Abstract
In this paper, following the work of Hohm and Zwiebach [arXiv:1905.06583], we show that in bosonic string theory nonperturbative anti-de Sitter (AdS) vacua could exist with all $\alpha^{\prime}$ corrections included. We also discuss the possibility of the coexistence of nonperturbative dS and AdS vacua.
Highlights
Whether bosonic string theory permits stable de Sitter or anti–de Sitter (AdS) vacua is a long-standing unsolved problem
It is well known from the work of Meissner and Veneziano [7] in 1991 that, at the zeroth order of α0, when all fields depend only on time the D 1⁄4 d þ 1-dimensional spacetime action of closed string theory reduces to an Oðd; dÞ-invariant reduced action
In the language of low-energy effective theory, the reduced action derived from such solutions possesses an Oðm; mÞ symmetry to all orders in α0. (ii) The m coordinates could be all spacelike or include one timelike coordinate, as explained in Ref. [9]. (iii) In the solution space, inequivalent solutions are connected by nondiagonal OðmÞ ⊗ OðmÞ transformations [Oðm − 1; 1Þ ⊗ O ðm − 1; 1Þ if one of the m coordinates is timelike]. (iv) Other generators of Oðm; mÞ
Summary
We start with the tree-level closed string spacetime action without α0 corrections, ðA1Þ where gμν is the string metric, φ is the dilaton, and Hijk 1⁄4 3∂1⁄2ibjk is the field strength of the antisymmetric KalbRamond field bij. The ansatz we use is ds2 1⁄4 −a2ðxÞdt þ dx þ a2ðxÞðdy þ dz þ ...Þ; bxμ 1⁄4 0; ðA2Þ. Oðd; dÞ symmetry and not its components, the time-like minus sign G11ðxÞ 1⁄4 −a2ðxÞ does not show up until we calculate the reduced action. In order to obtain the reduced action by using the ansatz (A3), we rotate between the time-like t and the first space-like x directions and rewrite the metric and bμν as. We want to point out the sign differences between our ansatz (A2) and the time-dependent FLRW metric: sign1⁄2Rxx 1⁄4 sign1⁄2Rtt; sign1⁄2Rtt 1⁄4 −sign1⁄2Rxx; sign1⁄2Rab 1⁄4 −sign1⁄2Rab; ðA13Þ sign1⁄2H2 1⁄4 −sign1⁄2H 2; sign1⁄2H2μν 1⁄4 −sign1⁄2H 2μν; sign1⁄2ð∂φÞ2 1⁄4 −sign1⁄2ð∂φ Þ2; ðA14Þ where Arepresents the quantities calculated in the timedependent FLRW background. This is the space-dependent duality corresponding to the scale-factor duality in the time-dependent FLRW background
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