Domain walls of gauged supergravity, Mbranes, and algebraic curves
Abstract
We provide an algebraic classification of all supersymmetric domain wall solutions of maximal gauged supergravity in four and seven dimensions, in the presence of nontrivial scalar fields in the coset SL(8,R)/SO(8) and SL(5,R)/SO(5) respectively. These solutions satisfy firstorder equations, which can be obtained using the method of Bogomol'nyi. From an elevendimensional point of view they correspond to various continuous distributions of M2 and M5branes. The ChristoffelSchwarz transformation and the uniformization of the associated algebraic curves are used in order to determine the Schrodinger potential for the scalar and graviton fluctuations on the corresponding backgrounds. In many cases we explicitly solve the Schrodinger problem by employing techniques of supersymmetric quantum mechanics. The analysis is parallel to the construction of domain walls of fivedimensional gauged supergravity, with scalar fields in the coset SL(6,R)/SO(6), using algebraic curves or continuous distributions of D3branes in ten dimensions. In seven dimensions, in particular, our classification of domain walls is complete for the full scalar sector of gauged supergravity. We also discuss some general aspects of Ddimensional gravity coupled to scalar fields in the coset SL(N,R)/SO(N).
 Publication:

arXiv eprints
 Pub Date:
 December 1999
 arXiv:
 arXiv:hepth/9912132
 Bibcode:
 1999hep.th...12132B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 46 pages, latex. v2: typos corrected and some references added. v3: minor corrections and improvements, references added, to appear in ATMP