Related papers: 3d N=2 Theories from Cluster Algebras

We study Seiberg-like dualities in three dimensional N=2 supersymmetric theories, emphasizing Chern-Simons terms for the global symmetry group, which affect contact terms in two-point functions of global currents and are essential to the…

We argue that 6d N=(2,0) theory on S^1 x S^3 x C_2 reduces to the 2d q-deformed Yang-Mills on C_2 at finite area, as a small extension to the result of Gadde, Rastelli, Razamat and Yan. This is done by computing the partition function on…

We show that a subcategory of the $m$-cluster category of type $\tilde{D_n}$ is isomorphic to a category consisting of arcs in an $(n-2)m$-gon with two central $(m-1)$-gons inside of it. We show that the mutation of colored quivers and…

We study the dynamics of a large class of N=1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau threefolds. These include N=2 (affine) A-D-E quiver theories deformed by superpotential…

There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…

For each simple Lie algebra $\mathfrak{g}$, we construct an algebra embedding of the quantum group $U_q(\mathfrak{g})$ into certain quantum torus algebra $D_\mathfrak{g}$ via the positive representations of split real quantum group. The…

The quantization of the Teichm\"uller theory has led to the formulation of the so-called Teichm\"uller TQFT for 3-manifolds. In this paper we initiate the study of "supersymmetrization" of the Teichm\"uller TQFT, which we call the super…

In this thesis we calculate the dimension of the conformal manifold (DCM) for a class of 3d $\mathcal{N}=4$ supersymmetric theories called the star-shaped-quiver (SSQ) theories. These theories are the mirror dual theories of class…

The goals of this expository article are on one hand to describe how to construct ($m$-) cluster categories from triangulations (resp. from $m+2$-angulations) of polygons. On the other hand, we explain how to use translation quivers and…

M5-branes on an associative three-cycle $M_3$ in a $G_2$-holonomy manifold give rise to a 3d $\mathcal{N}=1$ supersymmetric gauge theory, $T_{\mathcal{N}=1} [M_3]$. We propose an $\mathcal{N}=1$ 3d-3d correspondence, based on two…

We show that the $4d$ ${\cal N}=1$ $SU(3)$ $N_f=6$ SQCD is the model obtained when compactifying the rank one E-string theory on a three punctured sphere (a trinion) with a particular value of flux. The $SU(6)\times SU(6)\times U(1)$ global…

We investigate the combinatorics of quivers that arise from triangulations of even-dimensional cyclic polytopes. Work of Oppermann and Thomas pinpoints such quivers as the prototypes for higher-dimensional cluster theory. We first show that…

The objective of the present paper is to prove cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$. As corollaries, we obtain bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-bases established in [6], and…

Let $C$ be a simply laced generalized Cartan matrix. Given an element $b$ of the generalized braid semigroup related to $C$, we construct a collection of mutation-equivalent quivers with potentials. A quiver with potential in such a…

We work out Seiberg-like dualities for 3d $\mathcal{N}=2$ theories with SU(N) gauge group. We use the $SL(2,\mathbb{Z})$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\mathbb{Z})$ acts as…

We propose a construction of the quantum-corrected Coulomb branch of a general 3d gauge theory with $\mathcal{N}=4$ supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the…

Glaisher's theorem states that the number of partitions of $n$ into parts which repeat at most $m-1$ times is equal to the number of partitions of $n$ into parts which are not divisible by $m$. The $m=2$ case is Euler's famous partition…

We consider three-dimensional ${\mathcal N}=2$ supersymmetric field theories defined on general complex-valued backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We compute partition…

We propose a general way to complete supersymmetric theories with operators below the unitarity bound, adding gauge-singlet fields which enforce the decoupling of such operators. This makes it possible to perform all usual computations, and…

We discuss 3d brane webs and effective Chern-Simons levels for 3d $\mathcal{N}=2$ gauge theories. We find that turning on real masses for chiral multiplets leads to various equivalent brane webs that are related by flipping positions of…