions of these TBA equations agree with the quantum periods of the corresponding quantum Seiberg-Witten curves defined in the Nekrasov-Shatashvili limit of the Omega background, including a centrifugal correction. We study the variety of TBA systems across the Coulomb branch moduli space and find that they correspond to the Dynkin diagrams of $\textit{D}$ Lie algebras in the minimal chamber, and reproduce the TBA equations for reflectionless D scattering theories at the maximally symmetric point. Numerical computations demonstrate that the quantum periods obtained from the Borel-Padé resummation and their WKB expansions are in agreement with the solutions of the TBA equations.

Katsushi Ito

Jingjing Yang

TBA equations and quantum periods for D-type Argyres-Douglas theories

In large N chaotic quantum systems, the butterfly effect is mediated by a collective field mode known as the “scramblon.” We study self-interactions of the scramblon in variants of the Sachdev-Ye-Kitaev model. In spatially extended versions of the model and for large spatial separation, fluctuations described by loop diagrams can invalidate the single-scramblon approximation well before its contribution to out-of-time-order correlators becomes of order one. We find a qualitative difference between an incoherent regime at high temperaure (or in a Brownian version of the model) and a coherent regime at low temperature.

Shreya Vardhan

Shunyu Yao

Scramblon loops