Consistent truncation and de Sitter space from gravitational instantons

Abstract

We construct a four-dimensional consistent truncation to the bosonic part of the universal sector of Calabi-Yau IIA compactification (i.e. the gravity multiplet, one vectormultiplet, and one hypermultiplet) in the presence of background flux and fermionic condensates generated by gravitational instantons. The condensates are controlled by the ratio of the characteristic length of the Calabi-Yau to the string length, and can be fine-tuned to be dominant in a region of large volume and small string coupling. The consistent truncation admits de Sitter solutions supported by the condensates, subject to certain validity conditions that we discuss.

Consistent truncation on Calabi-Yau and Nearly-Kähler manifolds

“…The 4d actions thus derived are valid for generic gravitino condensates arising from gravitational instanton backgrounds with positive-chirality 4d zero modes. Specializing to the case of ALE gravitational instantons, in section 4 we show that the putative quartic gravitino condensate is non-negative, as required for the existence of (formal) de Sitter solutions of the 4d theory [31]. 1 There exist four homogeneous compact NK six-manifolds: S 6 , S 3 × S 3 , CP 3 and F 1,2 [32], and these were until recently the only known compact NK six-manifolds.…”

“…Let us recall the consistent truncation of [31]: it is obtained from massless IIA supergravity by the following form ansatz, cf. appendices A, B for our conventions,…”

“…In the present paper we complete and extend the analysis of [30,31] in several directions. In section 2 we put the 4d theory, arising from the IIA consistent truncation of the universal sector of Calabi-Yau compactification, in a form manifestly consistent with 4d N = 2 supergravity.…”

“…In [30,31] we initiated the study of CT's in the presence of fermionic condensates. As we review in the following, this approach offers a way to fix the dependence of the condensates on the moduli of the theory.…”

“…In [31] we constructed a universal CT of IIA compactified on Calabi-Yau (CY) manifolds, in the presence of background flux and gravitino condensates, comprising the gravity multiplet, one vectormultiplet, and one hypermultiplet. The effective 4d action resulting from type II compactification on CY manifolds has been constructed before both in the absence [46,47] and in the presence of background flux [48], and the consistency of the resulting 4d theory with (gauged) N = 2 supergravity has been established [49,50,51,52].…”