arXiv subjects

Henning Samtleben

Publications and source records attributed to Henning Samtleben.

At least 73 records · Page 4Linked to original sources

arXiv2016

E$_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry

We present the supersymmetric extension of the recently constructed E$_{8(8)}$ exceptional field theory -- the manifestly U-duality covariant formulation of the untruncated ten- and eleven-dimensional supergravities. This theory is formulated on a (3+248) dimensional spacetime (modulo section constraint) in which the extended coordinates transform in the adjoint representation of E$_{8(8)}$. All bosonic fields are E$_{8(8)}$ tensors and transform under internal generalized diffeomorphisms. The fermions are tensors under the generalized Lorentz group SO(1,2)$\times$SO(16), where SO(16) is the maximal compact subgroup of E$_{8(8)}$. Vanishing generalized torsion determines the corresponding spin connections to the extent they are required to formulate the field equations and supersymmetry transformation laws. We determine the supersymmetry transformations for all bosonic and fermionic fields such that they consistently close into generalized diffeomorphisms. In particular, the covariantly constrained gauge vectors of E$_{8(8)}$ exceptional field theory combine with the standard supergravity fields into a single supermultiplet. We give the complete extended Lagrangian and show its invariance under supersymmetry. Upon solution of the section constraint the theory reduces to full D=11 or type IIB supergravity.

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arXiv2016

The N>2 supersymmetric AdS vacua in maximal supergravity

We perform a systematic search for anti-de Sitter vacua of maximal supergravity with N>2 residual supersymmetries. We find that maximal supergravity admits two 1-parameter classes of N=3 and N=4 vacua, respectively. They are embedded, for the different values of an angular parameter, in the $ω$-rotated SO(8) (N=3) and SO(1,7) (N=4 and 3) gauged models. All vacua disappear in the limit when $ω$ tends to zero. We determine the mass spectra and the AdS-supermultiplet structure. These appear to be the first and only N>2 supersymmetric AdS vacua in maximal supergravity, aside from the N=8 vacua of the SO(8)-gauged models. We also prove on general grounds that no such vacua can exist for 4<N<8.

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arXiv2015

Dualising consistent IIA / IIB truncations

We use exceptional field theory to establish a duality between certain consistent 7-dimensional truncations with maximal SUSY from IIA to IIB. We use this technique to obtain new consistent truncations of IIB on $S^3$ and $H^{p,q}$ and work out the explicit reduction formulas in the internal sector. We also present uplifts for other gaugings of 7-d maximal SUGRA, including theories with a trombone gauging. Some of the latter can only be obtained by a non-geometric compactification.

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arXiv2015

E$_{6(6)}$ Exceptional Field Theory: Review and Embedding of Type IIB

We review E$_{6(6)}$ exceptional field theory with a particular emphasis on the embedding of type IIB supergravity, which is obtained by picking the GL$(5)\times {\rm SL}(2)$ invariant solution of the section constraint. We work out the precise decomposition of the E$_{6(6)}$ covariant fields on the one hand and the Kaluza-Klein-like decomposition of type IIB supergravity on the other. Matching the symmetries, this allows us to establish the precise dictionary between both sets of fields. Finally, we establish on-shell equivalence. In particular, we show how the self-duality constraint for the four-form potential in type IIB is reconstructed from the duality relations in the off-shell formulation of the E$_{6(6)}$ exceptional field theory.

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arXiv2015

Consistent Type IIB Reductions to Maximal 5D Supergravity

We use exceptional field theory as a tool to work out the full non-linear reduction ansaetze for the AdS$_5\times S^5$ compactification of IIB supergravity and its non-compact counterparts in which the sphere $S^5$ is replaced by the inhomogeneous hyperboloidal space $H^{p,q}$. The resulting theories are the maximal 5D supergravities with gauge groups SO(p,q). They are consistent truncations in the sense that every solution of 5D supergravity lifts to a solution of IIB supergravity. In particular, every stationary point and every holographic RG flow of the scalar potentials for the compact and non-compact 5D gaugings directly lift to solutions of IIB supergravity.

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arXiv2015

All timelike supersymmetric solutions of three-dimensional half-maximal supergravity

We first classify all supersymmetric solutions of the 3-dimensional half-maximal ungauged supergravity that possess a timelike Killing vector coming from the Killing spinor bilinear by considering their identification under the complexification of the local symmetry of the theory. It is found that only solutions that preserve $16/2^n, 1 \leq n \leq 3$ real supersymmetries are allowed. We then classify supersymmetric solutions under the real local symmetry of the theory and we are able to solve the equations of motion for all of them. It is shown that all such solutions can be expressed as a direct sum of solutions of the integrable Liouville and SU(3) Toda systems. This completes the construction of all supersymmetric solutions of the model since the null case has already been solved.

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arXiv2015

Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB

We present the details of the recently constructed $E_{6(6)}$ covariant extension of 11-dimensional supergravity. This theory requires a 5+27 dimensional spacetime in which the `internal' coordinates transform in the $\bar{\bf 27}$ of $E_{6(6)}$. All fields are $E_{6(6)}$ tensors and transform under (gauged) internal generalized diffeomorphisms. The `Kaluza-Klein' vector field acts as a gauge field for the $E_{6(6)}$ covariant `E-bracket' rather than a Lie bracket, requiring the presence of two-forms akin to the tensor hierarchy of gauged supergravity. We construct the complete and unique action that is gauge invariant under generalized diffeomorphisms in the internal and external coordinates. The theory is subject to covariant section constraints on the derivatives, implying that only a subset of the extra 27 coordinates is physical. We give two solutions of the section constraints: the first preserves GL(6) and embeds the action of the complete (i.e. untruncated) 11-dimensional supergravity; the second preserves GL(5) x SL(2) and embeds complete type IIB supergravity. As a by-product, we thus obtain an off-shell action for type IIB supergravity.

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arXiv2015

Consistent Kaluza-Klein Truncations via Exceptional Field Theory

We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO(p,q) and CSO(p,q,r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides $H^{p,q}$, thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D=11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS$_5\times S^5$), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.

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arXiv2015

Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions

We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six spacetime dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q, this higher bundle can be compactly described by means of a Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of spacetime equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q^2=0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being determined from a Q-derived bracket.

math-ph↗

arXiv2014

Fermions and Supersymmetry in $\rm E_{6(6)}$ Exceptional Field Theory

We construct the supersymmetric completion of E$_{6(6)}$-covariant exceptional field theory. The theory is based on a $(5+27)$-dimensional generalized space-time subject to a covariant section constraint. The fermions are tensors under the local Lorentz group ${\rm SO}(1,4)\times {\rm USp}(8)$ and transform as weighted scalars under the E$_{6(6)}$ (internal) generalized diffeomorphisms. We present the complete Lagrangian and prove its invariance under supersymmetry. Upon explicit solution of the section constraint the theory embeds full $D=11$ supergravity and IIB supergravity, respectively.

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arXiv2014

Matrix model holography

We set up the formalism of holographic renormalization for the matter-coupled two-dimensional maximal supergravity that captures the low-lying fluctuations around the non-conformal D0-brane near-horizon geometry. As an application we compute holographically one- and two-point functions of the BFSS matrix quantum mechanics and its supersymmetric $SO(3)\times SO(6)$ deformation.

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arXiv2014

A supersymmetric reduction on the three-sphere

We present the embedding of three-dimensional SO(4)$\ltimes\mathbb{R}^6$ gauged $N=4$ supergravity with quaternionic target space SO(4,4)$/$(SO(4)$\times$SO(4)) into $D=6$, $N=(1,0)$ supergravity coupled to a single chiral tensor multiplet through a consistent reduction on AdS$_3\times S^3$.

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arXiv2014

Exceptional Field Theory III: E$_{8(8)}$

We develop exceptional field theory for E$_{8(8)}$, defined on a (3+248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E$_{8(8)}$. The fields transform under E$_{8(8)}$ generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an `internal' dreibein and an E$_{8(8)}$-valued `zweihundertachtundvierzigbein' (248-bein). Crucially, the theory also features gauge vectors for the E$_{8(8)}$ E-bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained E$_{8(8)}$ gauge symmetry. The complete bosonic theory, with a novel Chern-Simons term for the gauge vectors, is uniquely determined by gauge invariance under internal and external generalized diffeomorphisms. The theory consistently comprises components of the dual graviton encoded in the 248-bein. Upon picking particular solutions of the constraints the theory reduces to D=11 or type IIB supergravity, for which the dual graviton becomes pure gauge. This resolves the dual graviton problem, as we discuss in detail.

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arXiv2014

Supersymmetric E$_{7(7)}$ Exceptional Field Theory

We give the supersymmetric extension of exceptional field theory for E$_{7(7)}$, which is based on a $(4+56)$-dimensional generalized spacetime subject to a covariant constraint. The fermions are tensors under the local Lorentz group ${\rm SO}(1,3)\times {\rm SU}(8)$ and transform as scalar densities under the E$_{7(7)}$ (internal) generalized diffeomorphisms. The supersymmetry transformations are manifestly covariant under these symmetries and close, in particular, into the generalized diffeomorphisms of the 56-dimensional space. We give the fermionic field equations and prove supersymmetric invariance. We establish the consistency of these results with the recently constructed generalized geometric formulation of $D=11$ supergravity.

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arXiv2014

Supersymmetric Warped AdS in Extended Topologically Massive Supergravity

We determine the most general form of off-shell N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell supergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS_3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS_3. This occurs when the coefficient of the Lorentz-Chern-Simons term is related to the AdS radius by $μ\ell=2$. We find that the spacelike-squashed AdS_3 can be modded out by a suitable discrete subgroup of the isometry group, yielding an extremal black hole solution which avoid closed timelike curves.

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arXiv2014

Exceptional Field Theory II: E$_{7(7)}$

We introduce exceptional field theory for the group E_{7(7)}, based on a (4+56)-dimensional spacetime subject to a covariant section condition. The `internal' generalized diffeomorphisms of the coordinates in the fundamental representation of E_{7(7)} are governed by a covariant `E-bracket', which is gauged by 56 vector fields. We construct the complete and unique set of field equations that is gauge invariant under generalized diffeomorphisms in the internal and external coordinates. Among them feature the non-abelian twisted self-duality equations for the 56 gauge vectors. We discuss the explicit solutions of the section condition describing the embedding of the full, untruncated 11-dimensional and type IIB supergravity, respectively. As a new feature compared to the previously constructed E_{6(6)} formulation, some components among the 56 gauge vectors descend from the 11-dimensional dual graviton but nevertheless allow for a consistent coupling by virtue of a covariantly constrained compensating 2-form gauge field.

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arXiv2013

Exceptional Form of D=11 Supergravity

Eleven-dimensional supergravity reveals large exceptional symmetries upon reduction, in accordance with the U-duality groups of M-theory, but their higher-dimensional geometric origin has remained a mystery. In this letter, we show that D=11 supergravity can be extended to be fully covariant under the exceptional groups E_{n(n)}, n=6,7,8. Motivated by a similar formulation of double field theory we introduce an extended `exceptional spacetime'. We illustrate the construction by giving the explicit E_{6(6)} covariant form: the full D=11 supergravity, in a 5+6 splitting of coordinates but without truncation, embeds into an E_{6(6)} covariant 5+27 dimensional theory. We argue that this covariant form likewise comprises type IIB supergravity.

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arXiv2013

Rotating D0-branes and consistent truncations of supergravity

The fluctuations around the D0-brane near-horizon geometry are described by two-dimensional SO(9) gauged maximal supergravity. We work out the U(1)^4 truncation of this theory whose scalar sector consists of five dilaton and four axion fields. We construct the full non-linear Kaluza-Klein ansatz for the embedding of the dilaton sector into type IIA supergravity. This yields a consistent truncation around a geometry which is the warped product of a two-dimensional domain wall and the sphere S^8. As an application, we consider the solutions corresponding to rotating D0-branes which in the near-horizon limit approach AdS2xM8 geometries, and discuss their thermodynamical properties. More generally, we study the appearance of such solutions in the presence of non-vanishing axion fields.

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