Related papers: Limiting configurations for the SU(1,2) Hitchin eq…
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).…
We consider several aspects of holomorphic brane configurations. We recently showed that an important part of the defining data of such a configuration is the gluing morphism, which specifies how the constituents of a configuration are…
We prove a Hitchin-Kobayashi correspondence for extensions of Higgs bundles. The results generalize known results for extensions of holomorphic bundles. Using Simpson's methods, we construct moduli spaces of stable objects. In an appendix…
Following the work of Mazzeo-Swoboda-Weiss-Witt and Mochizuki, there is a map $\overline{\Xi}$ between the algebraic compactification of the Dolbeault moduli space of $\mathsf{SL}(2,\mathbb{C})$ Higgs bundles on a smooth projective curve…
In 1992, Hitchin used his theory of Higgs bundles to construct an important family of representations of the fundamental group of a closed, oriented surface of genus at least two into the split real form of a complex adjoint simple Lie…
We update the constraints on two-Higgs-doublet models (2HDMs) focusing on the parameter space relevant to explain the present muon $g$$-$$2$ anomaly, $\Delta a_{\mu}$, in four different types of models, type I, II, "lepton specific" (or X)…
We present a comprehensive analysis of the Higgs boson spectra in several versions of the supersymmetric left--right model based on the gauge symmetry $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. A variety of symmetry breaking…
We present a fit to the 2012 LHC Higgs data in different supersymmetric frameworks using naturalness as a guiding principle. We consider the MSSM and its D-term and F-term extensions that can raise the tree-level Higgs mass. When adding an…
Performing a fit to all publicly available data, we analyze the extent to which the latest results from the LHC and Tevatron constrain the couplings of the Higgs boson-like state at ~ 125 GeV. To this end we assume that only Standard Model…
Let T be the one-dimensional complex torus. We consider the action of an automorphism of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed…
With the deeper study of Higgs particle, Higgs precision measurements can be served to probe new physics indirectly. In many new physics models, vector-like quarks $T_L,~T_R$ occur naturally. It is important to probe their couplings with…
In this paper, motivated by the recent discovery of a Higgs-like boson at the LHC with a mass m_H\simeq 126 GeV, we review different models where the hierarchy problem is solved by means of a warped extra dimension. In the Randall-Sundrum…
Let $M$ be a compact complex manifold equipped with a Gauduchon metric. If $TM$ is holomorphically trivial, and (V, \theta) is a stable SL(r,{\mathbb C})-Higgs bundle on $M$, then we show that $\theta= 0$. We show that the correspondence…
We study an extension of the Minimal Supersymmetric Standard Model with a gauge group $SU(2)_1\otimes SU(2)_2$ breaking to $SU(2)_L$. The extra wino has an enhanced gauge coupling to the SM-like Higgs boson and, if light, has a relevant…
This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space on a compact Riemann surface. Motivated by mirror symmetry, we give a detailed description of the fibres of the $G$-Hitchin fibration containing…
We study the scalar Higgs sector of the next-to-minimal supersymmetric standard model with an extra U(1), which has two Higgs doublets and a Higgs singlet, in the light leptophobic $Z'$ scenario where the extra neutral gauge boson $Z'$ does…
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the…
We study the properties of heavy fermions in the vector-like representation of the electro-weak gauge group $SU(2)_W\times U(1)_Y$ with Yukawa couplings to the standard model (SM) Higgs boson. Using the renormalization group analysis, we…
We study the cameral and spectral data for the moduli space of polystable $\mathrm{SU}(p+1,p)$-Higgs bundles and deduce the latter from the former. As an application, we obtain that the Toledo invariant classifies the connected components…
A gauge theoretic description of the Morgan-Shalen compactification of the $\SL$ character variety of the fundamental group of a hyperbolic surface is given in terms of a natural compactification of the moduli space of Higgs bundles via the…