Abstract
We use exceptional field theory to compute Kaluza-Klein mass spectra around {AdS_{3}}AdS3 vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of {N}=(2,0)N=(2,0) and {N}=(1,1)N=(1,1) six-dimensional supergravities on {AdS_{3}}\times S^{3}AdS3×S3 and of type II supergravity on {AdS_{3}}\times S^{3}\times S^{3}\times S^{1}AdS3×S3×S3×S1.
Highlights
The compactification of a higher-dimensional theory induces the appearance of infinitely many massive fields in the low-dimensional theory, which organize into multiplets of the symmetry group associated to the space of compactification
The truncation described by the embedding tensor (4.25) properly embedded into E8(8) exceptional field theory [10] is consistent by construction, and leads to the maximal three-dimensional supergravity constructed in Ref. [34]
We developed tools to compute the bosonic Kaluza-Klein spectrum around any vacuum of a half-maximal gauged supergravity in three dimensions that arises from a consistent truncation of higher-dimensional supergravity
Summary
The compactification of a higher-dimensional theory induces the appearance of infinitely many massive fields in the low-dimensional theory, which organize into multiplets of the symmetry group associated to the space of compactification. The computation of the Kaluza-Klein spectrum is in general involved It demands the linearization of the higher-dimensional equations of motion, the expansion of all fields in harmonics of the internal space and to disentangle the resulting equations to deduce the mass matrices. For a given low-dimensional background that arises from a consistent truncation, one can extend these ansätze so that they describe the linearized higher-dimensional fluctuations around the background This allows the computation of the mass matrices of the full Kaluza-Klein towers and, in particular, makes it possible to compute the spectrum around vacua with few or no remaining symmetries. We first test the formulas using N = (2, 0) six-dimensional supergravity on AdS3 × S3 This example is particular, as its structure is sufficiently constrained by supersymmetry to allow a computation of the spectrum using only group theory [17]. Its presence is necessary for the closure of the non-abelian gauge transformations [16]
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