Duality invariant actions and generalised geometry

We consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E 7(7) . Through the bein for the extended metric we derive dynamical (field-dependent) fluxes taking values in the representations allowed by supersymmetry, and obtain their quadratic constraints from gauge consistency conditions. A covariant generalized Ricci tensor is introduced, defined in terms of a connection for the generalized diffeomorphisms. We show that for any torsionless and metric-compatible generalized connection, the Ricci scalar reproduces the scalar potential of gauged maximal supergravity. We comment on how these results extend to other groups and dimensions.

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“…When E 7 is broken to SU (8), the fundamental 56 and adjoint 133 representations break according to 19) where i, j, · · · = 1, . .…”

Section: Generalized Metric Compatibilitymentioning

confidence: 99%

Extended geometry and gauged maximal supergravity

Aldazábal

Graña

Marqués

et al. 2013

J. High Energ. Phys.

117

185

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“…Finally we end with some comments on the extension of these ideas to the extended, exceptional geometries that occur in M-theory where the full U-duality groups are made a manifest symmetry [58,[60][61][62][63][64][65][66][67][68][69][70][71][72][73].…”

Section: Jhep09(2014)066mentioning

confidence: 99%

“…[58,[60][61][62][63][64][65][66][67][68][69][70][71][72][73]. We refer the reader to those papers or the reviews [16,17] for an introduction.…”

Section: Jhep09(2014)066mentioning

confidence: 99%

Global aspects of double geometry

Berman

Cederwall

Perry³

2014

J. High Energ. Phys.

Self Cite

123

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Abstract:We consider the concept of a generalised manifold in the O(d, d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are defined. Triple overlaps are trivial concerning their action on coordinates, but non-trivial on fields, including the generalised metric. A generalised manifold is an ordinary manifold, but the generalised metric on the manifold carries a gerbe structure. We show how the abelian behaviour of the gerbe is embedded in the non-abelian T-duality group. We also comment on possibilities and difficulties in the U-duality setting.

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“…The extended field theory, as the counterpart of double field theory, was first presented in [22,23], for d = 4, 5 and for d = 6, 7 using the E 11 non linear formalism in [24]. The geometric counterpart of DFT for the E 7 group in d = 7 was developed in [25].…”

Section: Jhep09(2015)153mentioning

confidence: 99%

On the exceptional generalised Lie derivative for d ≥ 7

Rosabal

2015

J. High Energ. Phys.

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In this work we revisit the E 8 × R + generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the E 7 × R + one. Compared to its E d × R + , d ≤ 7 counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the E 8 group, are needed to have a well defined theory. We discuss the implications of the structure of the E 8 × R + generalised transformation on the construction of the d = 8 generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions.

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Duality invariant actions and generalised geometry

Cited by 162 publications

References 83 publications

Extended geometry and gauged maximal supergravity

Extended geometry and gauged maximal supergravity

Global aspects of double geometry

On the exceptional generalised Lie derivative for d ≥ 7

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