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.

Italy

Simone Giacomelli

William Harding

Thailand

Noppadol Mekareeya

United States

Alessandro Mininno

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

This article is a status report on the anholonomic frame and connection deformation method, AFCDM, for constructing generic off-diagonal exact and parametric solutions in general relativity, GR, relativistic geometric flows and modified gravity theories, MGTs. Such models can be generalized to nonassociative and noncommutative star products on phase spaces and modelled equivalently as nonassociative Finsler–Lagrange–Hamilton geometries. Our approach involves a nonholonomic geometric reformulation of classical models of gravitational and matter fields described by Lagrange and Hamilton densities on relativistic phase spaces. Using nonholonomic dyadic variables, the Einstein equations in GR and MGTs can formulated as systems of nonlinear partial differential equations, PDEs, which can be decoupled and integrated in some general off-diagonal forms. In this approach, the Lagrange and Hamilton dynamics and related models of classical and quantum evolution, are equivalently described in terms of generalized Finsler-like or canonical metrics and (nonlinear) connection structures on deformed phase spaces defined by solutions of modified Einstein equations. New classes of exact and parametric solutions in (nonassociative) MGTs are formulated in terms of generating and integration functions and generating effective/matter sources. The physical interpretation of respective classes of solutions depends on the type of (non) linear symmetries, prescribed boundary/asymptotic conditions or posed Cauchy problems. We consider possible applications of the AFCDM with explicit examples of off-diagonal deformations of black holes, cylindrical metrics and wormholes, black ellipsoids and torus configurations. In general, such solutions encode nonassociative and/or with geometric flow variables. For another types of generic off-diagonal (nonassociative) solutions, we study models with nonholonomic cosmological solitonic and spheroid deformations involving vertices and solitonic vacua for voids. We emphasize that such new classes of generic off-diagonal solutions can not be considered, in general, in the framework of the Bekenstein–Hawking entropy paradigm. This motivates relativistic/nonassociative phase space extensions of the G. Perelman thermodynamic approach to geometric flows and MGTs defined by nonholonomic Ricci solitons. In Appendix, Tables 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, summarize the AFCDM for various classes of quasi-stationary and cosmological solutions in MGTs with 4-d and 10-d spacetimes and (nonassociative) phase space variables on (co) tangent bundles.

Romania

Laurenţiu Bubuianu

Ukraine

Julia Seti

Douglas Singleton

Greece

Panayiotis Stavrinos

Türkiye

Sergiu Vacaru

Elşen Veliev

The anholonomic frame and connection deformation method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler–Lagrange–Hamilton 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.

South Korea

Byeonggi Go

Qiang Jia

Heeyeon Kim

Sungjoon 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 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.

Japan

Katsushi Ito

Jingjing Yang

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

We consider a family of Argyres-Douglas theories, which are 4D   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 strongly coupled superconformal field theories (SCFTs) but share many features with 4D   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 SCFTs with a = c and their dual quantum gravity via the AdS/CFT correspondence.

United Kingdom

Hongliang Jiang

Modularity in Argyres-Douglas theories with a = c

The Seiberg-Witten solution to four-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 super-Yang-Mills theory with gauge group SU(N) and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type   <math> <mfenced> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>a</mi> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mfenced> </math>  $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$ . A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the ℤ 2N  symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for SU(3). The intrinsic periods and Kähler potential of the   <math> <mfenced> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>a</mi> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mfenced> </math>  $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$  superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kähler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions ∆ &gt; 1 acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to ∆ ≤ 1 operators spoils the positivity and convexity of the intrinsic Kähler potential.

Sriram Bharadwaj

Eric D’Hoker

Approaching Argyres-Douglas theories

Topological arguments are currently being used as a novel scheme to discern the properties of black holes while ignoring their detailed structure and specific field equations. Among various avenues of black hole physics, where this novel approach is being utilized, the phase transition in black hole thermodynamics lies at the forefront. There are several types of phase transition in black holes; such as the van der Waals type phase transition, Davies-type phase transition, extremal phase transition, and Hawking-Page (HP) transition. So far, the topological interpretation, where the critical point has been identified with the non-zero topological charge, has been obtained only for the van der Waals type phase transition and HP transition in different spacetimes. To complete the picture, here we provide the same interpretation for two other phase transitions: Davies-type phase transition and extremal phase transition. The entire analysis is general and is valid for any spacetime where these types of phase transitions are observed. More importantly, our analysis suggests that amid the apparent differences in these phase transitions, they share the same topological characteristics, i.e. non-zero topological charge arising from different thermodynamic potentials in different types of phase transition.

Krishnakanta Bhattacharya

Kazuharu Bamba

Topological interpretation of extremal and Davies-type phase transitions of black holes

We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is ‘compressed’ into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions.

Michael Bishop

Joey Contreras

Peter Martin

Germany

Piero Nicolini

Minimal lengths in 3D via the generalized uncertainty principle

One of the leading issues in quantum field theory and cosmology is the mismatch between the observed and calculated values for the cosmological constant in Einstein's field equations of up to 120 orders of magnitude. In this paper, we discuss new methods to potentially bridge this chasm using the generalized uncertainty principle (GUP). We find that if quantum gravity GUP models are the solution to this puzzle, then it may require the gravitationally modified position operator undergoes a parity transformation at high energies.

Quantum gravity, the cosmological constant, and parity transformation