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Register a new userA No-go theorem for de Sitter compactifications?
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N.D. Hari Dass
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A general framework for studying compactifications in supergravity and string theories was introduced by Candelas, Horowitz, Strominger and Witten. This was further generalised to take into account the warp factor by de Wit, Smit and Hari Dass. Though the prime focus of the latter was to find solutions with nontrivial warp factors (shown not to exist under a variety of circumstances), it was shown there that de Sitter compactifications are generically disfavoured. In this note we place these results in the context of a revived interest in de Sitter spacetimes .
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We consider warped compactifications in (4+d)-dimensional theories, with four dimensional de Sitter dS_4 vacua (with Hubble parameter H) and with a compact internal space. After introducing a gauge-invariant formalism for the generic metric perturbations of these backgrounds, we focus on modes which are scalar with respect to dS_4. The physical eigenmasses of these modes acquire a large universal tachyonic contribution -12d/(d+2) H^2, independently of the stabilization mechanism for the compact space, in addition to the usual KK masses, which instead encode the effects of the stabilization. General arguments, as well as specific examples, lead us to conjecture that, for sufficiently large dS curvature, the compactified geometry becomes gravitationally unstable due to the tachyonic growth of the scalar perturbations. This mean that for any stabilization mechanism the curvature of the dS geometry cannot exceed some critical value. We relate this effect to the anisotropy of the bulk geometry and suggest the end points of the instability. Of relevance for inflationary cosmology, the perturbations of the bulk metric inevitably induce a new modulus field, which describes the conformal fluctuations of the 4 dimensional metric. If this mode is light during inflation, the induced conformal fluctuations will be amplified with a scale free spectrum and with an amplitude which is disentangled from the standard result of slow-roll inflation. The conformal 4d metric fluctuations give rise to a very generic realization of the mechanism of modulated cosmological fluctuations, related to spatial variation of couplings during (p)reheating after inflation.
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.
We prove that a very large class of $15502$ general Argyres-Douglas theories cannot admit a UV lagrangian which flows to them via the Maruyoshi-Song supersymmetry enhancement mechanism. We do so by developing a computer program which brute-force lists, for any given 4d $mathcal{N}=2$ superconformal theory $mathcal{T}_{text{IR}}$, all possible UV candidate superconformal lagrangians $mathcal{T}_{text{UV}}$ satisfying some necessary criteria for the supersymmetry enhancement to happen. We argue that this is enough evidence to conjecture that it is impossible, in general, to find new examples of Maruyoshi-Song lagrangians for generalized Argyres-Douglas theories. All lagrangians already known are, on the other hand, recovered and confirmed in our scan. Finally, we also develop another program to compute efficiently Coulomb branch spectrum, masses, couplings and central charges for $(G,G)$ Argyres-Douglas theories of arbitrarily high rank.
We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodox Lagrangians.
It was recently proposed that type IIA string theory may allow classical de Sitter solutions with O8-planes as the only localized sources. We show that such solutions are incompatible with the integrated supergravity equations of motion, analogously to the no-go theorem due to Maldacena and Nu~{n}ez. We also discuss in detail divergences and discontinuities at the O8-plane positions and argue that they do not invalidate such an argument. We furthermore show that a recently proposed class of non-supersymmetric AdS solutions with O8-planes is in contrast with our results as well.
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