Abstract
We work out the consistent AdS$_3\times S^3$ truncations of the bosonic sectors of both the six-dimensional ${\cal N}=(1,1)$ and ${\cal N}=(2,0)$ supergravity theories. They result in inequivalent three-dimensional half-maximal ${\rm SO}(4)$ gauged supergravities describing 32 propagating bosonic degrees of freedom apart from the non-propagating supergravity multiplet. We present the full non-linear Kaluza-Klein reduction formulas and illustrate them by explicitly uplifting a number of AdS$_3$ vacua.
Highlights
Consistent sphere truncations have a long history in supergravity
We have used the framework of exceptional field theory (ExFT) to work out the consistent truncations of 6D N 1⁄4 ð1; 1Þ and N 1⁄4 ð2; 0Þ supergravity theories on AdS3 × S3
The resulting three-dimensional theories are SOð4Þ gauged supergravities coupled to four half-maximal scalar multiplets, describing the 32 bosonic degrees of freedom
Summary
Consistent sphere truncations have a long history in supergravity. Within maximal supergravity, this goes back to the seminal work of Ref. [1] on the consistent truncation of 11-dimensional supergravity on AdS4 × S7 to the lowest Kaluza-Klein multiplet, giving rise to four-dimensional SOð8Þ gauged supergravity. [1] on the consistent truncation of 11-dimensional supergravity on AdS4 × S7 to the lowest Kaluza-Klein multiplet, giving rise to four-dimensional SOð8Þ gauged supergravity. Using the reformulation of D 1⁄4 6, N 1⁄4 ð1; 0Þ supergravity as an ExFT based on the group SOð4; 4Þ [24], the nonlinear Kaluza-Klein Ansätze from Refs. The resulting threedimensional theories are SOð4Þ gauged supergravities coupled to four half-maximal scalar multiplets [25,26], i.e., with scalar target space given by SOð8; 4Þ=ðSOð8Þ × SOð4ÞÞ. IV and V, we use the explicit Scherk-Schwarz twist matrix U together with the ExFT-supergravity dictionary to work out the full nonlinear Kaluza-Klein Ansätze for all six-dimensional fields, defining the consistent truncation.
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