Intersecting Brane Worlds

TL;DR

Intersecting Brane Worlds develops a string-theoretic framework in which different SM gauge interactions live on intersecting D4-brane stacks, with chiral fermions localized at brane intersections. Yields natural family replication from multiple intersections and hierarchical Yukawas from worldsheet areas via $Y_{ijk} \sim e^{-A_{ijk}}$, enabling realistic textures at a potentially low string scale $M_s \sim 1$–$10$ TeV. Proton stability is ensured by discrete worldsheet selection rules, while new low-energy excitations such as KK and winding gauge bosons and gonions—stringy states tied to brane angles—provide distinctive collider signatures and phenomenology between the weak and string scales. The paper backs these ideas with explicit D4-brane constructions on $T^2 \times (T^2)^2/\mathbf{Z}_N$ that realize three-family spectra, examine gauge coupling relations from geometry, and discuss electroweak symmetry breaking via tachyonic Higgs-like states. Together, these results offer a concrete, testable alternative to SUSY scenarios in the search for TeV-scale string physics.

Abstract

It is known that chiral fermions naturally appear at certain intersections of branes at angles. Motivated by this fact, we propose a string scenario in which different standard model gauge interactions propagate on different (intersecting) brane worlds, partially wrapped in the extra dimensions. Quarks and leptons live at brane intersections, and are thus located at different positions in the extra dimensions. Replication of families follows naturally from the fact that the branes generically intersect at several points. Gauge and Yukawa couplings can be computed in terms of the compactification radii. Hierarchical Yukawa couplings appear naturally, since amplitudes involving three different intersections are proportional to exp{-A_{ijk}}, where A_{ijk} is the area of a string world-sheet extending among the intersections. The models are non-supersymmetric but the string scale may be lowered down to 1-10 TeV. The proton is however stable due to a set of discrete symmetries arising from world-sheet selection rules, exact to all orders in perturbation theory. The scenario has some distinctive features like the presence of KK, winding and other new excited states (`gonions'), with masses below the string scale and accessible to accelerators. The models contain scalar tachyons with the quantum numbers of standard SU(2) x U(1) Higgs doublets, and we propose that they induce electroweak symmetry breaking in a somewhat novel way. Specific string models with D4-branes wrapping on T^2 x (T^2)^2/Z_N, leading to three-family semirealistic spectra, are presented, in which the above properties are exemplified.

Figures (6)

• Figure 1: A simplified picture of the intersecting brane world scenario. Each gauge interaction propagates along a D-brane with four flat dimensions (not shown in the figure), and partially wrapped on a cycle in the internal space parameterized by $X_4$, $X_5$ (a two-torus in our models). All branes are transverse to the space parameterized by $X_6$, $X_7$, $X_8$, $X_9$. Chiral fermions, such as quarks and leptons, are localized at the intersections of the wrapped branes (for simplicity, we have shown only one such intersection, even though generically multiple intersection points exist).
• Figure 2: D4-branes wrapping on a two-torus yielding a three-generation $SU(3)\times SU(2)_L\times SU(2)_R\times U(1)$ model, example 1. Gauge bosons propagate along one world-volume internal dimension, depicted as lines. Quarks and leptons, appearing in three copies, are located at the intersection points of different pairs of branes.
• Figure 3: D4-branes wrapping on a torus yielding a three-generation standard model, example 2. Gauge bosons propagate along the lines, which indicate the wrapped D4-brane world-volumes. Quarks and leptons are however localized at the intersection points among the different branes. The vertical $U(1)$ brane is wrapped three times along the depicted cycles, hence leads to three (coincident) intersections with each of the remaining branes.
• Figure 4: The $SU(3)\times SU(2)_L\times SU(2)_R\times U(1)$ model of Fig. \ref{['phen1']}. Several torus fundamental domains are shown to highlight the relative size of the different Yukawa couplings. To avoid clutter, we do not show all the copies of the branes. Also, we only highlight the Yukawa couplings involving the Higgs field $H_3$, hence do not show other fields living at the relevant intersections. World-sheets giving rise to quark (lepton) Yukawa couplings correspond to triangles with one vertex ($H_3$) containing the Higgs and other two vertices $Q_L^i,Q_R^i$ ($L^i,R^i$) containing the quarks (leptons).
• Figure 5: A standard model-like configuration obtained from that in Fig. \ref{['inter17']} by splitting the $SU(2)_R$ D4-branes into two parallel $U(1)$-branes. Now the size of the triangles corresponding to u- and d-quark Yukawa couplings are different.