The Spectra of Heterotic Standard Model Vacua

Abstract

A formalism for determining the massless spectrum of a class of realistic heterotic string vacua is presented. These vacua, which consist of SU(5) holomorphic bundles on torus-fibered Calabi-Yau threefolds with fundamental group Z_2, lead to low energy theories with standard model gauge group (SU(3)_C x SU(2)_L x U(1)_Y)/Z_6 and three families of quarks and leptons. A methodology for determining the sheaf cohomology of these bundles and the representation of Z_2 on each cohomology group is given. Combining these results with the action of a Z_2 Wilson line, we compute, tabulate and discuss the massless spectrum.

Figures (3)

• Figure 1: A special rational elliptic surface $B$. It has 8 $I_1$ singular fibers. In addition, there are 2 $I_2$ fibers $f_1 = n_1 \cup o_1$ and $f_2 = n_2 \cup o_2$. Under the involution $\tau_B = t_\xi \circ \alpha_B$, there are 4 fixed points, which we have marked, on the fiber $f_\infty$.
• Figure 2: The Calabi-Yau threefold $\tilde{X}$ is constructed as the fiber product over $\mathbb{P}^1$ of two non-generic $dP_9$ surfaces $B$ and $B'$. We have matched the fibers $f_0$ and $f_\infty$ of $B$ with the fibers $f'_\infty$ and $f'_0$ of $B'$ respectively. The image points in $\mathbb{P}^1$ of these fibers, namely $0$ and $\infty$ for $B$ and $0'$ and $\infty'$ for $B'$, are identified as $0 = \infty'$ and $\infty = 0'$.
• Figure 3: The structure of the vector bundles $V_i$, $i=2,3$.