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High Energy Physics - Theory, hep-th
Abstract:
Consistent reductions of higher-dimensional (matter-coupled) gravity theories
on spheres have been constructed and classified in an important paper by
Cveti\v{c}, L\"u and Pope. We close a gap in the classification and study the
case when the resulting lower-dimensional theory is two-dimensional. We
construct the consistent reduction of Einstein-Maxwell-dilaton gravity on a
$d$-sphere $S^d$ to two-dimensional dilaton-gravity coupled to a gauged sigma
model with target space ${\rm SL}(d+1)/{\rm SO}(d+1)$. The truncation contains
solutions of type AdS$_2\times \Sigma_d$ where the internal space $\Sigma_d$ is
a deformed sphere. In particular, the construction includes the consistent
truncation around the near-horizon geometry of the boosted Kerr string. In
turn, we find that an AdS$_2\times S^d$ background with the round $S^d$ within
a consistent truncation requires $d>3$ and an additional cosmological term in
the higher-dimensional theory.
