Related papers: A Brief Survey of Higgs Bundles
We link the periodicity of Hitchin's uniformizing Higgs bundle with the arithmetic geometry of its underlying curve. Some new relations are discovered. We also speculate on the whole class of periodic Higgs bundles.
We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry.…
The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the…
Hyperbolic lattices underlie a new form of quantum matter with potential applications to quantum computing and simulation and which, to date, have been engineered artificially. A corresponding hyperbolic band theory has emerged, extending…
We find an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL(2) Higgs moduli space on a Riemann surface. On one side we have the components of the Lagrangian brane of U(1,1) Higgs…
We prove a gluing theorem for solutions of Hitchin's self-duality equations with logarithmic singularities on a rank-2 vector bundle over a noded Riemann surface representing a boundary point of Teichm\"uller moduli space.
In this article we give an explicit description of the Hitchin fiber of SU(1,2) Higgs bundles $(L,F,\gamma,\beta)$ over a compact Riemann surface $X$ of genus $\ge 2$ with $q=\gamma\circ\beta$ having simple zeros and Toledo invariant…
Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$.…
We describe the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one and its geometric structures in terms of the Hitchin map and a flat degeneration of the moduli space of Higgs bundles on an elliptic curve.
Within the mathematical framework of Quillen, one interprets the Higgs field as part of the superconnection on a superbundle. We propose to take as superbundle the exterior algebra obtained from a Hermitian bundle with structure group U(n).…
The Hitchin system is a completely integrable hamiltonian system (CIHS) on the cotangent space to the moduli space of semi-stable vector bundles over a curve. We consider the case of rank-two vector bundles with trivial determinant. Such a…
We consider the moduli space of vector bundles of rank $n$ and degree $ng$ over a fixed Riemann surface of genus $g\geq 2$. We use the explicit parametrization in terms of the Tyurin data. In the moduli space there is a "non-abelian" Theta…
In gauge theory, Higgs fields are responsible for spontaneous symmetry breaking. In classical gauge theory on a principal bundle P, a symmetry breaking is defined as the reduction of a structure group of this principal bundle to a subgroup…
In this paper, we construct a stable parabolic Higgs bundle of rank two, which corresponds to the uniformization associated with a conformal hyperbolic metric on a compact Riemann surface $\overline{X}$ with prescribed singularities. This…
A hermitian Higgs bundle is a triple $({\mathfrak E},h) = (E,\Phi, h)$, where ${\mathfrak E}=(E,\Phi)$ is a Higgs bundle and $(E,h)$ is a holomorphic hermitian vector bundle. It is well-known that several results on holomorphic vector…
We calculate the characteristic classes for flat SL(n,R) and Sp(2m,R)-bundles over a compact surface as functions of the spectral data in the Higgs bundle description, which consists of the points of order 2 in an abelian variety. Using…
We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with rigid geometric figures, namely pairs of polygons: one in the…
The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham…
We present a short review of theories based on warped extra dimensions (motivated by the hierarchy problem of the Standard Model) which can accomodate a Higgs boson in the range suggested by the recent LHC results at 7 TeV. Using the…
On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. The moduli spaces of these objects are…