A Geometric Construction of Solutions to 11D Supergravity

Teng, Fei; Guo, Bin; Phong, Duong H.

doi:10.1007/s00220-019-03322-w

Cited by 5 publications

(1 citation statement)

References 46 publications

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“…Solutions of the field equations can of course be supersymmetric or not supersymmetric, with explicit examples of both given in e.g. [12]. Returning to the problem of covariantly constant spinors, in the simpler case of no flux, a natural proposal by Ammann, Weiss, and Witt [1] was to consider the gradient flow of the energy functional…”

Section: Introductionmentioning

confidence: 99%

Spinor flows with flux, I: short-time existence and smoothing estimates

Collins¹,

Phong²

2021

Preprint

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Section: Introductionmentioning

confidence: 99%

Spinor flows with flux, I: short-time existence and smoothing estimates

Collins¹,

Phong²

2021

Preprint

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The Heterotic-Ricci Flow and Its Three-Dimensional Solitons

Moroianu,

Murcia,

Shahbazi

2024

J Geom Anal

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We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled curvature evolution flow, depending on a non-negative real parameter $$\kappa $$ κ , for a complete Riemannian metric and a three-form H on a manifold M. Its most salient feature is that it involves several terms quadratic in the curvature tensor of a metric connection with skew-symmetric torsion H. When $$\kappa = 0$$ κ = 0 the Heterotic-Ricci flow reduces to the generalized Ricci flow and hence it can be understood as a modification of the latter via the second-order correction prescribed by Heterotic string theory, whereas when $$H=0$$ H = 0 and $$\kappa >0$$ κ > 0 the Heterotic-Ricci flow reduces to a constrained version of the RG-2 flow and hence it can be understood as a generalization of the latter via the introduction of the three-form H. Solutions of Heterotic supergravity with trivial gauge bundle, which we call Heterotic solitons, define a particular class of three-dimensional solitons for the Heterotic-Ricci flow and constitute our main object of study. We prove a number of structural results for three-dimensional Heterotic solitons, obtaining, in particular, the complete classification of compact three-dimensional strong Heterotic solitons as hyperbolic three-manifolds or quotients of the Heisenberg group equipped with a left-invariant metric. Furthermore, we prove that all Einstein three-dimensional Heterotic solitons have constant dilaton and leave as open the construction of a Heterotic soliton with non-constant dilaton. In this direction, we prove that Einstein Heterotic solitons with constant dilaton are rigid and therefore cannot be deformed into a solution with non-constant dilaton. This is, to the best of our knowledge, the first rigidity result for compact supergravity solutions in the literature.

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Decomposable (5, 6)-solutions in eleven-dimensional supergravity

Chi

Chrysikos

Schneider

2023

Journal of Mathematical Physics

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We present decomposable (5, 6)-solutions M̃1,4×M6 in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. These constructions provide an analogy of the work performed by Chrysikos and Galaev [Classical Quantum Gravity 37, 125004 (2020)], who made similar computations for decomposable (6, 5)-solutions. We also present bosonic backgrounds that are products of Lorentzian Einstein manifolds with a negative Einstein constant (in the “mostly plus” convention) and Riemannian Kähler–Einstein manifolds with a positive Einstein constant. This conclusion generalizes a result of Pope and van Nieuwenhuizen [Commun. Math. Phys. 122, 281–292 (1989)] concerning the appearance of six-dimensional Kähler–Einstein manifolds in eleven-dimensional supergravity. In this setting, we construct infinitely many non-symmetric decomposable (5, 6)-supergravity backgrounds by using the infinitely many Lorentzian Einstein–Sasakian structures with a negative Einstein constant on the 5-sphere, known from the work of Boyer et al. [Commun. Math. Phys. 262, 177–208 (2006)].

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A Geometric Construction of Solutions to 11D Supergravity

Cited by 5 publications

References 46 publications

Spinor flows with flux, I: short-time existence and smoothing estimates

Spinor flows with flux, I: short-time existence and smoothing estimates

The Heterotic-Ricci Flow and Its Three-Dimensional Solitons

Decomposable (5, 6)-solutions in eleven-dimensional supergravity

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