Jumping spectra and vanishing couplings in heterotic Line Bundle Standard Models

Abstract

We study two aspects of the physics of heterotic Line Bundle Standard Models on smooth Calabi-Yau threefolds. First, we investigate to what degree modern moduli stabilization scenarios can affect the standard model spectrum in such compactifications. Specifically, we look at the case where some of the complex structure moduli are fixed by a choice of hidden sector bundle. In this context, we study the frequency with which the system tends to be forced to a point in moduli space where the cohomology groups determining the spectrum in the standard model sector jump in dimension. Second, we investigate to what degree couplings, that are permitted by all of the obvious symmetries of the theory, actually vanish due to certain topological constraints associated to their higher dimensional origins. We find that both effects are prevalent within the data set of heterotic Line Bundle Standard Models studied.

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

“…That is, the Yukawa coupling is a trilinear mapping (essentially a cup product composed with an anti-symmetrization) which takes three copies of the cohomologies associated with the families to a complex number. What has been observed in the literature is that the expressions (1.1) and (1.2) frequently lead to vanishing couplings upon direct computation, even in cases where no obvious symmetry is present that would forbid the associated term in the superpotential (as just some examples of this see [1,2,12,13,36]). There are two possibilities given the existence, and relative ubiquity [36], of such vanishing Yukawa couplings.…”

Heterotic complex structure moduli stabilization for elliptically fibered Calabi-Yau manifolds

“…The usual stabilization scenario of complex structure moduli by rank two vector bundles [14,16] translates to whether the coefficients of the spectral cover equation exists globally. Therefore one may generalize this type of stabilization to vector bundles of arbitrary ranks simply by asking if a holomorphic vector bundle with the Chern character ch(V ) = n + ση + ω[f ] is given, then does the divisor [S] = nσ + η have global section everywhere in the complex structure moduli?…”

“…Therefore, when we move to a generic point in the complex structure moduli where there are no jumps in a 2 and a 0 , the G 4 flux constructed above "disappears" i.e., G 4 becomes non-holomorphic, which by the Gukov-Vafa-Witten superpotential makes the corresponding complex structure deformation massive. 16 Type II. In this case, the spectral cover is smooth, and as explained in subsection 3.2, after the complex structure deformation, the spectral cover is not algebraic anymore.…”

“…Fluctuations of the complex structure and Kähler form of the base manifold and fluctuations of the bundle appear as moduli particles in the effective theory. Holomorphicity of the bundle has been used to stabilize the complex structure moduli in these models [12][13][14][15][16]. The idea is that only some of the deformations of the complex structure are consistent with the supersymmetry.…”

Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory

“…The moduli dependence and the possibility of jumps in the massless spectrum have been first discussed in the context of heterotic string theory in [1][2][3][4][5][6]. More recently, the complex structure moduli dependence of the cohomology dimensions has been studied in [7,8] and [9] in the context of instanton and perturbative superpotential terms, respectively.…”