Hadi Godazgar

Supersymmetric E7(7) exceptional field theory

A bstractWe give the supersymmetric extension of exceptional field theory for E7(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 SO(1, 3) × SU(8) and transform as scalar densities under the E7(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.

Generalised geometry from the ground up

A bstractExtending previous work on generalised geometry, we explicitly construct an E7(7)-valued vielbein in eleven dimensions that encompasses the would be scalar bosonic degrees of freedom after reduction to four dimensions of D = 11 supergravity, by identifying new “generalised vielbeine” in eleven dimensions associated with the dual 6-form potential and the dual graviton. By maintaining full on-shell equivalence with the original theory at every step our construction furnishes the non-linear ansatz for the dual (magnetic) 7-form flux for any non-trivial compactification of D = 11 supergravity, complementing the known non-linear ansätze for the metric and the 4-form flux. A preliminary analysis of the generalised vielbein postulate for the new vielbein components reveals tantalising hints of new structures beyond D = 11 supergravity and ordinary space-time covariancxe, and also points to the possible D = 11 origins of the embedding tensor. We discuss the extension of these results to E8(8).

Nonlinear Kaluza-Klein theory for dual fields

We present non-linear uplift ansatze for all the bosonic degrees of freedom and dual fields in the S 7 reduction of D = 11 supergravity to maximal SO(8) gauged supergravity and test them for the SO(7) ± invariant solutions. In particular, we complete the known ansatze for the internal components of the metric and 4-form flux by constructing a non-linear ansatz for the internal components of the dual 7-form flux. Furthermore, we provide ansatze for the complete set of 56 vector fields, which are given by more general structures than those available from standard Kaluza-Klein theory. The novel features encountered here have no conventional geometric inter- pretation and provide a new perspective on Kaluza-Klein theory. We study the recently found set of generalised vielbein postulates and, for the S 7 compactification, we show that they reduce to the E7(7) Cartan equation of maximal SO(8) gauged supergravity in four dimensions. The significance of this framework for a higher-dimensional understanding of the embedding tensor and other gauged maximal supergravities is briefly discussed.

Duality completion of higher derivative corrections

A bstractWe present a new method for completing higher derivative corrections for theories that exhibit duality symmetries under reduction. This proposal is based on the observation that duality symmetry in the reduced theory highly constrains the form of the unreduced theory. We apply this idea to closed bosonic string theory and complete the Riemann squared term to simply derive the known full tree-level effective action to order α′.

E8 duality and dual gravity

A bstractWe construct the non-linear realisation of the E8 motion group and compare this with the bosonic sector of eleven dimensional supergravity. The construction naturally leads to the introduction of a new potential field. We identify this new field with the dual gravity field by considering the reduction of the eleven-dimensional theory to three dimensions.

Testing the nonlinear flux ansatz for maximal supergravity

We put to test the recently proposed non-linear flux ansatz for maximal supergravity in eleven dimensions, which gives the seven-dimensional flux in terms of the scalars and pseudoscalars of maximal N = 8 supergravity, by considering a number of non-trivial solutions of gauged supergravity for which the higher dimensional solutions are known. These include the G2 and SU(4) invariant stationary points. The examples considered constitute a very non-trivial check of the ansatz, which it passes with remarkable success.

Einstein-Cartan calculus for exceptional geometry

A bstractIn this paper we establish and clarify the link between the recently found E7(7) generalised geometric structures, which are based on the SU(8) invariant reformulation of D = 11 supergravity proposed long ago, and newer results obtained in the framework of recent approaches to generalised geometry, where E7(7) duality is built in and manifest from the outset. In making this connection, the so-called generalised vielbein postulate plays a key role. We explicitly show how this postulate can be used to define an E7(7) valued affine connection and an associated covariant derivative, which yields a generalised curvature tensor for the E7(7) based exceptional geometry. The analysis of the generalised vielbein postulate also provides a natural explanation for the emergence of the embedding tensor from higher dimensions.

The embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions

We study the Scherk-Schwarz reduction of D = 11 supergravity with background fluxes in the context of a recently developed framework pertaining to D = 11 supergravity. We derive the embedding tensor of the associated four-dimensional maximal gauged theories directly from eleven dimensions by exploiting the generalised vielbein postulates, and by analysing the couplings of the full set of 56 electric and magnetic gauge fields to the generalised vielbeine. The treatment presented here will apply more generally to other reductions of D = 11 supergravity to maximal gauged theories in four dimensions.

Consistent 4-form fluxes for maximal supergravity

A bstractWe derive new ansätze for the 4-form field strength of D = 11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. In particular, the ansätze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity — in this way they provide an explicit uplift of all four-dimensional consistent truncations of D = 11 supergravity. The new ansätze provide a substantially simpler method for uplifting d = 4 flows compared to the previously available method using the 3-form and 6-form potential ansätze. The ansatz for the Freund-Rubin term allows us to conjecture a ‘master formula’ for the latter in terms of the scalar potential of d = 4 gauged supergravity and its first derivative. We also resolve a long-standing puzzle concerning the antisymmetry of the flux obtained from uplift ansätze.

Conformal anomalies and the Einstein field equations

A bstractWe compute corrections to the Einstein field equations which are induced by the anomalous effective actions associated to the type A conformal anomaly, both for the (non-local) Riegert action, as well as for the local action with dilaton. In all cases considered we find that these corrections can be very large.