Towards a Systematic Construction of Realistic D-brane Models on a del Pezzo Singularity

TL;DR

This paper develops a systematic method for constructing realistic D-brane models on toric del Pezzo singularities, leading to models with Standard Model features, realistic mass hierarchies, flavor mixing, and gauge coupling unification.

Contribution

It introduces a systematic approach to build local string models with realistic particle spectra, hierarchies, and flavor mixing, focusing on toric del Pezzo singularities and Pati-Salam extensions.

Findings

Constructed a supersymmetric local string model with MSSM spectrum and realistic flavor mixing.

Achieved gauge coupling unification at high energies with suppressed proton decay operators.

Demonstrated the generation of neutrino masses via see-saw mechanism and R-parity violation.

Abstract

A systematic approach is followed in order to identify realistic D-brane models at toric del Pezzo singularities. Requiring quark and lepton spectrum and Yukawas from D3 branes and massless hypercharge, we are led to Pati-Salam extensions of the Standard Model. Hierarchies of masses, flavour mixings and control of couplings select higher order del Pezzo singularities, minimising the Higgs sector prefers toric del Pezzos with dP3 providing the most successful compromise. Then a supersymmetric local string model is presented with the following properties at low energies: (i) the MSSM spectrum plus a local B-L gauge field or additional Higgs fields depending on the breaking pattern, (ii) a realistic hierarchy of quark and lepton masses and (iii) realistic flavour mixing between quark and lepton families with computable CKM and PMNS matrices, and CP violation consistent with observations. In this construction, kinetic terms are diagonal and under calculational control suppressing standard FCNC contributions. Proton decay operators of dimension 4, 5, 6 are suppressed, and gauge couplings can unify depending on the breaking scales from string scales at energies in the range 10^{12}-10^{16} GeV, consistent with TeV soft-masses from moduli mediated supersymmetry breaking. The GUT scale model corresponds to D3 branes at dP3 with two copies of the Pati-Salam gauge symmetry SU(4)\timesSU(2)R\timesSU(2)L. D-brane instantons generate a non-vanishing mu-term. Right handed sneutrinos can break the B-L symmetry and induce a see-saw mechanism of neutrino masses and R-parity violating operators with observable low-energy implications.