New regulators for quantum field theories with compactified extra dimensions. I. Fundamentals

Sky Bauman, Keith R Dienes

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper, we propose two new regulators for quantum field theories in spacetimes with compactified extra dimensions. We refer to these regulators as the "extended hard cutoff" and "extended dimensional regularization." Although based on traditional four-dimensional regulators, the key new feature of these higher-dimensional regulators is that they are specifically designed to handle mixed spacetimes in which some dimensions are infinitely large and others are compactified. Moreover, unlike most other regulators which have been used in the extra-dimension literature, these regulators are designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. This distinction is particularly relevant for calculations of the physics of the excited Kaluza-Klein modes themselves, and not merely their radiative effects on zero modes. By respecting the full higher-dimensional symmetries, our regulators avoid the introduction of spurious terms which would not have been easy to disentangle from the physical effects of compactification. As part of our work, we also derive a number of ancillary results. For example, we demonstrate that in a gauge-invariant theory, analogues of the Ward-Takahashi identity hold not only for the usual zero-mode (four-dimensional) photons, but for all excited Kaluza-Klein photons as well.

Original languageEnglish (US)
Article number125005
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume77
Issue number12
DOIs
StatePublished - Jun 3 2008

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Extra Dimensions
regulators
Quantum Field Theory
Regulator
High-dimensional
Compactification
Photon
symmetry
Space-time
Symmetry
Ward Identities
Invariant Theory
Gauge Symmetry
photons
Zero
Gauge Theory
Regularization
cut-off
Physics
analogs

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics
  • Mathematical Physics

Cite this

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abstract = "In this paper, we propose two new regulators for quantum field theories in spacetimes with compactified extra dimensions. We refer to these regulators as the {"}extended hard cutoff{"} and {"}extended dimensional regularization.{"} Although based on traditional four-dimensional regulators, the key new feature of these higher-dimensional regulators is that they are specifically designed to handle mixed spacetimes in which some dimensions are infinitely large and others are compactified. Moreover, unlike most other regulators which have been used in the extra-dimension literature, these regulators are designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. This distinction is particularly relevant for calculations of the physics of the excited Kaluza-Klein modes themselves, and not merely their radiative effects on zero modes. By respecting the full higher-dimensional symmetries, our regulators avoid the introduction of spurious terms which would not have been easy to disentangle from the physical effects of compactification. As part of our work, we also derive a number of ancillary results. For example, we demonstrate that in a gauge-invariant theory, analogues of the Ward-Takahashi identity hold not only for the usual zero-mode (four-dimensional) photons, but for all excited Kaluza-Klein photons as well.",
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