The Higgs boson of the Standard Model

An introduction is made to the key concepts of gauge invariance and spontaneous symmetry breaking which are the foundations of the Standard Model of particle physics. A new scalar field corresponding to a spin-0 particle, the Higgs boson, is a necessary consequence of this model. Properties of the Higgs boson are constrained; however, its mass is not. Searches using LEP have been both unique, intense, and also efficient: the Standard Model Higgs boson must be heavier than 114 GeV$/{\mathrm{c}}^2$. A hint of a signal was obtained at 115 GeV$/{\mathrm{c}}^2$, but will have to be confirmed (or falsified) by forthcoming experiments at the Tevatron and LHC. To cite this article: M. Davier, C. R. Physique 8 (2007).     

E7(7) symmetry and dual gauge algebra of M-theory on a twisted seven-torus

We consider M-theory compactified on a twisted 7-torus with fluxes when all the seven antisymmetric tensor fields in four dimensions have been dualized into scalars and thus the ${\mathrm{E}}_{7(7)}$ symmetry is recovered. We find that the Scherk–Schwarz and flux gaugings define a “dual” gauge algebra, subalgbra of ${\mathrm{E}}_{7(7)}$, where some of the generators are associated with vector fields which are dual to part of the original vector fields (deriving from the 3-form). In particular they are dual to those vector fields which have been “eaten” by the antisymmetric tensors in the original theory by the (anti-)Higgs mechanism. The dual gauge algebra coincides with the original gauge structure when the quotient with respect to these dual (broken) gauge generators is taken. The particular example of the S–S twist corresponding to a “flat group” is considered.     

On the magical supergravities in six dimensions

Magical supergravities are a very special class of supergravity theories whose symmetries and matter content in various dimensions correspond to symmetries and underlying algebraic structures of the remarkable geometries of the Magic Square of Freudenthal, Rozenfeld and Tits. These symmetry groups include the exceptional groups and some of their special subgroups. In this paper, we study the general gaugings of these theories in six dimensions which lead to new couplings between vector and tensor fields. We show that in the absence of hypermultiplet couplings the gauge group is uniquely determined by a maximal set of commuting translations within the isometry group SO(nT,1)$\mathit{SO}(n_T,1)$ of the tensor multiplet sector. Moreover, we find that in general the gauge algebra allows for central charges that may have nontrivial action on the hypermultiplet scalars. We determine the new minimal couplings, Yukawa couplings and the scalar potential.     

Naturally massless Higgs doublets in supersymmetric SU(5)

We construct a supersymmetric SU(5) model characterized by: (a) naturally massless doublet Higgs superfields; (b) the natural appearance of “light” coloured triplet Higgses of mass of the order 10¹⁰ GeV, and study proton decay as well as the generation of cosmic baryon asymmetry. We find that an appropriate choice of Higgs sector renders dimension-five operators kinematically irrelevant for the stability of the proton. Proton decay proceeds through Higgs boson exchange in terms of dimension-six operators mainly to ${\overline{v}}_{\mu }{K}^{+},v^{+}{K}^0$.     

Mesons and Higgs branch in defect theories

We consider the defect theory obtained by intersecting D3- and D5-branes along two common spatial directions. We work in the approximation in which the D5-brane is a probe in the AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ background. By adding worldvolume flux to the D5-brane and choosing an appropriate embedding of the probe in AdS₅×S⁵${\mathit{AdS}}_5\times S^5$, one gets a supersymmetric configuration in which some of the D3-branes recombine with the D5-brane. We check this fact by showing that the D5-brane can be regarded as a system of polarized D3-branes. On the field theory side this corresponds to the Higgs branch of the defect theory, where some of the fundamental hypermultiplet fields living on the intersection acquire a vacuum expectation value. We study the spectrum of mesonic bound states of the defect theory in this Higgs branch and show that it is continuous and gapless.     

The improved tensor multiplet in N = 2 supergravity

We construct a scale-invariant action for the N = 2 tensor multiplet which can be coupled to conformal supergravity. In spite of its non-polynomial form the action describes a free massless hypermultiplet. When used as a compensating multiplet it leads to a new minimal formulation of N = 2 Poincaré or de Sitter supergravity. We discuss its consequences and present a comparison with previous off-shell formulations.     

Topological phase transitions in Calabi‐Yau compactifications of M‐theory

In this thesis we construct five‐dimensional gauged supergravity actions which describe flop and conifold transitions in M‐theory compactified on Calabi‐Yau threefolds. While the vector multiplet sector is determined exactly, we use the Wolf spaces to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of M2‐branes. After specifying the hypermultiplet sector the actions are uniquely determined by M‐theory. As an application we consider five‐dimensional Kasner cosmologies. Including the dynamics of the winding modes, we find smooth cosmological solutions which undergo flop and conifold transitions. Instead of the usual runaway behavior the scalar fields of these solutions generically stabilize in the transition region where they oscillate around the transition locus. The scalar potential thereby induces short episodes of accelerated expansion in the space‐time.     

Sasakian and Parabolic Higgs Bundles

Let M be a quasi-regular compact connected Sasakian manifold, and let N = M/S ¹ be the base projective variety. We establish an equivalence between the class of Sasakian G–Higgs bundles over M and the class of parabolic (or equivalently, ramified) G–Higgs bundles over the base N.     

Vortices and the Abel–Jacobi map

The abelian Higgs model on a compact Riemann surface $\Sigma$ supports vortex solutions for any positive vortex number $d\in \mathbb{Z}$. Moreover, the vortex moduli space for fixed $d$ has long been known to be the symmetrized $d$-th power of $\Sigma$, in symbols, ${\mathrm{Sym}}^d\left(\Sigma \right)$. This moduli space is Kähler with respect to the physically motivated metric whose geodesics describe slow vortex motion.In this paper we appeal to classical properties of ${\mathrm{Sym}}^d\left(\Sigma \right)$ to obtain new results for the moduli space metric. Our main tool is the Abel–Jacobi map, which maps ${\mathrm{Sym}}^d\left(\Sigma \right)$ into the Jacobian of $\Sigma$. Fibres of the Abel–Jacobi map are complex projective spaces, and the first theorem we prove states that near the Bradlow limit the moduli space metric restricted to these fibres is a multiple of the Fubini–Study metric. Additional significance is given to the fibres of the Abel–Jacobi map by our second result: we show that if $\Sigma$ is a hyperelliptic surface, there exist two special fibres which are geodesic submanifolds of the moduli space. Even more is true: the Abel–Jacobi map has a number of fibres which contain complex projective subspaces that are geodesic.     

Higgs production in gluon fusion beyond NNLO

We construct an approximate expression for the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order (N³LO) in _αs${\alpha }_s$ with finite top mass. We argue that an accurate approximation can be constructed by exploiting the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummation. We support our argument with an explicit comparison of the approximate and the exact expressions up to the highest (NNLO) order at which the latter are available. We find that the approximate N³LO result amounts to a correction of 17%$17\text{\%}$ to the NNLO QCD cross section for production of a 125 GeV Higgs at the LHC (8 TeV), larger than previously estimated, and it significantly reduces the scale dependence of the NNLO result.     

Matter coupling and non-linear σ-models in N = 2 supergravity

Starting from an off-shell formulation of N = 2 supergravity, we construct the matter multiplet in its complex form (the scalar hypermultiplet) and in its real form. We construct the matter action which describes the coupling to supergravity. The interpretation where the 32 + 32 field components of the minimal gravitational multiplet are independent dynamical variables is known to be inconsistent for pure supergravity. We find it to be consistent when coupled to at least one matter multiplet, and to give rise to supersymmetric σ-models when coupled to at least two matter multiplets.