Abstract
This paper constructs the reduction of heterotic M-theory in eleven dimensions to a supergravity model on a manifold with boundary in five dimensions using a Calabi-Yau three-fold. New results are presented for the boundary terms in the action and for the boundary conditions on the bulk fields. Some general features of dualisation on a manifold with boundary are used to explain the origin of some topological terms in the action. The effect of gaugino condensation on the fermion boundary conditions leads to a ‘twist’ in the chirality of the gravitino which can provide an uplifting mechanism in the vacuum energy to cancel the cosmological constant after moduli stabilisation.
Highlights
Heterotic M -theory [1, 2] is based on the idea that one of the low-energy limits of M -theory can be formulated as 11-dimensional supergravity with matter fields living on two halves of a 10-dimensional boundary
The source of these problems lay in the presence of distributions in the supersymmetry transformations and in the Bianchi identity of the antisymmetric tensor flux. These terms prevented construction of a supersymmetric action beyond the leading terms in an expansion parameter κ112/3, where κ11 is the gravitational coupling. These problems have been resolved by a simple modification to the boundary conditions of the theory, allowing the supersymmetry transformations and the Bianchi identity to remain free of distributions and resulting in a low energy theory which is supersymmetric to all orders in κ112/3 [15,16,17]
The new results are the in the boundary action and the boundary conditions on the bulk fields
Summary
Heterotic M -theory [1, 2] is based on the idea that one of the low-energy limits of M -theory can be formulated as 11-dimensional supergravity with matter fields living on two halves of a 10-dimensional boundary. The original work on this reduction by Lukas et al [14] started from the bosonic sector of an E6 × E8 theory and constructed the bulk-fermion sector from the known five-dimensional supergravity models. This approach cannot be used on the boundary, where the bulk fields appear in the boundary action, and it says nothing about the boundary conditions. The gaugino condensate leads to a small chiral ‘twist’ between the fermions on the two separate boundary components This creates a five dimensional vacuum energy due to quantum effects [23]. Description 11-dimensional coordinates 10-dimensional coordinates outward normal 5-dimensional coordinates 4-dimensional coordinates holomorphic Calabi-Yau coordinates SU(2) spinor indices fundamental E6-group representation H1,1 Calabi-Yau moduli E6 or E8 Lie algebra chiral components
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