Abstract
In the exceptional field theory, there are two natural parameterizations for the generalized metric; in terms of bosonic fields in the eleven-dimensional supergravity (M-theory parameterization) and the type IIB supergravity (type IIB parameterization). In order to translate various results known in the M-theory to the type IIB theory or vice versa, an explicit map between the two parameterizations will be useful. In this note, we present such a linear map. Comparing the two parameterizations under the linear map, we reproduce the known T-duality transformation rules for the supergravity fields. We also obtain the T-duality rules for non-geometric $\beta$-/$\gamma$-fields appearing in the type II theory on a torus.
Highlights
The Exceptional Field Theory (EFT) [1,2,3,4,5,6,7,8,9,10,11,12,13] has been developed for a manifestly U -duality covariant formulation of supergravities
If we consider a parameterization in terms of the bosonic fields in the type IIB supergravity the action of the type IIB supergravity can be reproduced [9, 14]
We show that, using the relation of fields in the eleven-dimensional supergravity and the type IIA supergravity, the above identifications are nothing but the T -duality transformation rules between the type IIA and the type IIB supergravity, known as Buscher’s rules [20,21,22,23,24]
Summary
The Exceptional Field Theory (EFT) [1,2,3,4,5,6,7,8,9,10,11,12,13] has been developed for a manifestly U -duality covariant formulation of supergravities. We show that, using the relation of fields in the eleven-dimensional supergravity and the type IIA supergravity, the above identifications are nothing but the T -duality transformation rules between the type IIA and the type IIB supergravity, known as Buscher’s rules [20,21,22,23,24] In both the M-theory and the type IIB theory, we can consider a different parameterization for MIJ , called the non-geometric parameterization [16, 25,26,27,28,29,30,31,32], in terms of the non-geometric potentials introduced in [33, 34]. We obtain Buscher’s rules for non-geometric potentials (see [35] for a recent work on a similar topic)
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