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arXiv · 2109.13781

Heterotic $M$-Theory Hidden Sectors with an Anomalous $U(1)$ Gauge Symmetry

Sebastian Dumitru·Burt A. Ovrut
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Abstract

The hidden sector of heterotic $M$-theory vacua whose gauge bundle contains an anomalous $U(1)$ factor is discussed in detail. The mathematical formalism for computing the inhomogeneous transformation of the dilaton and K\"ahler moduli axions under an anomalous $U(1)$ transformation is presented. Along with matter multiplets, which transform homogeneously under $U(1)$, the relevant part of the $U(1)$ invariant low energy hidden sector Lagrangian is presented and analyzed. A detailed mathematical formalism is given for rotating these field to a new basis of chiral superfields with normalized kinetic energy and a diagonal mass matrix. It is shown that the scalar and fermionic components of one such chiral superfield give rise to a massive $U(1)$ vector superfield, whose mass is composed of both anomalous and Higgs contributions associated with the inhomogeneous and homogeneous transformations respectively. Two explicit examples are presented, with vanishing and non-zero Fayet-Iliopoulos term respectively. The canonically normalized hidden sector Lagrangian given here is restricted to gauge interactions only. A study of higher order interactions of the moduli and matter multiplets, as well as the coupling to supergravity, will be presented elsewhere.

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Sebastian Dumitru, Burt A. Ovrut. 2021-09-28. Heterotic $M$-Theory Hidden Sectors with an Anomalous $U(1)$ Gauge Symmetry. https://arxiv.org/abs/2109.13781

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