Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Half-BPS Flux Solutions in M-theory I, Local Solutions   The complete eleven-dimensional supergravity solutions with 16
supersymmetries on manifolds of the form $AdS_3 \times S^3 \times S^3 \times
\Sigma$, with isometry $SO(2,2) \times SO(4) \times SO(4)$, and with either
$AdS_4 \times S^7$ or $AdS_7 \times S^4$ boundary behavior, are obtained in
exact form. The two-dimensional parameter space $\Sigma$ is a Riemann surface
with boundary, over which the product space $AdS_3 \times S^3 \times S^3$ is
warped. By mapping the reduced BPS equations to an integrable system of the
sine-Gordon/Liouville type, and then mapping this integrable system onto a
linear equation, the general local solutions are constructed explicitly in
terms of one harmonic function on $\Sigma$, and an integral transform of two
further harmonic functions on $\Sigma$. The solutions to the BPS equations are
shown to automatically solve the Bianchi identities and field equations for the
4-form field, as well as Einstein's equations. The solutions we obtain have
non-vanishing 4-form field strength on each of the three factors of $AdS_3
\times S^3 \times S^3$, and include fully back-reacted M2-branes in $AdS_7
\times S^4$ and M5-branes in $AdS_4 \times S^7$. No interpolating solutions
exist with mixed $AdS_4 \times S^7$ and $AdS_7 \times S^4$ boundary behavior.
Global regularity of these local solutions, as well as the existence of further
solutions with neither $AdS_4 \times S^7$ nor $AdS_7 \times S^4$ boundary
behavior will be studied elsewhere.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph