Abstract
Abstract We study properties of D = 4 $$ \mathcal{N} \geqslant {2} $$ extended supergravities (and related compactifications of superstring theory) and their consistent truncation to the phenomenologically interesting models of $$ \mathcal{N} = {1} $$ supergravity. This involves a detailed classification of the “degenerations” of the duality groups of type E 7, when the corresponding quartic invariant polynomial built from the symplectic irreducible representation of G4 “degenerates” into a perfect square. With regard to cosmological applications, minimal coupling of vectors in consistent truncation to $$ \mathcal{N} = {1} $$ from higher-dimensional or $$ {\text{higher}} - \mathcal{N} $$ theory is non-generic. On the other hand, non-minimal coupling involving vectors coupled to scalars and axions is generic. These features of supergravity, following from the electric-magnetic duality, may be useful in other applications, like stabilization of moduli, and in studies of non-perturbative black-hole solutions of supergravity/string theory.
Highlights
In the present investigation, we relate a physical property of supergravity couplings to a mathematical property of the underlying electric-magnetic duality symmetries1 of N 2 extended supergravity in D = 4 space-time dimensions.In the textbook [4], the coupling of N = 1 vector and chiral multiplets to supergravity is presented in its minimal form, i.e. it is assumed that the vector kinetic term − 1 4 δαβ Fμαν F β|μν (1.1)is scalar independent
We study properties of D = 4 N 2 extended supergravities and their consistent truncation to the phenomenologically interesting models of N = 1 supergravity
The minimal vector coupling in N = 1 supergravity corresponds to the choice of the constant vector kinetic term as shown in eq (1.1), when instead of a holomorphic function of scalars, fαβ(z), as in eq (1.2), one has fαβ = δαβ
Summary
The present paper is intended to generalize the results of [5], because we believe that the issue of minimal coupling in N 2 extended supergravities deserves some attention Such theories never exhibit a constant fαβ, and in [5] this fact was pointed out to be a consequence of electric-magnetic-duality, which requires a special coupling of the non-linear sigma model of scalars to the vector sector [6, 7]. In the systematic approach of the present paper, we will provide a detailed list of examples in which minimal coupling is impossible in the higher-dimensional or higher-N theory, but it can be achieved by a further suitable consistent truncation to N = 1 This is related to the mathematical property of the U -duality group G4 of type E7 [16]. Appendix A, containing some details on the structure of Pauli terms, concludes the paper
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