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We elaborate on the construction of de Sitter solutions from IIA orientifolds of SU(3)-structure manifolds that solve the 10-dimensional equations of motion at tree-level in the approximation of smeared sources. First we classify geometries that are orbifolds of a group manifold covering space which, upon the proper inclusion of O6 planes, can be described within the framework of 𝒩 = 1 supergravity in 4D. Then we scan systematically for de Sitter solutions, obtained as critical points of an effective 4D potential. Apart from finding many new solutions we emphasize the challenges in constructing explicit classical de Sitter vacua, which have sofar not been met. These challenges are interesting avenues for further research and include finding solutions that are perturbatively stable, satisfy charge and flux quantization, and have genuine localized (versus smeared) orientifold sources. This paper intends to be self-contained and pedagogical, and thus can serve as a guide to the necessary technical tools required for this line of research. In an appendix we explain how to study flux and charge quantization in the presence of a non-trivial H-field using twisted homology. [ABSTRACT FROM AUTHOR]

We investigate the holographic dual to supergravity instanton solutions in AdS5 × S5/ ℤk, which are described entirely in terms of geodesics on the AdS moduli space. These instantons are expected to be holographically dual to instantons in an N = 2 necklace quiver gauge theory in four dimensions with k gauge nodes, at large N. For the supersymmetric instantons we find a precise match between the on-shell actions and the vevs of Tr[F2] and Tr[F ∧ F ] computed on both sides of the duality. This correspondence requires an exact identification between the massless supergravity scalars and the dual gauge couplings which we give in detail. We also find a candidate for the supergravity dual of a quasi-instanton in the quiver theory, which is a non-supersymmetric extremal solution. [ABSTRACT FROM AUTHOR]

We elaborate on the recent work of Moritz et al. where it is argued that anti‐brane uplifting in KKLT models never leads to dS vacua. This is due to flattening effects in the effective potential found when treating the gaugino condensate energy momentum in ten‐dimensional supergravity. We point out that the Silverstein‐Saltman uplift, which effectively dissolves the anti‐brane in 3‐form fluxes, is a conceptually simpler setting in which flattening effects can be present, without requiring assumptions about UV/IR mixings. Along the way we revise and improve on the arguments of Moritz et al. and discuss various subleties when studying gaugino condensates from a ten‐dimensional point‐of‐view. In particular, the "no dS" argument is slightly weaker and we emphasize a technical loophole that might allow dS vacua. Finally we suggest that AdS vacua which are parametrically controlled from these flattening effects belong to the Swampland. We comment on the relation with the recent refined dS Swampland inequalities. The authors elaborate on the recent work of Moritz et. al. where it is argued that anti‐brane uplifting in KKLT models never leads to dS vacua. This is due to attening effects in the effective potential found when treating the gaugino condensate energy momentum in ten‐dimensional supergravity. It is pointed out that the Silverstein‐Saltman uplift, which effectively dissolves the anti‐brane in 3‐form uxes, is a conceptually simpler setting in which attening effects can be present, without requiring assumptions about UV/IR mixings. Along the way a revision and improvement on the arguments of Moritz et. al. is performed and a discussion of various subleties is done when studying gaugino condensates from a ten‐dimensional point‐of‐view. In particular, the "no dS" argument is slightly weaker and a technical loophole that might allow dS vacua is emphasized. Finally the authors suggest that AdS vacua which are parametrically controlled from these attening effects belong to the Swampland and comment on the relation with the recent refined dS Swampland inequalities. [ABSTRACT FROM AUTHOR]

Abstract: We prove that all stationary and spherical symmetric black hole solutions to theories with symmetric target spaces are integrable and we provide an explicit integration method. This exact integration is based on the description of black hole solutions as geodesic curves on the moduli space of the theory when reduced over the time-like direction. These geodesic equations of motion can be rewritten as a specific Lax pair equation for which mathematicians have provided the integration algorithms when the initial conditions are described by a diagonalizable Lax matrix. On the other hand, solutions described by nilpotent Lax matrices, which originate from extremal regular (small) black holes can be obtained as suitable limits of solutions obtained in the diagonalizable case, as we show on the generating geodesic (i.e. most general geodesic modulo global symmetries of the model) corresponding to regular (and small) black holes. As a byproduct of our analysis we give the explicit form of the “Wick rotation” connecting the orbits of BPS and non-BPS solutions in maximally supersymmetric supergravity and its STU truncation. [Copyright &y& Elsevier]

Abstract: We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike p-brane solutions when they are lifted over a p-dimensional flat space. In particular, we consider the problem of constructing the minimal generating solution: A geodesic with the minimal number of free parameters such that all other geodesics are generated through isometries. We give an intrinsic characterization of this solution in a wide class of orbits for various supergravities in different dimensions. We apply our method to three cases: (i) Einstein vacuum solutions, (ii) extreme and non-extreme black holes in supergravity and their relation to STU black holes and (iii) Euclidean wormholes in . In case (iii) we present an easy and general criterium for the existence of regular wormholes for a given scalar coset. [Copyright &y& Elsevier]

We investigate the holographic dual to supergravity instanton solutions in AdS5 × S5/ ℤk, which are described entirely in terms of geodesics on the AdS moduli space. These instantons are expected to be holographically dual to instantons in an N = 2 necklace quiver gauge theory in four dimensions with k gauge nodes, at large N. For the supersymmetric instantons we find a precise match between the on-shell actions and the vevs of Tr[F2] and Tr[F ∧ F ] computed on both sides of the duality. This correspondence requires an exact identification between the massless supergravity scalars and the dual gauge couplings which we give in detail. We also find a candidate for the supergravity dual of a quasi-instanton in the quiver theory, which is a non-supersymmetric extremal solution. [ABSTRACT FROM AUTHOR]

We find new and compelling evidence for the metastability of supersymmetry-breaking states in holographic backgrounds whose consistency has been the source of ongoing disagreements in the literature. As a concrete example, we analyze anti-D3 branes at the tip of the Klebanov-Strassler throat. Using the blackfold formalism we examine how temperature affects the conjectured metastable state and determine whether and how the existing extremal results generalize when going beyond extremality. In the extremal limit we exactly recover the results of Kachru, Pearson, and Verlinde, in a regime of parameter space that was previously inaccessible. Away from extremality we uncover a metastable black Neveu-Schwarz five-brane (NS5) state that disappears near a geometric transition where black anti-D3 branes and black NS5 branes become indistinguishable. This is remarkably consistent with complementary earlier results based on the analysis of regularity conditions of backreacted solutions. We therefore provide highly nontrivial evidence for the metastability of antibranes in noncompact throat geometries since we find a consistent picture over different regimes in parameter space. [ABSTRACT FROM AUTHOR]