Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Giuseppe Dibitetto, Nicolò Petri

TL;DR

The paper develops and analyzes BPS flows in minimal $\\mathcal{N}=1$, $D=7$ gauged supergravity with an $\\mathrm{SU}(2)$ gauging and nonzero topological mass, extending domain-wall solutions to dyonic 3-form configurations on backgrounds with $\\mathrm{Mkw}_{3}$ and $\\mathrm{AdS}_{3}$ slicing. It provides analytic solutions for flows with running $B_{(3)}$ and partially decorates them with $\\mathrm{SU}(2)$ vectors (solved numerically in general), uncovering a spectrum of asymptotically $AdS_{7}$ geometries and warped $AdS_{3}$ sectors. The eleven-dimensional interpretation identifies these seven-dimensional flows with M2–M5 bound states, including reductions on $\\mathbb{T}^{4}$ and uplifts to $S^{4}$-reduced $11$D supergravity, connecting flux parameters to embedding-tensor data. The work highlights warped $AdS_{3}$ solutions as potential holographic duals for defect theories and RG flows across dimensions, and suggests future directions toward $D=3$ truncations and a brane-picture for the wrapped M2–M5 configurations.

Abstract

We study several different types of BPS flows within minimal $\mathcal{N}=1$, $D=7$ supergravity with $\textrm{SU}(2)$ gauge group and non-vanishing topological mass. After reviewing some known domain wall solutions involving only the metric and the $\mathbb{R}^{+}$ 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 $\textrm{Mkw}_{3}$ as well as an $\textrm{AdS}_{3}$ slicing, write down the corresponding flow equations, and integrate them analytically to obtain many examples of asymptotically $\mathrm{AdS}_7$ 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 $\mathrm{M2}-\mathrm{M5}$ bound states.

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

TL;DR

The paper develops and analyzes BPS flows in minimal , gauged supergravity with an gauging and nonzero topological mass, extending domain-wall solutions to dyonic 3-form configurations on backgrounds with and slicing. It provides analytic solutions for flows with running and partially decorates them with vectors (solved numerically in general), uncovering a spectrum of asymptotically geometries and warped sectors. The eleven-dimensional interpretation identifies these seven-dimensional flows with M2–M5 bound states, including reductions on and uplifts to -reduced D supergravity, connecting flux parameters to embedding-tensor data. The work highlights warped solutions as potential holographic duals for defect theories and RG flows across dimensions, and suggests future directions toward truncations and a brane-picture for the wrapped M2–M5 configurations.

Abstract

We study several different types of BPS flows within minimal , supergravity with gauge group and non-vanishing topological mass. After reviewing some known domain wall solutions involving only the metric and the 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 as well as an slicing, write down the corresponding flow equations, and integrate them analytically to obtain many examples of asymptotically 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 bound states.

Paper Structure

This paper contains 19 sections, 88 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Minimal gauged supergravities in $D=7$
  3. Domain wall solutions
  4. BPS flows with the 3-form potential
  5. Charged flow on the background $\mathrm{Mkw}_{3}\times \mathbb{R}^3$
  6. Charged flow on the background $\mathrm{Mkw}_{3}\times S^3$
  7. Background $\mathrm{AdS}_3\times S^3$: $\mathrm{AdS}_7$ charged domain wall
  8. Background $\mathrm{AdS}_3\times S^3$: general flow $\mathrm{AdS}_7 \rightarrow \mathrm{AdS}_3\times \mathbb{T}^4$
  9. Coupling to the $\mathrm{\mathrm{SU(2)}}$ vectors
  10. Killing spinors and twisting condition
  11. Vectors coupled to the background $\mathrm{Mkw}_{3}\times S^3$
  12. Vectors coupled to the background $\mathrm{AdS}_3\times S^3$
  13. M-theory lifts
  14. Dyonic solutions and $\mathrm{M2-M5}$ bound state on $\mathbb{T}^4$
  15. $\mathrm{AdS}_7$ flows and $S^4$ reductions
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Flows of $e^{2U(r)},\,e^{2W(r)},\,X(r),\,A(r),\,l(r),\,k(r)$ plotted in the interval $r\in (0,1.4]$ with $g=1$, $h=\frac{1}{2\sqrt{2}}$, $\kappa=1$ and $V(r)=0$.
  • Figure 2: Flows of $e^{2U(r)},\,e^{2W(r)},\,X(r),\,A(r),\,l(r),\,k(r)$ plotted in the interval $r\in (0.5,1]$ with $g=\frac{3^{1/5}\,7^{3/10}}{2^{1/10}}$, $h=\frac{g}{2\sqrt{2}}$, $\kappa=2$, $L=0.3$ and $V(r)=0$.