相关论文: Mirror Symmetry in Flavored Affine D-type Quivers

We prove that the Hilbert scheme of $k$ points on $\mathbb{C}^2$ (Hilb$^k[\mathbb{C}^2]$) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding…

We develop a framework to construct worldvolume gauge theories on D2-branes probing compound Du Val (cDV) Calabi-Yau threefold singularities. By viewing these singularities as ADE surface fibrations over the complex $w$-plane, we encode…

We propose a family of IR dualities for 3d $\mathcal{N}=4$ $U(N)$ SQCD with $N_f$ fundamental flavors and $P$ Abelian hypermultiplets i.e. $P$ hypermultiplets in the determinant representation of the gauge group. These theories are good in…

We study some arithmetic properties of the mirror maps and the quantum Yukawa coupling for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to…

To a quiver with involution, we study the Coulomb branch of the 3d $\mathcal{N} = 4$ involution-fixed part of the quiver gauge theory. We show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the…

We study the moduli space of 3d $\mathcal{N}=4$ quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise…

We generalize the free Fermi-gas formulation of certain 3d ${\cal N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition…

Recently an algorithm to build $SL(2,\mathbb{Z})$ duals, including mirror duals, of 3d $\mathcal{N}=4$ quiver theories and their 4d $\mathcal{N}=1$ uplift has been introduced. In this work we use this new tool to study the so-called bad…

We extend the dictionary between Type IIB branes and representations of the Ding-Iohara-Miki (DIM) algebra to the case when one of the space directions is a circle. It is well-known that the worldvolume theory on branes wrapping the circle…

We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra $\mathfrak g$. We analyse classes of quiver theories, with Classical gauge and flavour…

We consider homological mirror symmetry in the context of hypertoric varieties, showing that appropriate categories of B-branes (that is, coherent sheaves) on an additive hypertoric variety match a category of A-branes on a Dolbeault…

We perform a Hodge theoretic study of parameter dependent families of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifcations. Starting from a geometric Gauss-Manin connection for B type branes we study the…

We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$…

We show that for a large subclass of Argyres-Douglas-type theories, the Higgs branch admits multiple hyperkahler quotient realizations as Higgs branches of three dimensional $\mathcal{N}=4$ quiver gauge theories, which are related by a…

We consider the compactification of the 6d N=(2,0) theories, or equivalently of M-theory 5-branes, on a punctured Riemann surface times a circle. This gives rise to what we call 3d N=4 Sicilian theories, and we find that their mirror…

The product-group unification is a model of unified theories, in which masslessness of the two Higgs doublets and absence of dimension-five proton decay are guaranteed by a symmetry. It is based on SU(5) x U(N) (N=2,3) gauge group. It is…

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric…

't Hooft anomalies of discrete global symmetries and gaugings thereof have rich mathematical structures and far-reaching physical consequences. We examine each subgroup $G$, up to automorphisms, of the permutation group $S_4$ that acts on…

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…

We clarify how mirror symmetry acts on 3d theories with N=2,3 or 4 supersymmetries and non-abelian Chern-Simons terms and then construct many new examples. We identify a new duality, geometric duality, that allows us to generate large…