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Supersymmetric Domain-Wall World from D=5 Simple Gauged Supergravity

Klaus Behrndt, Mirjam Cvetic

TL;DR

This work constructs and analyzes supersymmetric domain walls in five-dimensional N=2 U(1) gauged supergravity, deriving the Killing spinor equations and showing that BPS walls preserve four supercharges, yielding a flat 4D world with N=1 SUSY on the wall. The authors relate the wall tension to the cosmological constants of the asymptotic AdS vacua via $\sigma_{BPS}= - \frac{g}{2} (W_{+\infty}-W_{-\infty})$, and classify possible BPS wall geometries. In the explicit one-vector multiplet case, the potential and superpotential exhibit at most two SUSY extrema separated by a pole where critical quantities diverge, forcing domain walls to interpolate across a singular region; typical solutions are Type IV with characteristic exponential asymptotics for $A(z)$. A concrete numerical example illustrates the slow-down of the scalar profile near the pole and a pronounced feature in the warp factor, highlighting the nuanced structure of supersymmetric domain walls in minimal gauged supergravity and their implications for AdS/CFT RG flows and brane-world scenarios.

Abstract

We address a supersymmetric embedding of domain walls with asymptotically anti-deSitter (AdS) space-times in five-dimensional simple, N=2 U(1) gauged supergravity theory constructed by Gunaydin, Townsend and Sierra. These conformally flat solutions interpolate between supersymmetric AdS vacua, satisfy the Killing spinor (first order) differential equations, and the four-dimensional world on the domain wall is a flat world with N=1 supersymmetry. Regular solutions in this class have the energy density related to the cosmological constants of the supersymmetric AdS vacua. An analysis of such solutions is given for the example of one (real, neutral) vector supermultiplet with the most general form of the prepotential. There are at most two supersymmetric AdS vacua that are in general separated by a singularity in the potential. Nevertheless the supersymmetric domain wall solution exists with the scalar field interpolating continuously across the singular region.

Supersymmetric Domain-Wall World from D=5 Simple Gauged Supergravity

TL;DR

This work constructs and analyzes supersymmetric domain walls in five-dimensional N=2 U(1) gauged supergravity, deriving the Killing spinor equations and showing that BPS walls preserve four supercharges, yielding a flat 4D world with N=1 SUSY on the wall. The authors relate the wall tension to the cosmological constants of the asymptotic AdS vacua via , and classify possible BPS wall geometries. In the explicit one-vector multiplet case, the potential and superpotential exhibit at most two SUSY extrema separated by a pole where critical quantities diverge, forcing domain walls to interpolate across a singular region; typical solutions are Type IV with characteristic exponential asymptotics for . A concrete numerical example illustrates the slow-down of the scalar profile near the pole and a pronounced feature in the warp factor, highlighting the nuanced structure of supersymmetric domain walls in minimal gauged supergravity and their implications for AdS/CFT RG flows and brane-world scenarios.

Abstract

We address a supersymmetric embedding of domain walls with asymptotically anti-deSitter (AdS) space-times in five-dimensional simple, N=2 U(1) gauged supergravity theory constructed by Gunaydin, Townsend and Sierra. These conformally flat solutions interpolate between supersymmetric AdS vacua, satisfy the Killing spinor (first order) differential equations, and the four-dimensional world on the domain wall is a flat world with N=1 supersymmetry. Regular solutions in this class have the energy density related to the cosmological constants of the supersymmetric AdS vacua. An analysis of such solutions is given for the example of one (real, neutral) vector supermultiplet with the most general form of the prepotential. There are at most two supersymmetric AdS vacua that are in general separated by a singularity in the potential. Nevertheless the supersymmetric domain wall solution exists with the scalar field interpolating continuously across the singular region.

Paper Structure

This paper contains 4 sections, 25 equations, 1 figure.

Table of Contents

  1. Introduction
  2. D=5 N=2 U(1) Gauged Supergravity
  3. BPS Domain Walls with One Vector Supermultiplet
  4. Conclusions

Figures (1)

  • Figure 1: The domain wall solution for the scalar field $\phi(z)$ and the metric coefficient $A(z)^{-1}$ is depicted for the choice of parameters $\chi=1.4$ and $\xi=-0.6$. Note the "slow-down" of the kink and a "spike" of the metric coefficient $A(z)^{-1}$ in the region in the middle of the wall.