Related papers: 3-dimensional mirror symmetry
This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…
This paper presents new developments in the study of 3d mirror symmetry and the phase structure of Abelian gauge theories. Previous works identified 3d mirrors for a specific class of theories, termed ``simple" Abelian theories. This work…
3d mirror symmetry is a mysterious duality for certian pairs of hyperk\"ahler manifolds, or more generally complex symplectic manifolds/stacks. In this paper, we will describe its relationships with 2d mirror symmetry. This could be…
We study three dimensional gauge theories with N=2 supersymmetry. We show that the Coulomb branches of such theories may be rendered compact by the dynamical generation of Chern-Simons terms and present a new class of mirror symmetric…
This is the companion paper of the letter arXiv:2410.15695, containing all the details and series of examples on a 4d mirror symmetry for the class-$\mathcal{S}$ theories which relates the representation theory of the chiral quantization of…
We discuss non-trivial fixed points of the renormalization group with dual descriptions in $N=4$ gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories.…
We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.
We give a brief survey of some of the geometry of mirror symmetry, written in 2004 for the "Encyclopaedia of Mathematical Physics". Probably a little bit out of date now in a few places, but hey.
We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an ADE quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled…
The B-side of Kontsevich's Homological Mirror Symmetry Conjecture is discussed. We give first a self-contained study of derived categories and their homological algebra, and later restrict to the bounded derived category of schemes and…
Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications…
Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the…
In this letter, we propose a 4d mirror symmetry for the class-$\mathcal{S}$ theories which relates the representation theory of the chiral quantization of the Higgs branch and the geometry of the Coulomb branch. We study the representation…
The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the best-understood mirror statements relate certain small corners of the moduli spaces of X…
The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d $\mathcal{N}=4$ theories. In this paper, starting with known mirror pairs of 3d $\mathcal{N}=4$ quiver gauge theories and gauging discrete…
We describe how the geometry of the Higgs branch of 5d superconformal field theories is transformed under movement along the extended Coulomb branch. Working directly with the (unitary) magnetic quiver, we demonstrate a correspondence…
A distinctive duality present in 3d $\mathcal{N}=4$ theories is the 3d mirror symmetry. Under this duality, the Coulomb (Higgs) branch of one theory corresponds to the Higgs (Coulomb) branch of its mirror dual. This paper is divided into…
The first part of this paper is a survey of mathematical results on mirror symmetry phenomena between Hitchin systems for Langlands dual groups. The second part introduces and discusses multiplicity algebras of the Hitchin system on…
We review some of the interplay between mirror symmetry and K3 surfaces.
We construct three-dimensional N=1 QED with N_f flavors using branes of type IIB string theory. This theory has a mirror, which can be realized using the S-dual brane configuration. As in examples with more supersymmetry, the Higgs branch…