Domain walls of gauged supergravity, M-branes, 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 non-trivial scalar e-print archive: http://xxx.lanl.gov/hep-th/9912132 1658 I. BAKAS, A. BRANDHUBER, AND K. SFETSOS fields in the coset SL(8,R)/ SO(8) and SL(5,R)/SO(b) respectively. These solutions satisfy first-order equations, which can be obtained using the method of Bogomol'nyi. Prom an elevendimensional point of view they correspond to various continuous distributions of M2-and M5-branes. The Christoffel-Schwarz 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 five-dimensional gauged supergravity, with scalar fields in the coset S , L(6,R)/5 , 0(6), using algebraic curves or continuous distributions of D3-branes 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 D-dimensional gravity coupled to scalar fields in the coset SL(N,R)/SO(N).

Non-supersymmetric membrane flows from fake supergravity and multi-trace deformations

“…4 We will not consider further such domain walls here since we are interested in scalar potentials that arise from gauged supergravities, and such potentials are guaranteed to be expressible in the form (1.8) since this is at least possible using the true superpotential W o (φ). 5 Although one often views fake supergravity as an effective subsector of some gauged supergravity, by identifying both the scalar potential and the fake superpotential of fake supergravity with the true potential and superpotential respectively of the gauged supergravity [4,3,6], we will instead treat fake supergravity as a powerful solution generating technique for non-supersymmetric solutions of a given gauged supergravity. In particular, we will treat (1.8) as a first order non-linear differential equation for the fake superpotential W (φ) [10,11,2,12] (see also [13] where a very similar perspective is adopted).…”

“…4 Note though the analysis of [7], which suggests that any potential that admits domain wall solutions can be written in the form (1.8) and so there are no 'non-BPS' domain walls. 5 Generically the superpotential Wo(φ) will be a matrix, however, instead of a scalar quantity. See e.g.…”

“…6 Following [18,14,5], we specialize to an SL(N, R) subgroup of E 11−D , where N = 4(D − 2)/(D − 3), and consider the 1 2 N (N + 1) − 1 scalars of the coset SL(N, R)/ SO(N ). This scalar sector is common to all maximal supergravities in any dimension.…”

“…Given the expression (1.8) for the scalar potential in terms of the function W , the first order equations (1.7) can be derivedá la Bogomol'nyi by extremizing the energy functional E[A, φ] that has (1.6) as its Euler-Lagrange equations [4,5]. In the context of gauged supergravity, a function W (φ) satisfying (1.8) arises naturally as the superpotential, W o (φ), which enters the gravitino and dilatino variations…”

Noncommutative geometry, quantum effects and DBI-scaling in the collapse of D0-D2 bound states

“…This is exactly the g-gap Lamé equation for the ground state of the corresponding onedimensional quantum mechanical problem, which has solutions in terms of ratios of Weierstrass σ-functions ( for an application in supersymmetric gauge theories see for example [30] ).…”