We attempt a systematic analysis of string-theoretic quintessence models as an alternative to metastable de Sitter vacua. It appears that, within the boundaries of what is known, largevolume type-IIB flux compactifications are preferred. Here the quintessence scalar is the ratio of certain 4-cycle volumes. It has already been noticed that the volume modulus, which must be stabilized, tends to remain too light. One may call this the "light volume problem". In addition, we identify an "F -term problem": The positive energy density of standard-model SUSY breaking is higher than the depth of all known negative contributions. We discuss what it would take to resolve these issues and comment on partially related challenges for axionic quintessence. In particular, large cancellations between positive and negative potential terms appear unavoidable in general. As a further challenge, one should then explain why a small de-tuning cannot be used to uplift into a deep slow-roll regime, violating de Sitter swampland conjectures.
Motivated by a possibility of solving non-supersymmetric type 0 string theory in AdS5× S5 background using integrability, we revisit the construction of type 0 string spectrum in some solvable examples of backgrounds with RR fluxes that are common to type IIB and type 0B theories. The presence of RR fluxes requires the use of a Green-Schwarz description for type 0 string theory. Like in flat space, the spectrum of type 0 theory can be derived from the type II theory spectrum by a (−1)F orbifolding, i.e. combining the untwisted sector where GS fermions are periodic with the twisted sector where GS fermions are antiperiodic (and projecting out all spacetime fermionic states). This construction of the type 0 spectrum may also be implemented using Melvin background that allows to continuously interpolate between the type II and type 0 theories. As an illustration, we discuss the type 0B spectrum in the pp-wave background which is the Penrose limit of AdS5× S5 with RR 5-form flux and also in the pp-wave background which is the Penrose limit of AdS3× S3× T4 supported by mixed RR and NSNS 3-form fluxes. We show that increasing the strength of the RR flux increases the value of the effective normal ordering constant (which determines the mass of the type 0 tachyon in flat space) and thus effectively decreases the momentum-space domain of instability of the ground state. We also comment on the semiclassical sector of states of type 0B theory in AdS5× S5.
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We elaborate on the treatment of orbifolds of type IIB string theory on $AdS_5\times S^5$ and their dual gauge theories with integrability techniques. The implementation of orbifolds via twisted spin-chains, thermodynamic Bethe Ansatz equations with chemical potentials and $Y$- and $T$-systems with modified asymptotics is confronted with twisted boundary conditions of the string sigma-model. This allows us to consistently twist the quantum spectral curve, which is believed to bridge the two sides of the AdS/CFT duality. We discuss Abelian orbifolds of $PSU(2,2|4)$ and treat the special cases of $\mathcal{N}=2$ supersymmetric $\mathbb{Z}_2$-orbifolds and type 0B string theory on $AdS_5\times S^5$ as primary examples. This opens a pathway to probe the validity of the duality and to study the long-standing question of tachyon stabilisation in non-supersymmetric AdS/CFT. We comment on the current understanding of this issue and point out the next steps in this challenge.
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