Related papers: On Charge-3 Cyclic Monopoles

I review, with some pedagogy, two different approaches to the computation of BPS spectra in N=2 supersymmetric QCD with gauge group SU(2). The first one is semiclassical and has been widely used in the literature. The second one makes use…

We compute the class of the closure of the locus of hyperelliptic curves in the moduli space of stable genus-3 curves in terms of the tautological class $\lambda$ and the boundary classes $\delta_0$ and $\delta_1$. The expression of this…

In this paper we investigate the behavior of the sigma function over the family of cyclic trigonal curves $X_s$ defined by the equation $y^3 =x(x-s)(x-b_1)(x-b_2)$ in the affine $(x,y)$ plane, for $s\in D_\varepsilon:=\{s \in \mathbb{C} |…

We clarify some issues concerning the central charges saturated by the extended objects in the SUSY $U(1)$ $4d$ gauge theory in the $\Omega$-background. The configuration involving the monopole localized at the domain wall is considered in…

We prove some sharp systolic inequalities for compact $3$-manifolds with boundary. They relate the (relative) homological systoles of the manifold to its scalar curvature and mean curvature of the boundary. In the equality case, the…

A Richelot isogeny between Jacobian varieties is an isogeny whose kernel is included in the $2$-torsion subgroup of the domain. A Richelot isogeny whose codomain is the product of two or more principally polarized abelian varieties is…

We extend the topological classification scheme of Weyl semimetals via cohomology and the Mayer-Vietoris sequence to account for nodal line semimetals with space-time inversion symmetry. These are semimetals where bands meet generally in…

We present general results on generating $\text{AdS}_2$ solutions to Type II supergravity from $\text{AdS}_3$ solutions via U(1) and SL(2) T-dualities. We focus on a class of Type IIB solutions with small $\mathcal{N}=4$ supersymmetry, that…

We study genus $g$ coverings of full moduli dimension of degree $d=[\frac {g+3} 2]$. There is a homomorphism between the corresponding Hurwitz space $\H$ of such covers to the moduli space $\M_g$ of genus $g$ curves. In the case $g=3$,…

Using Seiberg-Witten theory it is known that the dynamics of N=2 supersymmetric SU(n) Yang-Mills theory is determined by a Riemann surface. In particular the mass formula for BPS states is given by the periods of a special differential on…

We find the spectrum of magnetic monopoles produced in the symmetry breaking SU(5) to [SU(3)\times SU(2)\times U(1)']/Z_6 by constructing classical bound states of the fundamental monopoles. The spectrum of monopoles is found to correspond…

We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth…

We study the relation between spectral data of magnetic monopoles in hyperbolic space and the curve of the spectral parameter of generalized chiral Potts models (gCPM) through the lens of (semi-)holomorphic field theories. We realize the…

We present new static axially symmetric solutions of SU(2) Yang-Mills-Higgs theory, representing chains of monopoles and antimonopoles in static equilibrium. They correspond to saddlepoints of the energy functional and exist both in the…

We study the adjacency spectrum of the toroidal three-dimensional queen graph $G_n$ on $(\mathbb{Z}_n)^3$. Since $G_n$ is a Cayley graph on an abelian group, its adjacency matrix is diagonalized by Fourier characters. For each frequency…

In this paper we study bielliptic curves of genus 3 defined over an algebraically closed field $k$ and the intersection of the moduli space $\M_3^b$ of such curves with the hyperelliptic moduli $\H_3$. Such intersection $\S$ is an…

To each non-isotropic almost-complex immersion of a 2-torus into $ S ^ 6 $ we associate an algebraic curve, called the spectral curve, and a linear flow in the intersection of two Prym varieties on this spectral curve. We show that…

We study relations among the classical thetanulls of cyclic curves, namely curves $\mathcal X$ (of genus $g(\mathcal X)>1$) with an automorphism $\sigma$ such that $\sigma$ generates a normal subgroup of the group $G$ of automorphisms, and…

The spectral problem of three-dimensional manifolds M_A admitting Sol-geometry in Thurston's sense is investigated. Topologically M_A are torus bundles over a circle with a unimodular hyperbolic gluing map A. The eigenfunctions of the…

We formulate a correspondence between SU(2) monopole chains and ``spectral data'', consisting of curves in $\mathbb{CP}^1\times\mathbb{CP}^1$ equipped with parabolic line bundles. This is the analogue for monopole chains of Donaldson's…