Geometry of Particle Physics

Recent scenarios of phenomenologically realistic string compactifications involve the existence of gauge sectors localized on D-branes at singular points of Calabi-Yau threefolds. The spectrum and interactions in these gauge sectors are determined by the local geometry of the singularity, and can be encoded in quiver diagrams. We discuss the physical models arising for the simplest case of orbifold singularities, and generalize to non-orbifold singularities and orientifold si...

We argue that the Standard Model quiver can be embedded into compact Calabi-Yau geometries through orientifolded D3-branes at del Pezzo singularities $\mathrm{dP}_n$ with $n\geq 5$ in a framework including moduli stabilisation. To illustrate our approach, we explicitly construct a local $\mathrm{dP}_{5}$ model via a combination of Higgsing and orientifolding. This procedure reduces the original $\mathrm{dP}_{5}$ quiver gauge theory to the Left-Right symmetric model with three...

We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation) into so-called symplectic leaves, which are related to each other by transverse slices. We identify this foliation with the pattern of partial Higgs mechanism of the theory and, using brane systems and recently introduced notions of magnetic quivers and quiver subtr...

This paper discusses the minimal quiver gauge theory embedding of the standard model that could arise from brane world type string theory constructions. It is based on the low energy effective field theory of D-branes in the perturbative regime. The model differs from the standard model by the addition of one extra massive gauge boson, and contains only one additional parameter to the standard model: the mass of this new particle. The coupling of this new particle to the stan...

In this note we explore the possibility of obtaining gauge bosons and fermionic spectrum as close as possible to the Standard Model content, by placing D3-branes at a ZN orbifold-like singularity in the presence of D7-branes. Indeed, we find that this is plausible provided a sufficiently high N is allowed for and the singular point is also fixed by an orientifold action. If extra charged matter is not permitted then the singularity should necessarily be non-supersymmetric. Co...

In this paper we present simplifying techniques which allow one to compute the quiver diagrams for various D-branes at (non-Abelian) orbifold singularities with and without discrete torsion. The main idea behind the construction is to take the orbifold of an orbifold. Many interesting discrete groups fit into an exact sequence $N\to G\to G/N$. As such, the orbifold $M/G$ is easier to compute as $(M/N)/(G/N)$ and we present graphical rules which allow fast computation given th...

We construct three quasi-supersymmetric $G^3$ GUT models with $S_3$ symmetry and gauge coupling unification from intersecting D6-branes on Type IIA orientifolds. The Standard Model fermions and Higgs doublets can be embedded into the bifundamental representations in these models, and there is no any other unnecessary massless representation. Especially in Model I with gauge group $U(4)^3$, we just have three-family SM fermions and three pairs of Higgs particles. The $G^3$ gau...

We present a class of supersymmetric models in which the lightest Higgs-boson mass can be as large as a few hundred GeV (200 - 300 GeV) while the successful MSSM prediction for gauge coupling unification is preserved. The theories are formulated on a 5D warped space truncated by two branes, and a part of the Higgs sector is localized on the infrared brane. The structure of the Higgs sector in the four dimensional effective theory below the Kaluza-Klein mass scale is essential...

Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories, representation theory, and algebraic geometry. The questions originate from the study of supersymmetric gauge theories in different dimensions with different supersymmetries. Although these constitute merely the tip of a vast iceberg, we hope th...

Recently we proposed a TeV-scale Supersymmetric Standard Model in which the gauge coupling unification is as precise (at one loop) as in the MSSM, and occurs in the TeV range. One of the key ingredients of this model is the presence of new states neutral under $SU(3)_c\otimes SU(2)_w$ but charged under $U(1)_Y$ whose mass scale is around that of the electroweak Higgs doublets. In this paper we show that introduction of these states allows to gauge novel anomaly free discrete ...