TeV-Scale Z' Bosons from D-branes

Generic D-brane string models of particle physics predict the existence of extra U(1) gauge symmetries beyond hypercharge. These symmetries are not of the E_6 class but rather include the gauging of Baryon and Lepton numbers as well as certain Peccei-Quinn-like symmetries. Some of the U(1)'s have triangle anomalies, but they are cancelled by a Green-Schwarz mechanism. The corresponding gauge bosons typically acquire a mass of order the string scale M_S by combining with two-index antisymmetric fields coming from the closed string sector of the theory. We argue that in string models with a low string scale M_S proportional to 1-10 TeV, the presence of these generic U(1)'s may be amenable to experimental test. Present constraints from electroweak precision data already set important bounds on the mass of these extra gauge bosons. In particular, for large classes of models, rho-parameter constraints imply M_S >= 1.5 TeV. In the present scheme some fraction of the experimentally measured Z^0 mass would be due not to the Higgs mechanism, but rather to the mixing with these closed string fields. We give explicit formulae for recently constructed classes of intersecting D6- and D5-brane models yielding the Standard Model (SM) fermion spectrum.Comment: 46 pages, LaTeX, JHEP.cls, 21 Figures. minor correction

SUSY Quivers, Intersecting Branes and the Modest Hierarchy Problem

We present a class of chiral non-supersymmetric D=4 field theories in which quadratic divergences appear only at two loops. They may be depicted as ``SUSY quivers'' in which the nodes represent a gauge group with extended e.g., N=4 SUSY whereas links represent bifundamental matter fields which transform as chiral multiplets with respect to different N=1 subgroups. One can obtain this type of field theories from simple D6-brane configurations on Type IIA string theory compactified on a six-torus. We discuss the conditions under which this kind of structure is obtained from D6-brane intersections. We also discuss some aspects of the effective low-energy field theory. In particular we compute gauge couplings and Fayet-Iliopoulos terms from the Born-Infeld action and show how they match the field theory results. This class of theories may be of phenomenological interest in order to understand the modest hierarchy problem i.e., the stability of the hierarchy between the weak scale and a fundamental scale of order 10-100 TeV which appears e.g. in low string scale models. Specific D-brane models with the spectrum of the SUSY Standard Model and three generations are presented.Comment: 36 pages, using JHEP3.cls, 8 figures. References update

Intersecting Brane Models of Particle Physics and the Higgs Mechanism

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-supersymmetric models of the type introduced in hep-th/0201205 which may be depicted in terms of SUSY-quivers and may stabilize the hierarchy between the weak scale and a fundamental scale of order 10-100 TeV present in low string scale models. Several explicit D6-brane models with three generations of quarks and leptons and different SUSY-quiver structure are presented. One can prove on general grounds that if one wants to build a (factorizable) D6-brane configuration with the SM gauge group and N = 1 SUSY (or quasi-SUSY), also a massless (B-L) generator must be initially present in any model. If in addition we insist on lef- and right-handed fermions respecting the same N=1 SUSY, the brane configurations are forced to have intersections giving rise to Higgs multiplets, providing for a rationale for the very existence of the SM Higgs sector.Comment: 58 pages, using JHEP3.cls, 13 figures. Minor corrections and references update

Yukawa couplings in intersecting D-brane models

We compute the Yukawa couplings among chiral fields in toroidal Type II compactifications with wrapping D6-branes intersecting at angles. Those models can yield realistic standard model spectrum living at the intersections. The Yukawa couplings depend both on the Kahler and open string moduli but not on the complex structure. They arise from worldsheet instanton corrections and are found to be given by products of complex Jacobi theta functions with characteristics. The Yukawa couplings for a particular intersecting brane configuration yielding the chiral spectrum of the MSSM are computed as an example. We also show how our methods can be extended to compute Yukawa couplings on certain classes of elliptically fibered CY manifolds which are mirror to complex cones over del Pezzo surfaces. We find that the Yukawa couplings in intersecting D6-brane models have a mathematical interpretation in the context of homological mirror symmetry. In particular, the computation of such Yukawa couplings is related to the construction of Fukaya's category in a generic symplectic manifold.Comment: 47 pages, using JHEP3.cls, 11 figures. Typos and other minor corrections. References adde