Moduli and Hidden Matter in Heterotic M-Theory with an Anomalous $U(1)$ Hidden Sector

Abstract

This paper discusses the dilaton, Kähler moduli and hidden sector matter chiral superfields of heterotic M -theory vacua in which the hidden sector gauge bundle is chosen to be a line bundle with an anomalous U(1) structure group. For simplicity of notation, the theory is compactified on a Calabi-Yau threefold with h 1,1 = 1, although all methods and results apply to more general heterotic compactifications. After introducing a non-perturbative F -term potential and coupling to supergravity, the canonically normalized scalar and fermion mass eigenstates, evaluated around a fixed supersymmetry breaking vacuum, are computed and the explicit expressions for their masses presented. In addition, the relevant couplings of these eigenstates to themselves and to chiral matter in the observable sector are evaluated. The decay rates of generic observable sector scalars into both moduli and hidden sector matter scalars and fermions are then presented. This opens the door to explicit calculations of the decay of an observable sector cosmological inflaton into moduli and hidden sector dark matter candidates. Finally, an explicit flux and gaugino condensate induced nonperturbative superpotential is introduced which is shown to stabilize three of the four real components of the moduli fields.

FIMP Dark Matter in Heterotic M-Theory

“…The moduli metrics are g S S = ∂ S ∂ S K S and g S T = ∂ T ∂ T K T , where K S and K T are given in (2.8). As shown in [66,67], the modulus eigenstate ξ 1 has an anomalous mass m anom ∼ O(M U ), where M U = 3.15 × 10 16 GeV. Hence, it is very heavy and can, to leading order, be integrated out of the low energy effective Lagrangian.…”

“…Several of these admissible hidden sectors have gauge bundles which contain an "anomalous" U (1) factor [60][61][62]. For example, this has been accomplished within the context of the so-called B −L MSSM theory [46][47][48][49][50][51][52], using only a single line bundle in the hidden sector [42,59] It follows that the dilaton S and Kähler modulus T transform inhomogeneously as [66,67]…”

“…The real fields φ 2 and η 2 are canonically normalized and, prior to spontaneously breaking supersymmetry, are massless. It is well known that within the context of heterotic string theories, spontaneously breaking N = 1 supersymmetry via some combination of gaugino condensation, non-vanishing flux and five-brane instantons can generate a non-vanishing hidden sector superpotential Ŵ and, hence, an F-term potential energy V F [56,58,66,68,69]. Since the supersymmetry breaking scale m SU SY is defined as…”

“…More explicitly, the exact expressions for m φ 2 and m η 2 , obtained by minimizing the complete potential energy V = V D + V F assuming that F I = 0, were given in [66]. These can be simplified using the fact that, to lowest order in κ 2/3 4 , the superpotential Ŵ generated by gaugino condensation and flux is generically a function of S only.…”

“…To proceed further, it is necessary to introduce an explicit non-perturbative superpotential and the associated V F potential. Let us choose the example presented in [66], in which the Kähler potentials are identical to (2.8) and the non-perturbative superpotential on the hidden sector was taken to be…”