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Register a new userNo--scale supergravity and the Multiple Point Principle
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We review symmetries protecting a zero value for the cosmological constant in no--scale supergravity and reveal the connection between the Multiple Point Principle, no--scale and superstring inspired models.
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No-scale supergravity is the appropriate general framework for low-energy effective field theories derived from string theory. The simplest no-scale Kahler potential with a single chiral field corresponds to a compactification to flat Minkowski space with a single volume modulus, but generalizations to single-field no-scale models with de Sitter vacua are also known. In this paper we generalize these de Sitter constructions to two- and multi-field models of the types occurring in string compactifications with more than one relevant modulus. We discuss the conditions for stability of the de Sitter solutions and holomorphy of the superpotential, and give examples whose superpotential contains only integer powers of the chiral fields.
In the present paper we argue that the correction to the Higgs mass coming from the bound state of 6 top and 6 anti-top quarks, predicted early by C.D. Froggatt and ourselves, leads to the Standard Model vacuum stability and confirms the accuracy of the multiple point principle (principle of degenerate vacua) for all experimentally valued parameters (Higgs mass, top-quark mass, etc.). Fitting to get the vacuum degeneracy requires a mass of the bound state, just in the region of the new two photon state in LHC, 750-760 GeV.
We argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no-scale supergravities in low-energy 4D EFTs. We identify 4 nested types of no-scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no-scale properties (including non-supersymmetric flat directions). We use these ideas to classify corrections to the low-energy 4D supergravity action in perturbative 10D string vacua, including both bulk and brane contributions. Our prediction for the Kahler potential at any fixed order in $alpha$ and string loops agrees with all extant calculations. p-form fields play two important roles: they spawn many (generalised) shift symmetries; and space-filling 4-forms teach 4D physics about higher-dimensional phenomena like flux quantisation. We argue that these robust symmetry arguments suffice to understand obstructions to finding classical de Sitter vacua, and suggest how to get around them in UV complete models.
The requirement for an ultraviolet completable theory to be well-behaved upon compactification has been suggested as a guiding principle for distinguishing the landscape from the swampland. Motivated by the weak gravity conjecture and the multiple point principle, we investigate the vacuum structure of the standard model compactified on $S^1$ and $T^2$. The measured value of the Higgs mass implies, in addition to the electroweak vacuum, the existence of a new vacuum where the Higgs field value is around the Planck scale. We explore two- and three-dimensional critical points of the moduli potential arising from compactifications of the electroweak vacuum as well as this high scale vacuum, in the presence of Majorana/Dirac neutrinos and/or axions. We point out potential sources of instability for these lower dimensional critical points in the standard model landscape. We also point out that a high scale $AdS_4$ vacuum of the Standard Model, if exists, would be at odd with the conjecture that all non-supersymmetric $AdS$ vacua are unstable. We argue that, if we require a degeneracy between three- and four-dimensional vacua as suggested by the multiple point principle, the neutrinos are predicted to be Dirac, with the mass of the lightest neutrino O(1-10) meV, which may be tested by future CMB, large scale structure and $21$cm line observations.
The principle of multiple point criticality (PMPC), which allowed the prediction of the Higgs boson mass before its discovery, has so far been applied to radiatively generated vacua. If this principle is fundamental, following from some presently unknown underlying physics, the PMPC must apply to all vacua, including the multiple vacua of multi-scalar models dominated by tree-level terms. We first motivate this idea and then exemplify it by applying the PMPC to various realizations of singlet scalar dark matter models. We derive constraints on the dark matter properties from the requirement of degenerate vacua and show that some scalar dark matter models are ruled out by the PMPC, while in others the allowed parameters space is constrained.
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