Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-02-03
Nucl.Phys.B583:211-236,2000
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, latex, no figures, references added, typos corrected
Scientific paper
10.1016/S0550-3213(00)00214-5
We address some issues related to the construction of general Kaluza-Klein (KK) ans\"atze for the compactification of a supergravity (sugra) theory on a sphere $S_m$. We first reproduce various ans\"atze for compactification to 7d from the ansatz for the full nonlinear KK reduction of 11d sugra on $AdS_7\times S_4$. As a side result, we obtain a lagrangian formulation of 7d ${\cal N}=2$ gauged sugra, which so far had only a on-shell formulation, through field equations and constraints. The $AdS_7\times S_4$ ansatz generalizes therefore all previous sphere compactifications to 7d. Then we consider the case when the scalars in the lower dimensional theory are in a coset $Sl(m+1)/SO(m+1)$, and we keep the maximal gauge group $SO(m+1)$. The 11-dimensional sugra truncated on $S_4$ fits precisely the case under consideration, and serves as a model for our construction. We find that the metric ansatz has a universal expression, with the internal space deformed by the scalar fluctuations to a conformally rescaled ellipsoid. We also find the ansatz for the dependence of the antisymmetric tensor on the scalars. We comment on the fermionic ansatz, which will contain a matrix $U$ interpolating between the spinorial $SO(m+1)$ indices of the spherical harmonics and the $R$-symmetry indices of the fermionic fields in the lower dimensional sugra theory. We derive general conditions which the matrix $U$ has to satisfy and we give a formula for the vielbein in terms of $U$. As an application of our methods we obtain the full ansatz for the metric and vielbein for 10d sugra on $AdS_5\times S_5$ (with no restriction on any fields).
Nastase Horatiu
Vaman Diana
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