BPS objects in D = 7 supergravity and their M-theory origin

Abstract

We study several different types of BPS flows within minimal N = 1, D = 7 supergravity with SU(2) gauge group and non-vanishing topological mass. After reviewing some known domain wall solutions involving only the metric and the R + scalar field, we move to considering more general flows involving a "dyonic" profile for the 3-form gauge potential. In this context, we consider flows featuring a Mkw 3 as well as an AdS 3 slicing, write down the corresponding flow equations, and integrate them analytically to obtain many examples of asymptotically AdS 7 solutions in presence of a running 3-form. Furthermore, we move to adding the possibility of non-vanishing vector fields, find the new corresponding flows and integrate them numerically. Finally, we discuss the eleven-dimensional interpretation of the aforementioned solutions as effective descriptions of M2 − M5 bound states.

Supersymmetric solutions of 7D maximal gauged supergravity

“…In the limit r → 0, the solution is singular similar to the solution studied in [12]. For SO(4, 1) gauge group with ρ = −1, there is no AdS 7 asymptotic since this gauge group does not admit a supersymmetric AdS 7 vacuum.…”

“…Since the four-form field strengths do not enter the supersymmetry transformations of fermionic fields, the functions k M (r) and l M (r) will appear, in this case, algebraically in the resulting BPS equations. This is in constrast to the pure N = 2 gauged supergravity considered in [12] in which the four-form field strength of the massive three-form field appears in the supersymmetry transformations. Therefore, in that case, the BPS conditions result in differential equations for k(r) and l(r).…”

“…In this case, we look for domain wall solutions with Mkw 3 × S 3 slice. Following [12], we choose the follwing gauge choice…”

“…We now consider more complicated solutions with an AdS 3 × S 3 slice. As in [12], we begin with a simpler solution with a single warp factor U = W . From the BPS equations (66) -(71), imposing…”

“…The solutions under consideration here take the form of Mkw 3 ×S 3 and AdS 3 ×S 3 -sliced domain walls. This type of solutions has originally been considered in the minimal N = 2 gauged supergravity in [12], see also [13] for similar solutions in the matter-coupled N = 2 gauged supergravity. Some of these solutions have been interpreted as surface defects within N = (1, 0) superconformal field theory (SCFT) in six dimensions in [14], see [15,16] for similar solutions in six dimensions and [17,18,19,20,21,22] for examples of another holographic description of conformal defects in terms of Janus solutions.…”