Mapping an Island in the Landscape

TL;DR

The paper tackles the problem of connecting string theory to particle phenomenology by exhaustively classifying N=1 vacua in Type IIA orientifolds with intersecting D6-branes on T^6/\mathbb{Z}'_6. It develops an explicit algebraic framework to compute the full massless spectrum, including non-chiral states, and proves the solution space is finite. Through large-scale enumeration, it characterizes the distribution of gauge sectors, identifying O(10^15) MSSM-like, O(10^11) Pati-Salam, and smaller SU(5) model classes, while revealing substantial exotics in many cases; nevertheless, a non-negligible subset (~1.3×10^7) achieves zero chiral exotics. The work demonstrates that realistic-like sectors emerge abundantly in the landscape and provides concrete examples and statistical insights that could guide phenomenological model-building and future explorations of string vacua.

Abstract

We provide a complete classification and statistical analysis of all type IIA orientifold compactifications with intersecting D6-branes on the orbifold T^6/Z'_6. The total number of four dimensional N=1 supersymmetric models is found to be O(10^23). After a statistical analysis of the gauge sector properties of all possible solutions, we study three subsets of configurations which contain the chiral matter sector of the standard model, a Pati-Salam or SU(5) GUT model, respectively. We find O(10^15) compactifications with an MSSM and O(10^11) models with a Pati-Salam sector. Along the way we derive an explicit algebraic formulation for the computation of the non-chiral matter spectrum for all Z_N orbifolds.

Figures (10)

• Figure 1: Fixed points of the $T^6/\mathbb{Z}'_6$ orbifold. Circles on $T^2_2 \times T^2_3$ denote fixed points of $\theta$. $T^2_3$ is fixed under $\theta^2$, $T^2_2$ is fixed under $\theta^3$. On $T^2_1$, point 1 is fixed under $\theta$, points 4,5,6 are fixed under $\theta^3$ and points 2,3 are fixed under $\theta^2$. The horizontal radius along $\pi_5 - b \pi_6$ on $T^2_3$ is called $R_1$, the vertical extension along $\pi_6$ is denoted by $R_2$. Both options for an untilted ( a) and tilted ( b) shape of $T^2_3$, parametrised by $b=0,1/2$, are shown.
• Figure 2: Number of pure bulk solutions for the different geometries. The four groups of bars represent the geometry on the first two tori, while the geometry of the third torus is represented by the blue bars on the left ($b=0$) and the red bars on the right ($b=1/2$) in each group.
• Figure 3: Frequency distributions of the total rank of the gauge group for (a) pure bulk solutions and (b) the full set of solutions.
• Figure 4: Frequency distributions of the probability to find a gauge factor of rank $N$ for (a) pure bulk solutions and (b) the full ensemble of solutions.
• Figure 5: Frequency distribution of the total number of solutions for the different geometries. As in Figure \ref{['fig_bulk_num']} the four groups of bars represent the geometry on the first two tori, while the geometry of the third torus is represented by the blue bars on the left ($b=0$) and the red bars on the right ($b=1/2$) in each group.