Geometry of Particle Physics

By reinterpreting the familiar tools and ideas of M-theory model building, we show how a G2-manifold locally engineered to give rise to massless matter representations of an SU(5) grand unified model can be smoothly unfolded into a G2-manifold giving rise to SU(3)xSU(2) gauge theory with the corresponding matter representations. These ideas could lead to new insights in string phenomenology because much of the arbitrariness of M-theory model building can be removed by supposi...

We construct four dimensional three generation non-supersymmetric $SU(3)_c \times SU(2)_L \times U(1)_Y$ intersecting D6-brane models with $\nu_R$\rq{s}. At three stacks we find exactly the MSSM chiral fermion matter spectrum. At 4-, 5-stacks we find models with the massless fermion spectrum of the N=1 Standard Model and massive exotic non-chiral matter; these models flow also to only the SM. At 8-stacks we find MSSM-like models, with minimal massless exotics, made from two d...

We analyze a recently constructed class of D-brane theories with the fermion spectrum of the SM at the intersection of D6-branes wrapping a compact toroidal space. We show how the SM Higgs mechanism appears as a brane recombination effect in which the branes giving rise to U(2)_L \times U(1) recombine into a single brane related to U(1)_{em}. We also show how one can construct D6-brane models which respect some supersymmetry at every intersection. These are quasi-supersymmetr...

We investigate supersymmetric SU(5) grand-unified theories (GUTs) realized in 5 space-time dimensions and broken down to the MSSM by SU(5)-violating boundary conditions on a S^1/(Z_2 x Z_2') orbifold with two 3-branes. The doublet-triplet splitting problem is entirely avoided by locating the MSSM Higgs doublets on the brane on which SU(5) is not a good symmetry. An extremely simple model is then described in which the MSSM matter is also located on this SU(5)-violating brane....

Intersecting D-brane models seem to be one of the most promising avenues to embed the Standard Model physics within the string context. We review here different aspects of these models. Topics include the question of SUSY and quasi-SUSY in intersecting brane models, model-building, the brane recombination interpretation of the SM Higgs mechanism, Yukawa couplings, the lowering of the string scale and possible new Z's accessible to accelerators.

We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale supersymmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo $n$ ($dP_n$) singularities including both D3 and D7 branes. We provide supersymmetric examples with three quark/lepton families and the gau...

We study various aspects of N=2 quiver-Chern-Simons theories, conjectured to be dual to M2-branes at toric Calabi-Yau four-fold singularities, under Higgsing. In particular we study in detail the orbifold C^4/Z_2^3, obtaining a number of different quiver-Chern-Simons phases for this model, and all 18 toric partial resolutions thereof. In the process we develop a general un-Higgsing algorithm that allows one to construct quiver-Chern-Simons theories by blowing up, thus obtaini...

In the first part of the review article, we discuss the possibility of realizing "mu-split-like SUSY" scenario from a phenomenological model, which we show could be realizable locally as the large volume limit of a type IIB Swiss-Cheese Calabi-Yau orientifold involving a mobile space-time filling D3-brane localized at a nearly special Lagrangian three-cycle embedded in the "big" divisor and multiple fluxed stacks of space-time filling D7-branes wrapping the same "big" divisor...

We study brane configurations in the presence of orientifold six-planes. After deriving the curves for N=2 supersymmetric SU(Nc) gauge theories with one flavor in the symmetric or antisymmetric representation and Nf fundamental flavors, we rotate the brane configuration, reducing the supersymmetry to N=1. For the case of an antisymmetric flavor and less than two fundamental flavors, nonperturbative effects lead to a brane configuration that is topologically a torus. Using the...

We initiate a systematic study of 2d (0,2) quiver gauge theories on the worldvolume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theor...