Abstract
A truncation of the SL(5) Exceptional Field Theory that allows to describe spacetimes of the form M4 × M7 with the 4-form flux on M4 is constructed. The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS4 × mathbbm{S} 7 solution of d = 11 supergravity. We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS4 × mathbbm{S} 7.
Highlights
Is sufficient for the deformed fields G, B to be a supergravity solution [22, 23]
The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS4 × S7 solution of d = 11 supergravity
We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS4 × S7
Summary
The SL(5) exceptional field theory describes supergravity dynamics, while being explicitly covariant under the transformations of the SL(5) U-duality group. In order to obtain an explicit relationship between the 11-dimensional fields and those of the full SL(5) exceptional field theory one must perform the Kaluza-Klein decomposition under the 7 + 4 split, and rearrange the resulting fields into combinations covariant under the generalised Lie derivative of the SL(5) theory. In order to perform this in a consistent manner, we rescale the generalised metric so as to absorb the degrees of freedom contained in det hμν As explained below, this makes a connection between the full exceptional field theory defined above and its truncated version described in [53]. We will truncate the theory to describe only a special class of backgrounds that are relevant for our discussion
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