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Gauge coupling renormalization in RS1

K. Agashe, A. Delgado, R. Sundrum

TL;DR

This work computes the one-loop correction to the 4D gauge coupling in the RS1 framework with bulk gauge fields and charged matter, using a 5D gauge-invariant Pauli-Villars regulator to control divergences. It decomposes the UV structure into bulk and brane contributions via a 5D position-space analysis and identifies the finite, KK-mode–driven piece f(q, r_c, m_5, k) through a careful KK spectrum analysis. The results reveal a robust logarithmic sensitivity to the 4D Planck scale, matching expectations from AdS/CFT and large-N reasoning, and they provide explicit forms in distinct mass regimes of the bulk scalar m_5. The findings have direct relevance to grand unification in RS1 and demonstrate a consistent dual CFT interpretation of RS1 loop corrections as subleading large-N effects, including TeV-scale threshold behavior.

Abstract

We compute the 4D low energy effective gauge coupling at one-loop order in the compact Randall-Sundrum scenario with bulk gauge fields and charged matter, within controlled approximations. While such computations are subtle, they can be important for studying phenomenological issues such as grand unification. Ultraviolet divergences are cut-off using Pauli-Villars regularization so as to respect 5D gauge and general coordinate invariance. The structure of these divergences on branes and in the bulk is elucidated by a 5D position-space analysis. The remaining finite contributions are obtained by a careful analysis of the Kaluza-Klein spectrum. We comment on the agreement between our results and expectations based on the AdS/CFT correspondence, in particular logarithmic sensitivity to the 4D Planck scale.

Gauge coupling renormalization in RS1

TL;DR

This work computes the one-loop correction to the 4D gauge coupling in the RS1 framework with bulk gauge fields and charged matter, using a 5D gauge-invariant Pauli-Villars regulator to control divergences. It decomposes the UV structure into bulk and brane contributions via a 5D position-space analysis and identifies the finite, KK-mode–driven piece f(q, r_c, m_5, k) through a careful KK spectrum analysis. The results reveal a robust logarithmic sensitivity to the 4D Planck scale, matching expectations from AdS/CFT and large-N reasoning, and they provide explicit forms in distinct mass regimes of the bulk scalar m_5. The findings have direct relevance to grand unification in RS1 and demonstrate a consistent dual CFT interpretation of RS1 loop corrections as subleading large-N effects, including TeV-scale threshold behavior.

Abstract

We compute the 4D low energy effective gauge coupling at one-loop order in the compact Randall-Sundrum scenario with bulk gauge fields and charged matter, within controlled approximations. While such computations are subtle, they can be important for studying phenomenological issues such as grand unification. Ultraviolet divergences are cut-off using Pauli-Villars regularization so as to respect 5D gauge and general coordinate invariance. The structure of these divergences on branes and in the bulk is elucidated by a 5D position-space analysis. The remaining finite contributions are obtained by a careful analysis of the Kaluza-Klein spectrum. We comment on the agreement between our results and expectations based on the AdS/CFT correspondence, in particular logarithmic sensitivity to the 4D Planck scale.

Paper Structure

This paper contains 11 sections, 33 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Model
  3. Review of Classical Approximation
  4. Quantum Divergence Structure and Renormalization
  5. KK mode analysis
  6. Set-up
  7. Summary of results
  8. Derivation of results
  9. $m_5 \ll q \ll m_{KK}$
  10. $\hbox{TeV} \ll m_5 \ll k$
  11. The dual CFT: subleading corrections

Figures (1)

  • Figure 1: One-loop diagrams contributing to the vacuum polarization