Related papers: N=1 curves for trifundamentals

Cachazo and Vafa studied $\mathcal{N}=1$ dynamics of U(N) gauge theory from a viewpoint of type IIB superstring compactified on a Calabi-Yau manifold with fluxes. They proved the equivalence between the dynamics and that of $\mathcal{N}=2$…

We obtain the Seiberg-Witten geometry for four-dimensional N=2 gauge theory with gauge group SO(2N_c) (N_c \leq 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N=2 $E_6$ theory with…

This is an announcement of some of the results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin…

We show that, for a generic choice of a point on the Coulomb branch of any N=2 supersymmetric gauge theory, it is possible to find a superpotential perturbation which generates a metastable vacuum at the point. For theories with SU(N) gauge…

We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space P. The connection is given by a triple of forms A,B,H: a potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength 3-form H=dB.…

The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on…

Let M denote a compact, orientable, 3-dimensional manifold and let a denote a contact 1-form on M; thus the wedge product of a with da is nowhere zero. This article explains how the Seiberg-Witten Floer homology groups as defined for any…

We derive the singularity conditions of the N=1 generalized (general yukawa couplings and quark masses) form of hyperelliptic curves of SU(N_c) with N_f flavors. The results reproduce the known form of N=2 curves when the yukawa couplings…

$U(n)$ is a semi-direct product group that is characterized by non-trivial homomorphisms mapping $U(1)$ into the automorphism group of $SU(n)$. For $U(3)$, there are three non-trivial homomorphisms that induce three separate defining…

We continue our study of the N=1* supersymmetric gauge theory and its relation to elliptic integrable systems. Upon compactification on a circle, we show that the semi-classical analysis of the massless and massive vacua depends on the…

Gauged linear sigma-models at critical coupling on Riemann surfaces yield self-dual field theories, their classical vacua being described by the vortex equations. For local models with structure group ${\rm U}(r)$, we give a description of…

We study the transition between a Coulomb phase and a dimer crystal observed in numerical simulations of the three-dimensional classical dimer model, by mapping it to a quantum model of bosons in two dimensions. The quantum phase transition…

We study a three-dimensional $\mathcal{N}=2$ supersymmetric $G_2$ gauge theory with and without fundamental matters. We find that a classical Coulomb branch of the moduli space of vacua is partly lifted by monopole-instantons and the…

We construct the Seiberg-Witten theory on 3-manifolds with Euclidean ends (connected sums of $\R^3$ and a compact manifold) with perturbations which approximate $*dx_3$ at infinity, and describe the structure of the moduli spaces. The setup…

We study the four-dimensional N=2 superconformal field theories that describe D3-branes probing the recently constructed N=2 S-folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to S-fold…

We give a mathematically rigorous construction of the moduli space and vacuum geometry of a class of quantum field theories which are N=2 supersymmetric Wess-Zumino models on a cylinder. These theories have been proven to exist in the sense…

We elaborate on s-confinement phases in three-dimensional $\mathcal{N}=2$ supersymmetric gauge theory, especially focusing on the $SU(N)$ and $USp(2N)$ gauge theories with anti-symmetric tensors and (anti-)fundamental matters. This will…

We systematically extend the elementary differential and Riemannian geometry of classical $\mathrm{U}(1)$-gauge theory to the noncommutative setting by combining recent advances in noncommutative Riemannian geometry with the theory of…

We study the three-point quantum $\mathfrak{sl_2}$-Gaudin model. In this case the compactification of the parameter space is $\overline{M_{0,4}(\mathbb{C})}$, which is the Riemann sphere. We analyze sphere coverings by the joint spectrum of…

We study the different quantum phases that occur in massive ${\cal N}=2$ supersymmetric QCD with gauge groups $SU(2)$ and $SU(3)$ as the coupling $\Lambda/M$ is gradually increased from 0 to infinity. The phases can be identified by…