Only two kinds of compactification are known that lead to four-dimensional supersymmetric AdS vacua with moduli stabilisation and separation of scales at tree-level. The most studied ones are compactifications of massive IIA supergravity on SU(3) structures with smeared O6 planes, for which a general ten-dimensional expression for the solution in terms of the SU(3) structure was found. Less studied are compactifications of IIB supergravity with smeared O5/O7 planes. In this paper we derive a general ten-dimensional expression for the smeared O5/O7 solutions in terms of SU(2) structures. For a specific choice of orientifold projections, we recover the known examples and we also provide new explicit solutions.

https://link.springer.com/content/pdf/10.1007/JHEP11(2013)010.pdf

AdS vacua with scale separation from IIB supergravity

We construct nonsingular cyclic cosmologies that respect the null energy condition, have a large hierarchy between the minimum and maximum size of the universe, and are stable under linearized fluctuations. The models are supported by a combination of positive curvature, a negative cosmological constant, cosmic strings and matter that at the homogeneous level behaves as a perfect fluid with equation of state −1 < w < −1/3. We investigate analytically the stability of the perturbation equations and discuss the role of parametric resonances and nonlinear corrections. Finally, we argue that Casimir energy contributions associated to the compact spatial slices can become important at short scales and may lift nonperturbative decays towards vanishing size. This class of models (particularly in the static limit) can then provide a useful framework for studying the question of the ultimate (meta)stability of an eternal universe.

/pdf/exploring-eternal-stability-with-the-simple-harmonic-1w600skx2o.pdf

Exploring eternal stability with the simple harmonic universe

Three-dimensional smooth compact toric varieties (SCTV) admit SU(3) structures, and may thus be relevant for string compactifications, if they have even first Chern class (c1). This condition can be fulfilled by infinitely many SCTVs, including CP3 and CP1 bundles over all two-dimensional SCTVs. We show that as long as c1 is even, toric SU(3) structures can be constructed using a method proposed in arXiv:1005.2194. We perform a systematic study of the parametric freedom of the resulting SU(3) structures, with a particular focus on the metric and the torsion classes. Although metric positivity constrains the SU(3) parameters, we find that every SCTV admits several toric SU(3) structures and that parametric choices can sometimes be made to match requirements of string vacua. We also provide a short review on the constraints that an SU(3) structure must meet to be relevant for four-dimensional, maximally symmetric N=1 or N=0 string vacua.

Revisiting toric SU(3) structures

We study the probability that all eigenvalues of the moduli mass matrix at extremal points are positive in concrete multi-K\"ahler moduli models of type IIB string theory compactifications in the large volume regime. Our analysis is motivated by the open question if vacua which are uplifted to de Sitter remain stable. We derive a simple analytical condition for the mass matrix to be positive definite, and estimate the corresponding probability in a supersymmetric moduli stabilization model along the lines of KKLT and a non-supersymmetric Large Volume Scenario type of model, given a reasonable range of compactification parameters. Under identical conditions, the probability for the supersymmetric model is moderately higher than that of the Large Volume Scenario type model.

Probability of Vacuum Stability in Type IIB Multi-K\"ahler Moduli Models

We study the probability that all eigenvalues of the moduli mass matrix at extremal points are positive in concrete multi-Kahler moduli models of type IIB string theory compactifications in the large volume regime. Our analysis is motivated by the open question if vacua which are uplifted to de Sitter remain stable. We derive a simple analytical condition for the mass matrix to be positive definite, and estimate the corresponding probability in a supersymmetric moduli stabilization model along the lines of KKLT and a non-supersymmetric Large Volume Scenario type of model, given a reasonable range of compactification parameters. Under identical conditions, the probability for the supersymmetric model is moderately higher than that of the Large Volume Scenario type model.

Probability of vacuum stability in type IIB multi-Kähler moduli models

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in arXiv:1206.1885. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is explored, and such instabilities are investigated in the context of de Sitter vacua. We prove existence results for the equations of motion in the case of a slowly varying warp factor, and the stability of such solutions is also addressed. These solutions are a family of meta-stable de Sitter vacua from type IIB string theory in a general non-supersymmetric setup.

Remarks on positive energy vacua via effective potentials in string theory

In this note, we construct a family of non-singular time-dependent solutions of a six-dimensional gravitational theory that are warped products of a four dimensional bouncing cosmological solution and a two dimensional internal manifold. The warp factor is time-dependent and breaks translation invariance along one of the internal directions. When the warp factor is periodic in time, the non-compact part of the geometry bounces periodically. The six dimensional geometry is supported by matter that does not violate the null energy condition. We show that this 6D geometry does not admit a closed trapped surface and hence the Hawking-Penrose singularity theorems do not apply to these solutions. We also present examples of singular solutions where the topology of the internal manifold changes dynamically.

Time-Dependent Warping and Non-Singular Bouncing Cosmologies

We study how to use smooth, compact toric varieties for supersymmetric $AdS_4$ flux compactifications using tools of SU(3) structures, similar to $CP3$ solution. A non-vanishing globally well defined complex 3-form plays a key role in such constructions. Necessary topological conditions associated with it will be understood to put constraints on large class of these manifolds for supersymmetric flux compactification. Local analysis of SU(3)-structure is carried out, which might help to explore more flux vacua.

Toric manifolds for Flux compactification

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in (On the boundedness of effective potentials arising from string compactifications. Communications in Mathematical Physics 325(3):847–878, 2014). Under physically reasonable assumptions, we provide a mathematically rigorous proof of the existence of positive local minima of a large class of effective potentials. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is explored, and such instabilities are investigated in the context of de Sitter vacua. We prove existence results for the equations of motion in the case of a slowly varying warp factor, and the stability of such solutions is also addressed. These solutions are a family of meta-stable de Sitter vacua from type IIB string theory in a general non-supersymmetric setup.

Sujan P. Dabholkar

Papers

Remarks on positive energy vacua via effective potentials in string theory

Time-Dependent Warping and Non-Singular Bouncing Cosmologies

Toric manifolds for Flux compactification

Remarks on Positive Energy Vacua via Effective Potentials in String Theory