Related papers: Quiver Polymerisation
We study moduli spaces of a class of three dimensional N=4 gauge theories which are in one-to-one correspondence with a certain set of ordered pairs of integer partitions. It was found that these theories can be realised on brane intervals…
The $\imath$quiver algebras were introduced recently by the authors to provide a Hall algebra realization of universal $\imath$quantum groups, which is a generalization of Bridgeland's Hall algebra construction for (Drinfeld doubles of)…
Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-K\"ahler…
We classify the singularities in the unframed Nakajima quiver varieties associated with extended Dynkin quivers and the corresponding minimal imaginary root with a small restriction on the parameter and use this to construct a number of…
We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh and involves mutations of quivers and diagrams defined in the…
Polymerized quantum spin chains (i.e. spin chains with a periodic modulation of the coupling constants) exhibit plateaux in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling…
We study transverse equivariant Hilbert schemes of affine hypertoric varieties equipped with a symplectic action of a Weyl group. In particular, we show that the Coulomb branches of Braverman, Finkelberg, and Nakajima can be obtained either…
We construct N=1 supersymmetric theories on worldvolumes of D5 branes wrapped around 2-cycles of threefolds which are A-D-E fibrations over a plane. We propose large N duals as geometric transitions involving blowdowns of two cycles and…
We define three families of quivers in which the braid relations of the symmetric group $S_n$ are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the longest element of $S_4$ yields three…
The purpose of this thesis is to present certain viewpoints on the geometric representation theory of Nakajima cyclic quiver varieties, in relation to the Maulik-Okounkov stable basis. Our main technical tool is the shuffle algebra, which…
This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586. This is an expanded version of an article…
We study the spectrum of BPS particles on the Coulomb branch of five-dimensional superconformal field theories (5d SCFTs) compactified on a circle. By engineering these theories in M-theory on ${\mathbf X} \times S^1 $, for ${\mathbf X}$ an…
Three dimensional supersymmetric field theories have large moduli spaces of circular Wilson loops preserving a fixed set of supercharges. We simplify previous constructions of such Wilson loops and amend and clarify their classification.…
We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One…
We study three-dimensional supersymmetric quiver gauge theories with a non-simply laced global symmetry primarily focusing on framed affine $B_{N}$ quiver theories. Using a supersymmetric partition function on a three sphere, and its…
We investigate the IR dynamics of N=2 SUSY gauge theories in 3D with antisymmetric matter. The presence of the antisymmetric fields leads to further splitting of the Coulomb branch. Counting zero modes in the instanton background suggests…
We compute the quiver of any monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term…
In study of four-dimensional BPS states, quiver quantum mechanics plays a central role. The Coulomb phases capture the multi-centered nature of such states, and are well understood in the context of wall-crossing. The Higgs phases are given…
We study new symmetries between A and D type quiver gauge theories with different numbers of colors. We realize these gauge theories with twisted masses via a brane construction that reproduces all the parameters of the Gauge/Bethe…
For further investigating the underlying structures of the D=3, N=4 Chern-Simons-matter (CSM) theories, we suggest a new concept and procedure for "fusing" two superalgebras into a single new superalgebra. The starting superalgebras may be…