Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Supersymmetry of AdS and flat IIB backgrounds   We present a systematic description of all warped $AdS_n\times_w M^{10-n}$
and ${\mathbb{R}}^{n-1,1}\times_w M^{10-n}$ IIB backgrounds and identify the a
priori number of supersymmetries $N$ preserved by these solutions. In
particular, we find that the $AdS_n$ backgrounds preserve $N=2^{[{n\over2}]} k$
for $n\leq 4$ and $N=2^{[{n\over2}]+1} k$ for $4<n\leq 6$ supersymmetries and
for $k\in {\mathbb{N}}_{+}$ suitably restricted. In addition under some
assumptions required for the applicability of the maximum principle, we
demonstrate that the Killing spinors of $AdS_n$ backgrounds can be identified
with the zero modes of Dirac-like operators on $M^{10-n}$ establishing a new
class of Lichnerowicz type theorems. Furthermore, we adapt some of these
results to ${\mathbb{R}}^{n-1,1}\times_w M^{10-n}$ backgrounds with fluxes by
taking the AdS radius to infinity. We find that these backgrounds preserve
$N=2^{[{n\over2}]} k$ for $2<n\leq 4$ and $N=2^{[{n+1\over2}]} k$ for $4<n\leq
7$ supersymmetries. We also demonstrate that the Killing spinors of
$AdS_n\times_w M^{10-n}$ do not factorize into Killing spinors on $AdS_n$ and
Killing spinors on $M^{10-n}$.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn