Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of BPS instantons in N=4 D=4 supergravity   This talk is based on the recent work in collaboration with M.
Azreg-A\"{\i}nou and G. Cl\'ement devoted to extremal instantons in the
one-vector truncation of the Euclidean $\mathcal{N}=4,\, D=4$ theory. Extremal
solutions satisfying the no-force condition can be associated with null
geodesic curves in the homogeneous target space of the three-dimensional sigma
model arising in toroidal reduction of the four-dimensional theory. Here we
(preliminarily) discuss the case of two vector fields sufficient to find all
relevant metrics in the full $\mathcal{N}=4,\, D=4$ theory. Classification of
instanton solutions is given along the following lines. The first is their
possible asymptotic structure: asymptotically locally flat (ALF),
asymptotically locally Euclidean (ALE) and ALF or ALE with the dilaton growing
at infinity. The second is the algebraic characterization of matrix generators
according to their rank and the nature of the charge vectors in an associated
Lorentzian space. Finally, solutions are distinguished by the number of
independent harmonic functions with unequal charges (up to four).

18
The categories of this paper are: econ
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: physics