Exact Standard model Structures from Intersecting D5-Branes

TL;DR

The paper constructs non-supersymmetric Standard Model vacua from type IIB orientifolds with D5-branes at angles on $T^4\times(\C/\Z_N)$, showing exact SM content can arise in four-, five-, and six-stack configurations. By embedding these configurations in $Z_3$ quiver diagrams and applying RR tadpole cancellation, the authors map a rich landscape of vacua, including novel reflected quivers, and demonstrate that many five- and six-stack vacua flow to four-stack counterparts via brane recombination. A key finding is that baryon number is gauged and subsequently broken, preserving proton stability, while a two-dimensional transverse space can realize a low string scale $M_s$ in the TeV range. The work also demonstrates a network of equivalences among different quiver constructions, implying continuous connections among seemingly distinct SM vacua and highlighting the role of moduli, scalars, and loop corrections in stabilizing tachyonic directions. Overall, the results provide a comprehensive framework for obtaining exactly the SM at low energies within string theory, with implications for testable TeV-scale phenomenology and proton stability.

Abstract

We discuss the appearance of non-supersymmetric compactifications with exactly the Standard Model (SM) at low energies, in the context of IIB orientifold constructions with D5 branes intersecting at angles on the $T^4$ tori, of the orientifold of $T^4 \times (\C /Z_N)$. We discuss constructions where the Standard Model embedding is considering within four, five and six stacks of D5 branes. The appearance of the three generation observable Standard Model at low energies is accompanied by a gauged baryon number, thus ensuring automatic proton stability. Also, a compatibility with a low scale of order TeV is ensured by having a two dimensional space transverse to all branes. The present models complete the discussion of some recently constructed four stack models of D5 branes with the SM at low energy. By embedding the four, five and six stack Standard Model configurations into quiver diagrams, deforming them around the QCD intersection numbers, we find a rich variety of vacua that may have exactly the Standard Model at low energy. Also by using brane recombination on the U(1)'s, we show that the five and six vacua flow into their four stack counterparts. Thus string vacua with five and six stack deformations are continuously connected to the four stack vacua.

Figures (8)

• Figure 1: Assignment of SM embedding in configurations of four stacks of D5 branes depicted by the 'reflected' $Z_3$ quiver diagrams. At low energy we get only the SM. Note that ${\tilde{\alpha}} = \alpha^{-1}$. These configurations give equivalent vacua, with exactly the SM at low energy, to those vacua coming from the 'image' quivers of figure (2), under the correspondence $a1 \iff Q1$, $a2 \iff Q2$, $a3 \iff Q3$, $a4 \iff Q4$.
• Figure 2: Assignment of SM embedding in configurations of four stacks of D5 branes depicted by $Z_3$ quiver diagrams. At low energy we get only the SM. Note that ${\tilde{\alpha}} = \alpha^{-1}$.
• Figure 3: Assignment of SM embedding in configurations of five stacks of D5 branes depicted by $Z_3$ quiver diagrams. At low energy we get the SM. Note that ${\tilde{\alpha}} = \alpha^{-1}$.
• Figure 4: Assignment of SM embedding in configurations of six stacks of D5 branes depicted in $Z_3$ quiver diagrams; six out of a total of ten quivers. In all the cases we get the SM at low energy. Note that ${\tilde{\alpha}} = \alpha^{-1}$.
• Figure 5: Recombination flow for some of the six-stack quivers. All models flow to four stack SM quivers after recombination.