Related papers: Even More On Twisted $A_{2n}$ Class-S Theories
The twisted Alexander polynomials of a space, associated to a linear representation $\sigma$ of the fundamental group, are non-abelian refinements of the classical Alexander polynomial from knot theory. In this paper, we show that they…
To a quiver with involution, we show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the quantized Coulomb branch algebra of the 3d $\mathcal{N}=4$ involution-fixed part of the quiver gauge theory in…
It is known that some theories of class $S$ are actually factorized into multiple decoupled nontrivial four-dimensional $N=2$ theories. We propose a way of constructing examples of this phenomenon using the physics of half-BPS surface…
A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…
This is the third in a series of papers which outlines an approach to the classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via the study of their Coulomb branch geometries. Here we use the fact that the encoding…
Twisted homomorphisms of bialgebras are bialgebra homomorphisms from the first into Drinfeld twistings of the second. They possess a composition operation extending composition of bialgebra homomorphisms. Gauge transformations of twists,…
We study theories of type $D_4$ in class-S, with nonabelian outer-automorphism twists around various cycles of the punctured Riemann surface $C$. We propose an extension of previous formul\ae\ for the superconformal index to cover this case…
We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators…
We obtain a large class of new 4d Argyres-Douglas theories by classifying irregular punctures for the 6d (2,0) superconformal theory of ADE type on a sphere. Along the way, we identify the connection between the Hitchin system and…
We extend recent work by Howie, Mathews and Purcell to simplify the calculation of A-polynomials for any family of hyperbolic knots related by twisting. The main result follows from the observation that equations defining the deformation…
We develop a systematic method to describe the moduli space of vacua of four dimensional $\mathcal{N}=2$ class ${\cal S}$ theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed…
We study the partition functions of topologically twisted 3d $\mathcal{N}=2$ gauge theories on a hemisphere spacetime with boundary $HS^2 \times S^1$. We show that the partition function may be localised to either the Higgs branch or the…
The 6d $(2,0)$ theory has codimension-one symmetry defects associated to the outer-automorphism group of the underlying ADE Lie algebra. These symmetry defects give rise to twisted sectors of codimension-two defects that are either regular…
Twists of four-dimensional supersymmetric quantum field theories (SQFTs) isolate protected sectors with rich algebraic structures. We develop a unified framework for analyzing symmetries and anomalies in four-dimensional holomorphically…
We consider two families of algebraic varieties $Y_n$ indexed by natural numbers $n$: the configuration space of unordered $n$-tuples of distinct points on $\mathbb{C}$, and the space of unordered $n$-tuples of linearly independent lines in…
We study the stratification of the singular locus of four dimensional $\mathcal{N}=2$ Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant…
We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…
We study three-dimensional ${\mathcal N}=2$ supersymmetric gauge theories on ${\Sigma_g \times S^1}$ with a topological twist along $\Sigma_g$, a genus-$g$ Riemann surface. The twisted supersymmetric index at genus $g$ and the correlation…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant…