arXiv subjects

J. B. Gutowski

Publications and source records attributed to J. B. Gutowski.

At least 19 recordsLinked to original sources

arXiv2024

Real Supersymmetric Solutions of (3,2) Signature Five-Dimensional Supergravity

We classify supersymmetric solutions of D=5 (3,2) signature supergravity with either vanishing or imaginary gauge coupling constant preserving the minimal N=2 supersymmetry. We prove that the geometry of such solutions is characterized by a nilpotent integrable endomorphism, and obtain the necessary and sufficient conditions on the fluxes imposed by supersymmetry. We also construct examples of supersymmetric domain wall solutions for which the nilpotent integrable endomorphism is associated with a Killing-Yano 2-form, as well as a new descendant preon solution which preserves N=6 supersymmetry. This is notable as such N=6 descendant solutions do not exist in the standard signature D=5 supergravity.

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arXiv2020

Neutral Signature Gauged Supergravity Solutions

We classify all supersymmetric solutions of minimal D=4 gauged supergravity with (2,2) signature and a positive cosmological constant which admit exactly one Killing spinor. This classification produces a geometric structure which is more general than that found for previous classifications of N=2 supersymmetric solutions of this theory. We illustrate how the N=2 solutions which consist of a fibration over a 3-dimensional Lorentzian Gauduchon-Tod base space can be written in terms of this more generic geometric structure.

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arXiv2019

Anomaly Corrected Heterotic Horizons

We consider supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory. We identify the conditions for the horizons to admit enhancement of supersymmetry. We show that solutions which undergo supersymmetry enhancement exhibit an sl(2,R) symmetry, and we describe the geometry of their horizon sections. We also prove a modified Lichnerowicz type theorem, incorporating $α'$ corrections, which relates Killing spinors to zero modes of near-horizon Dirac operators. Furthermore, we demonstrate that there are no AdS2 solutions in heterotic supergravity up to second order in $α'$ for which the fields are smooth and the internal space is smooth and compact without boundary. We investigate a class of nearly supersymmetric horizons, for which the gravitino Killing spinor equation is satisfied on the spatial cross sections but not the dilatino one, and present a description of their geometry.

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arXiv2019

Real Killing Spinors in Neutral Signature

Spinorial geometry methods are used to classify solutions admitting Majorana Killing spinors of the minimal 4-dimensional supergravity in neutral signature, with vanishing cosmological constant and a single Maxwell field strength. Two classes of solutions preserving the minimal amount of supersymmetry are found. The first class admits a null-Kahler structure and corresponds to a class of self-dual solutions found by Bryant. The second class admits a null and rotation-free geodesic congruence with respect to which a parallel frame can be chosen. Examples of solutions in the former class are pseudo-hyper-Kahler manifolds; and examples in the latter class include self-dual solutions, as well as a neutral-signature IWP-type solution.

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arXiv2018

Solutions of D=4 Gauged Pseudo-Supergravity

The techniques of spinorial geometry are used to classify solutions admitting Killing spinors in the theory of minimal anti-de Sitter $N=2$, $D=4$ supergravity, where the gauge kinetic term comes with the opposite sign. There are four classes of solutions. One class is described by metrics corresponding to gravitational waves propagating on $AdS_2\times H^2$. The second class of solution is a new solution corresponding to a special limiting case of the Killing spinor. The third class of solution corresponds to fibrations over a Lorentzian three dimensional manifold which has a Lorentzian Gauduchon-Tod structure. The fourth class of solution is a cosmological extension of a Majumdar-Papapetrou type solution, described by a function satisfying the wave equation on $\mathbb{R}^{2,1}$ .

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arXiv2018

Solutions of Minimal Four Dimensional de Sitter Supergravity

Pseudo-supersymmetric solutions of minimal $N=2$, $D=4$ de Sitter supergravity are classified using spinorial geometry techniques. We find three classes of solutions. The first class of solution consists of geometries which are fibrations over a 3-dimensional manifold equipped with a Gauduchon-Tod structure. The second class of solution is the cosmological Majumdar-Papapetrou solution of Kastor and Traschen, and the third corresponds to gravitational waves propagating in the Nariai cosmology.

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arXiv2017

On supersymmetric AdS6 solutions in 10 and 11 dimensions

We prove a non-existence theorem for smooth, supersymmetric, warped AdS6 solutions with connected, compact without boundary internal space in D=11 and (massive) IIA supergravities. In IIB supergravity we show that if such AdS6 solutions exist, then the NSNS and RR 3-form fluxes must be linearly independent and certain spinor bi-linears must be appropriately restricted. Moreover we demonstrate that the internal space admits an so(3) action which leaves all the fields invariant and for smooth solutions the principal orbits must have co-dimension two. We also describe the topology and geometry of internal spaces that admit such a so(3) action and show that there are no solutions for which the internal space has topology F * S^2, where F is an oriented surface.

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arXiv2016

Moduli Spaces of Transverse Deformations of Near-Horizon Geometries

We investigate deformations of extremal near-horizon geometries in Einstein-Maxwell-Dilaton theory, including various topological terms, and also in D=11 supergravity. By linearizing the field equations and Bianchi identities over the compact spatial cross-sections of the near-horizon geometry, we prove that the moduli associated with such deformations are constrained by elliptic systems of PDEs. The moduli space of deformations of near-horizon geometries in these theories is therefore shown to be finite dimensional.

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arXiv2016

On supersymmetric Anti-de-Sitter, de-Sitter and Minkowski flux backgrounds

We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter spaces. We find that there are supersymmetric de Sitter solutions in supergravity theories including maximally supersymmetric ones in 10- and 11-dimensional supergravities. Moreover, warped flux Minkowski backgrounds can admit Killing spinors which are not Killing on the Minkowski subspace and therefore cannot be put in a factorized form.

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arXiv2016

AdS5 Backgrounds with 24 Supersymmetries

We prove a non-existence theorem for smooth AdS5 solutions with connected, compact without boundary internal space that preserve strictly 24 supersymmetries. In particular, we show that D=11 supergravity does not admit such solutions, and that all such solutions of IIB supergravity are locally isometric to the AdS_5 * S^5 maximally supersymmetric background. Furthermore, we prove that (massive) IIA supergravity also does not admit such solutions, provided that the homogeneity conjecture for massive IIA supergravity is valid. In the context of AdS/CFT these results imply that if strictly N=3 superconformal theories in 4-dimensions exist, their gravitational dual backgrounds are either singular or their internal spaces are not compact.

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arXiv2015

Geometry and supersymmetry of heterotic warped flux AdS backgrounds

We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with $n\not=3$. Moreover the warp factor of AdS$_3$ backgrounds is constant, the geometry is a product $AdS_3\times M^7$ and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of $M^7$ has been specified in all cases. For 2 supersymmetries, it has been found that $M^7$ admits a suitably restricted $G_2$ structure. For 4 supersymmetries, $M^7$ has an $SU(3)$ structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, $M^7$ has an $SU(2)$ structure and can be described locally as a $S^3$ fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-Kähler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of $α'$ corrections.

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arXiv2015

Index Theory and Supersymmetry of 5D Horizons

We prove that the near-horizon geometries of minimal gauged five-dimensional supergravity preserve at least half of the supersymmetry. If the near-horizon geometries preserve a larger fraction, then they are locally isometric to $AdS_5$. Our proof is based on Lichnerowicz type theorems for two horizon Dirac operators constructed from the supercovariant connection restricted to the horizon sections, and on an application of the index theorem. An application is that all half-supersymmetric five-dimensional horizons admit an $\mathfrak{sl}(2, {\mathbb{R}})$ symmetry subalgebra.

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arXiv2015

Supersymmetry of AdS and flat IIB backgrounds

We present a systematic description of all warped $AdS_n\times_w M^{10-n}$ and ${\mathbb{R}}^{n-1,1}\times_w M^{10-n}$ IIB backgrounds and identify the a priori number of supersymmetries $N$ preserved by these solutions. In particular, we find that the $AdS_n$ backgrounds preserve $N=2^{[{n\over2}]} k$ for $n\leq 4$ and $N=2^{[{n\over2}]+1} k$ for $4<n\leq 6$ supersymmetries and for $k\in {\mathbb{N}}_{+}$ suitably restricted. In addition under some assumptions required for the applicability of the maximum principle, we demonstrate that the Killing spinors of $AdS_n$ backgrounds can be identified with the zero modes of Dirac-like operators on $M^{10-n}$ establishing a new class of Lichnerowicz type theorems. Furthermore, we adapt some of these results to ${\mathbb{R}}^{n-1,1}\times_w M^{10-n}$ backgrounds with fluxes by taking the AdS radius to infinity. We find that these backgrounds preserve $N=2^{[{n\over2}]} k$ for $2<n\leq 4$ and $N=2^{[{n+1\over2}]} k$ for $4<n\leq 7$ supersymmetries. We also demonstrate that the Killing spinors of $AdS_n\times_w M^{10-n}$ do not factorize into Killing spinors on $AdS_n$ and Killing spinors on $M^{10-n}$.

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arXiv2015

Supersymmetry of IIA warped flux AdS and flat backgrounds

We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that $AdS_n\times_w M^{10-n}$ preserve $2^{[{n\over2}]} k$ for $n\leq 4$ and $2^{[{n\over2}]+1} k$ for $4 0}$. In addition we show that, for suitably restricted fields and $M^{10-n}$, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on $M^{10-n}$. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to $\bR^{1,n-1}\times_w M^{10-n}$ backgrounds which underpin flux compactifications to $\bR^{1,n-1}$ and show that these preserve $2^{[{n\over2}]} k$ for $2<n\leq 4$, $2^{[{n+1\over2}]} k$ for $4<n\leq 8$, and $2^{[{n\over2}]} k$ for $n=9, 10$ supersymmetries.

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arXiv2014

Supersymmetry of AdS and flat backgrounds in M-theory

We give a systematic description of all warped $AdS_n$ and ${\mathbb{R}}^{n-1,1}$ backgrounds of M-theory and identify the a priori number of supersymmetries that these backgrounds preserve. In particular, we show that $AdS_n$ backgrounds preserve $N= 2^{[{n\over2}]} k$ for $n\leq4$ and $N= 2^{[{n\over2}]+1} k$ for $4<n\leq 7$ supersymmetries while ${\mathbb{R}}^{n-1,1}$ backgrounds preserve $N= 2^{[{n\over2}]} k$ for $n\leq4$ and $N= 2^{[{n+1\over2}]} k$ for $4<n\leq7$, supersymmetries. Furthermore for $AdS_n$ backgrounds that satisfy the requirements for the maximum principle to hold, we show that the Killing spinors can be identified with the zero modes of Dirac-like operators on $M^{11-n}$ coupled to fluxes thus establishing a new class of Lichnerowicz type theorems. We also demonstrate that the Killing spinors of generic warped $AdS_n$ backgrounds do not factorize into products of Killing spinors on $AdS_n$ and Killing spinors on the transverse space.

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arXiv2013

Para-Complex Geometry and Gravitational Instantons

We give a complete classification of supersymmetric gravitational instantons in Euclidean N=2 supergravity coupled to vector multiplets. An interesting class of solutions is found which corresponds to the Euclidean analogue of stationary black hole solutions of N=2 supergravity theories.

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arXiv2013

Index theory and dynamical symmetry enhancement of M-horizons

We show that near-horizon geometries of 11-dimensional supergravity preserve an even number of supersymmetries. The proof follows from Lichnerowicz type theorems for two horizon Dirac operators, the field equations and Bianchi identities, and the vanishing of the index of a Dirac operator on the 9-dimensional horizon sections. As a consequence of this, we also prove that all M-horizons with non-vanishing fluxes admit a sl(2,R) subalgebra of symmetries.

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arXiv2013

Supersymmetric AdS Black Rings

It has been proven in arXiv:1303.0853 that all regular supersymmetric near-horizon geometries in minimal five-dimensional gauged supergravity admit automatic supersymmetry enhancement. Using this result, the integrability conditions associated with the existence of the additional supersymmetry are analysed, and the near-horizon geometries are determined explicitly. We show that they all correspond to previously constructed examples. Hence, there are no supersymmetric black ring solutions in minimal five-dimensional gauged supergravity.

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