Standard Model at Intersecting D5-branes: Lowering the String Scale

TL;DR

The paper constructs explicit Type IIB orientifold models on $T^4 \times \mathbb{C}/\mathbb{Z}_N$ with intersecting D5-branes at angles that reproduce the Standard Model (and Left-Right extensions) in a non-supersymmetric ($N=0$) bulk. The setup uses O5-planes and twisted RR fields, with anomaly cancellation completed by a generalized Green-Schwarz mechanism, yielding a massless hypercharge while other $U(1)$s become massive. By choosing brane stacks and intersection data, they realize SM-like spectra from bifundamentals and obtain a low string scale $M_s$ (1–10 TeV) made compatible with a large 4D Planck scale $M_p$ via two large transverse dimensions. The models predict extra scalar states and heavy $Z'$-like vectors, while baryon number remains gauged, ensuring proton stability; the work provides concrete D-brane realizations of Low String Scale scenarios with SM fermions and gauge group at low energies. The paper also discusses tachyonic instabilities, electroweak breaking via Higgs doublets from specific intersections, and avenues for further realistic model-building and phenomenology.

Abstract

Recently a class of Type IIA orientifold models was constructed yielding just the fermions of the SM at the intersections of D6-branes wrapping a 6-torus. We generalize that construction to the case of Type IIB compactified on an orientifold of T^4 \times (C/Z_N) with D5-branes intersecting at angles on T^4. We construct explicit models in which the massless fermion spectrum is just the one of a three-generation Standard Model. One of the motivations for these new constructions is that in this case there are 2 dimensions which are transverse to the SM D5-brane configuration. By making those two dimensions large enough one can have a low string scale M_s of order 1-10 TeV and still have a large M_{Planck} in agreement with observations. From this point of view, these are the first explicit D-brane string constructions where one can achieve having just the fermionic spectrum and gauge group of the SM embedded in a Low String Scale scenario. The cancellation of U(1) anomalies turns out to be quite analogous to the toroidal D6-brane case and the proton is automatically stable due to the gauging of baryon number. Unlike the D6-brane case, the present class of models has N = 0 SUSY both in the bulk and on the branes and hence the spectrum is simpler.

Figures (4)

• Figure 1: Intersecting brane world setup. We consider configurations of D5-branes filling four-dimensional Minkowski spacetime, wrapping factorizable 2-cycles of ${\bf T^2 \times T^2}$ and sitting at a singular point of some compact two-dimensional space ${\bf B}_2$. In the figure, two such branes are depicted, with wrapping numbers $(1,2)(1,\frac{3}{2})$ (solid line) and $(1,-1)(1,\frac{1}{2})$ (dashed line). The fractional wrapping numbers arise from a tilted complex structure: $b^{(1)} = 0$, $b^{(2)} = \frac{1}{2}$.
• Figure 2: Quiver diagram of a ${\bf Z}_N$ orbifold singularity. The nodes of such diagram represent the phases associated to each different gauge group in the theory, whereas each arrow represents a chiral fermion transforming in a bifundamental of the two groups it links.
• Figure 4: Four possible embeddings of the brane content of a SM configuration in a ${\bf Z}_3$ quiver.
• Figure 5: Intersecting D5-world set up. The $Z_i$, $i=1,2,3$ represent complex compact dimensions. The D5-branes $a,b,c,d$ (corresponding to the gauge group $U(3)\times U(2)\times U(1)\times U(1)$) wrap cycles on ${\bf T^2\times T^2}$. At the intersections lie quarks and leptons. This system is transverse to a 2-dimensional compact space ${\bf B_2}$ (e.g., ${\bf T^2/Z_N}$) whose volume may be quite large so as to explain $M_p>>M_s$. This would be a D-brane realization of the scenario in ref.aadd.