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Brane Induced Gravity: Codimension-2

Nemanja Kaloper

TL;DR

This work analyzes brane induced gravity on regulated codimension-$2$ branes in $6D$, showing that near-critical tensions trap the brane in a deep throat that compactifies one bulk dimension and generates a controlled sequence of gravity regimes ($4D$ to $5D$ to $6D$). The crossover scales, notably $r_c = M_5^3/M_6^4$, emerge from the throat geometry and are largely independent of tension for the $4D$ to $5D$ transition, but depend on tension for the $5D$ to $6D$ transition, shifting the cosmological constant problem into tuning of these scales. Linearized perturbation theory around near-critical vacua remains reliable below the crossover and reveals a scalar-tensor character due to a suppressed radion, while sub-critical branes exhibit a strongly coupled scalar sector and potential breakdowns in perturbation theory. Overall, the results indicate that BIG on codimension-$2$ branes can reproduce $4D$ gravity over a wide range of scales with calculable corrections, though tuning of brane tension is needed to achieve desired crossover hierarchies and to potentially address cosmological constant issues without overtly altering $4D$ curvature.

Abstract

We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG) in 6D. Among a large diversity of regulated codimension-2 branes, we find that for near-critical tensions branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent of the tension, but the crossover from 5D to 6D is not. This shows how the vacuum energy problem manifests in BIG: instead of tuning vacuum energy to adjust the 4D curvature, generically one must tune it to get the desired crossover scales and the hierarchy between the scales governing the 4D \to 5D \to 6D transitions. In the near-critical limit, linearized perturbation theory remains under control below the crossover scale, and we find that linearized gravity around the vacuum looks like a scalar-tensor theory.

Brane Induced Gravity: Codimension-2

TL;DR

This work analyzes brane induced gravity on regulated codimension- branes in , showing that near-critical tensions trap the brane in a deep throat that compactifies one bulk dimension and generates a controlled sequence of gravity regimes ( to to ). The crossover scales, notably , emerge from the throat geometry and are largely independent of tension for the to transition, but depend on tension for the to transition, shifting the cosmological constant problem into tuning of these scales. Linearized perturbation theory around near-critical vacua remains reliable below the crossover and reveals a scalar-tensor character due to a suppressed radion, while sub-critical branes exhibit a strongly coupled scalar sector and potential breakdowns in perturbation theory. Overall, the results indicate that BIG on codimension- branes can reproduce gravity over a wide range of scales with calculable corrections, though tuning of brane tension is needed to achieve desired crossover hierarchies and to potentially address cosmological constant issues without overtly altering curvature.

Abstract

We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG) in 6D. Among a large diversity of regulated codimension-2 branes, we find that for near-critical tensions branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent of the tension, but the crossover from 5D to 6D is not. This shows how the vacuum energy problem manifests in BIG: instead of tuning vacuum energy to adjust the 4D curvature, generically one must tune it to get the desired crossover scales and the hierarchy between the scales governing the 4D \to 5D \to 6D transitions. In the near-critical limit, linearized perturbation theory remains under control below the crossover scale, and we find that linearized gravity around the vacuum looks like a scalar-tensor theory.

Paper Structure

This paper contains 7 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Regulated Near-critical Branes
  3. Matter on Thick Branes
  4. Shocks
  5. Scales of Gravity
  6. Gravity of Slow Sources
  7. Summary

Figures (2)

  • Figure 1: $2D$ bulk geometry of the resolved brane.
  • Figure 2: $2D$ bulk geometry of the near-critical resolved 3-brane.