Related papers: Higgs bundles and applications
Given a smooth complex projective variety $M$ and a smooth closed curve $X \subset M$ such that the homomorphism of fundamental groups $\pi_1(X) \rightarrow \pi_1(M)$ is surjective, we study the restriction map of Higgs bundles, namely from…
We examine some of the theoretical and phenomenological implications of the Higgs boson discovery and discuss what these imply for future Higgs studies at the LHC and future colliders. In particular, one of the outstanding unanswered…
In this paper we continue our study on the moduli spaces of flat G-bundles, for any semi-simple Lie group G, over a Riemann surface by using heat kernel and Reidemeister torsion. Formulas for intersection numbers on the moduli spaces over a…
We summarize the results presented in the `Physics at large p_T^2 and Q^2' working group at the DIS'2002 Workshop. Higgs searches, precision measurements as well as searches for physics beyond the Standard Model at current and future…
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.
These notes form part of a lecture course on gauge theory. The material covered is standard in the physics literature, but perhaps less well-known to mathematicians. The purpose of these notes is to make spontaneous symmetry breaking and…
A brief overview is given of the theory of Higgs bosons and electroweak symmetry breaking that is relevant for the Higgs physics program at the Linear Collider.
This is a summary of the workshop A.6 on Alternative Theories of Gravity, prepared for the proceedings for the GR15 conference.
The variety of ideas put forward in the context of a "composite" picture for the Higgs boson calls for a simple and effective description of the related phenomenology. Such a description is given here by means of a "minimal" model and is…
This document presents an interim framework in which the coupling structure of a Higgs-like particle can be studied. After discussing different options and approximations, recommendations on specific benchmark parametrizations to be used to…
We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As applications, we deduce a closed formula for the…
These notes partly touch the topic of the talk given by the author at the XXXVIII Workshop on Geometric Methods in Physics, hold in June-July 2019 in Bia\l{}owie\.{z}a, Poland. They consist of a short and self-contained introduction to the…
In this article, we investigate a weakened version of the spectral correspondence for twisted Higgs bundles. Namely, we construct twisted Higgs bundles from a finite covering map and a vector bundle on that covering but without requiring…
We establish a Kobayashi-Hitchin correspondence between solutions of the extended Bogomolny equation with a Dirac type singularity and Hecke modifications of Higgs bundles. This correspondence was conjectured by Witten and plays an…
We study the summands of the decomposition theorem for the Hitchin system for $\mathrm{GL}_n$, in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology…
These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…
This discovery of the Higgs boson last year has created new possibilities for testing candidate theories for explaining physics beyond the Standard Model. Here we explain the ways in which new physics can leave its marks in the experimental…
We extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold solutions of the Yang-Mills-Higgs equations and construct…
This document summarises the current theoretical and experimental status of the di-Higgs boson production searches, and of the direct and indirect constraints on the Higgs boson self-coupling, with the wish to serve as a useful guide for…
We present preliminary results of the first convergent global fits of several minimal composite Higgs models. Our fits are performed using the differential evolution optimisation package $\texttt{Diver}$. A variety of physical constraints…