Related papers: Reflection groups and 3d $\mathcal{N}\ge $ 6 SCFTs

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…

It is shown that except in three cases conjugacy classes of classical Weyl groups $W(B_{n})$ and $W(D_{n})$ are of type ${\rm D}$. This proves that Nichols algebras of irreducible Yetter-Drinfeld modules over the classical Weyl groups…

Following Vinberg, we find the criterions for a subgroup generated by reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed…

With a large, unique spectroscopic survey in the fields of 28 galaxy-scale strong gravitational lenses, we identify groups of galaxies in the 26 adequately-sampled fields. Using a group finding algorithm, we find 210 groups with at least…

In [arXiv:0808.1677] 3 dimensional field theories are proposed to on-shell represent N=8 SUSY algebra and SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphism. They are theories of 8 scalar and 8 spinor matrix fields with Yukawa,…

We present a generalization of the theory of quantum symmetric pairs as developed by Kolb and Letzter. We introduce a class of generalized Satake diagrams that give rise to (not necessarily involutive) automorphisms of the second kind of…

In this work we uncover a connection that relates the 1-form and the 2-group symmetries of 5D SCFTs derived from geometric engineering methods to monodromies of the corresponding B-models via mirror symmetry. Viewing defects as branes…

We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1)…

Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have…

We study the Higgs branches of the superconformal points of four-dimensional N=2 super Yang-Mills (SYM) which appear due to the occurrence of mutually local monopoles having appropriate charges. We show, for example, that the maximal…

We present the classification of reflective quadratic forms $-px_0^2+x_1^2+\ldots+x_n^2$ for $p$ prime. We show that for $p = 5$, it is reflective for $2\leq n\leq 8$, for $p = 7\text{ and }17$ it is reflective for $n = 2\text{ and }3$, for…

Supersymmetric and non-supersymmetric deformations of large $N=(4,4)$ SCFT with superconformal symmetry $D^1(2,1;\alpha)\times D^1(2,1;\alpha)$ are explored in the gravity dual described by a Chern-Simons $N=8$, $(SO(4)\times SO(4))\ltimes…

The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of selected topics within this framework: Euclidean and rotation…

This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D $\mathcal{N} = 1$ gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of…

The notion of formal Siegel modular forms for an arithmetic subgroup $\Gamma$ of the symplectic group of genus $n$ is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the…

We propose a unified scheme for finding the hyperelliptic curve of $N=2$ SUSY YM theory with any Lie gauge groups. Our general scheme gives the well known results for classical gauge groups and exceptional $G_2$ group. In particular, we…

Strongly motivated by a mathematical result by Lin and Yamashita (arXiv:2412.02298), we describe a long exact sequence formed by groups of equivalence classes of two-dimensional $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theories…

New series of $2^{2m}$-dimensional universally strongly perfect lattices $\Lambda_I $ and $\Gamma_J $ are constructed with $$2BW_{2m} ^{\#} \subseteq \Gamma _J \subseteq BW_{2m} \subseteq \Lambda _I \subseteq BW _{2m}^{\#} .$$ The lattices…

Given a genus two curve $X: y^2 = x^5 + a x^3 + b x^2 + c x + d$, we give an explicit parametrization of all other such curves $Y$ with a specified symplectic isomorphism on three-torsion of Jacobians $\mbox{Jac}(X)[3] \cong…

Gaiotto and Witten found that one can construct 3d $\mathcal{N}=4$ Chern-Simons matter theories by using $\mathcal{N}=4$ SCFT whose momentum map of global symmetries satisfy special condition. Usually, one uses free hypermultiplet and…