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A Satellite $N=2$ Superparticle in Extra Dimensions

F. E. A. de Souza, M. O. Tahim, R. I. O. Junior, I. M. Macedo

TL;DR

This work investigates whether an $N=2$ spinning particle can be localized on a five-dimensional Randall–Sundrum brane to realize localized $p$-form fields. It develops the $N=2$ spinning-particle action with Grassmann variables and a Chern–Simons term, analyzes the dynamics in RS geometry, and derives an effective potential $u_{ ext{eff}}$ governing motion in the extra dimension. The key finding is that localization would require $A''(0)=0$, but localized gravity models satisfy $A''(0)<0$, leading to non-confinement and hence non-localization of the $p$-forms on the membrane; this also reveals a satellite-like orbital behavior in extra dimensions. The results prompt reconsideration of $p$-form localization mechanisms in braneworld scenarios and suggest exploring higher-$N$ models or alternative backgrounds to achieve confinement and gravity localization.

Abstract

In this work we discuss the issue of localization of $N=2$ spinning particles. More specifically, we show that we can not confine the spinning particle within the Randall-Sundrum scenario. We argue that this result directly affects studies related to localization of $p$-form fields. We show that, due to the non confinement of the superparticle, we can not localize $p$-forms on the membrane.

A Satellite $N=2$ Superparticle in Extra Dimensions

TL;DR

This work investigates whether an spinning particle can be localized on a five-dimensional Randall–Sundrum brane to realize localized -form fields. It develops the spinning-particle action with Grassmann variables and a Chern–Simons term, analyzes the dynamics in RS geometry, and derives an effective potential governing motion in the extra dimension. The key finding is that localization would require , but localized gravity models satisfy , leading to non-confinement and hence non-localization of the -forms on the membrane; this also reveals a satellite-like orbital behavior in extra dimensions. The results prompt reconsideration of -form localization mechanisms in braneworld scenarios and suggest exploring higher- models or alternative backgrounds to achieve confinement and gravity localization.

Abstract

In this work we discuss the issue of localization of spinning particles. More specifically, we show that we can not confine the spinning particle within the Randall-Sundrum scenario. We argue that this result directly affects studies related to localization of -form fields. We show that, due to the non confinement of the superparticle, we can not localize -forms on the membrane.

Paper Structure

This paper contains 8 sections, 42 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Particle Mechanics and Antisymmetric Tensor Fields
  3. Action for Spinning Particles
  4. Quantization and P-Forms
  5. Confinement of N Spinning Particle
  6. D=5 Spinning Particle
  7. Some Braneworld models.
  8. Conclusions and Perspectives

Figures (4)

  • Figure 1: The effective potentials due to the Sine-Gordon (left side) and $\phi^{4}$ (right side) membrane models.
  • Figure 2: The effective potential due to the Bloch membrane model.
  • Figure 3: The effective potentials due to the Deformed membrane model: on the left side we plot the potential for $s=3$ and, on the right side, for $s=5$. In this last case, we start to see the appearance of a flat potential region around $y=0$.
  • Figure 4: The effective potential due to the Deformed membrane case with $s=7$. Here clearly the flat region shows up. In this case, the satellite particle goes to the left far from $y=0$.