Related papers: A Note on the Hitchin System in a Background B-fie…

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…

We argue that the hierarchy problem of the standard model of particle physics can be solved by adding a state-dependent term to the Higgs sector. We present an example of a scalar field with a Higgs-like potential with an additional term…

We extend the previous treatment of Liouville theory on the torus, to the general case in which the distribution of charges is not necessarily symmetric. This requires the concept of Fuchsian differential equation on Riemann surfaces. We…

The most commonly used parameterizations of the Yukawa couplings in the two Higgs doublet model are revisited. Their similitudes and differences are emphasized and relations between the different notations used in the literature are…

We argue that identifying the electroweak Higgs particle with the extra components of the gauge field in $4+d$ dimensions provides a solution to the hierarchy problem. The absence of ultraviolate quadratic divergences is due to the fact…

We prove the Strominger--Yau--Zaslow and topological mirror symmetries for parabolic Hitchin systems of types B and C. In contrast to type A, a geometric reinterpretation of Springer duality is necessary. Furthermore, unlike Hitchin's…

We investigate several models described by real scalar fields, searching for topological defects. Some models are described by a single field, and support one or two topological sectors, and others are two-field models, which support…

We study the naturalness problem using a model independent bottom up approach by considering models where only the interaction terms needed to cancel the Higgs quadratic divergences are present. If quadratic divergences are canceled by…

Alternative forms of the solutions to the quantum field equations and their implications for physical theory are considered. Incorporation of these alternative solution forms, herein deemed "supplemental solutions", into the development of…

A two Higgs doublet model with flavorful Yukawa structure, in which the two doublets give mass to the third and the first two generations respectively, is combined with the twin Higgs mechanism to stabilize the Higgs mass against radiative…

The natural cutoff scale for the quadratically divergent top quark contribution to the Higgs mass parameter can be significantly raised above the surprisingly low standard model value, with important consequences for the LHC: the physics…

We classify the first few brane tilings on a genus 2 Riemann surface and identify their toric Calabi-Yau moduli spaces. These brane tilings are extensions of tilings on the 2-torus, which represent one of the largest known classes of 4d N=1…

Singular limits of 6D F-theory compactifications are often captured by T-branes, namely a non-abelian configuration of intersecting 7-branes with a nilpotent matrix of normal deformations. The long distance approximation of such 7-branes is…

The quadratic divergences of the Higgs mass may be cancelled either accidentally or by the exchange of some new particles. Alternatively its impact on naturalness may be weakened by raising the Higgs mass, which requires changing the…

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…

The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin…

We describe how the geometry of the Higgs branch of 5d superconformal field theories is transformed under movement along the extended Coulomb branch. Working directly with the (unitary) magnetic quiver, we demonstrate a correspondence…

In twin Higgs models, a discrete Z2 symmetry between the standard model Higgs and the twin Higgs is introduced to address the hierarchy problem. In this work, we propose another discrete symmetry in twin Higgs: the T parity, which maps the…

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 consider multicenter supergravity solutions corresponding to Higgs phases of supersymmetric Yang-Mills theories with Z_N symmetric vacua. In certain energy regimes, we find a description in terms of a generalized wormhole solution that…