[Paper Review] Trapping of Nonabelian Gauge Fields on a Brane

Ichiro Oda|ArXiv.org|Mar 30, 2001

Orbital Angular Momentum in Optics3 citations

TL;DR

This paper proposes a topological Higgs mechanism to trap nonabelian gauge fields—such as gluons—on a brane in the Randall-Sundrum model using gravitational interactions. By leveraging a five-dimensional topologically massive Yang-Mills theory with a kink-like profile, the mechanism localizes almost massless gauge modes on the brane, though exactly massless modes remain unlocalized, posing a subtle but potentially resolvable issue in nonabelian gauge theories.

ABSTRACT

We show that as in abelian gauge fields, nonabelian gauge fields are also trapped on a brane in the Randall-Sundrum model by applying a new mechanism based on topological Higgs mechanism. It is pointed out that although almost massless gauge fields are localized on the brane by the new mechanism, exactly massless gauge fields are not localized. This fact does not yield any problem to abelian gauge fields, but may give some problem to nonabelian gauge fields since it is known that there is a discontinuity between massless and massive gauge fields in the case of nonabelian gauge groups.

Motivation & Objective

• To extend a recently proposed localization mechanism for abelian gauge fields to nonabelian gauge fields in the Randall-Sundrum brane world scenario.
• To investigate whether nonabelian gauge fields such as gluons can be localized on a 3-brane using gravitational interactions alone.
• To analyze the subtlety arising when the gauge field is exactly massless, particularly the discontinuity between zero-mass and finite-mass theories in nonabelian gauge theories.
• To determine whether the mechanism remains viable despite the non-localization of exactly massless modes, considering experimental and theoretical constraints.

Proposed method

• The model uses a five-dimensional AdS5 metric with a warped extra dimension, where the brane is located at r=0 and the metric function A(r) = 2k|r|.
• The action is based on a topologically massive nonabelian gauge theory in five dimensions, including a Yang-Mills term, a top-form kinetic term, and a Chern-Simons-like coupling with a mass parameter m.
• The gauge field A^a_M and a 3-form potential C^a_MNP are introduced, with a non-dynamical 2-form auxiliary field V^a_MN to restore gauge invariance of the kinetic term.
• The zero-mode wavefunction for the gauge field is derived by solving the field equations in the background of the kink profile, yielding a localized mode proportional to e^{-m|r|}.
• The 3-form field c^a_μνρ is shown to be non-localized when m - 2k ≤ 0, ensuring it does not contribute to the brane action.
• The effective four-dimensional action for the gauge field on the brane is derived, showing a massive gauge theory with mass term ∝ m³/(m+k), which becomes small when k ≫ m.

Experimental results

Research questions

• RQ1 Can nonabelian gauge fields be localized on a brane using only gravitational interactions, similar to the mechanism for abelian gauge fields?
• RQ2 What is the role of the topological Higgs mechanism in localizing nonabelian gauge fields in a five-dimensional bulk?
• RQ3 Why does the localization mechanism fail for exactly massless nonabelian gauge fields, and what are the implications?
• RQ4 How does the behavior of nonabelian gauge fields differ from abelian ones in the massless limit, particularly regarding the discontinuity between massless and massive theories?

Key findings

• Nonabelian gauge fields are successfully trapped on the brane via a gravitational interaction using a topological Higgs mechanism, analogous to the abelian case.
• The effective four-dimensional action on the brane is a massive Yang-Mills theory with a mass term proportional to m³/(m+k), which becomes small when k ≫ m.
• Exactly massless gauge fields (m=0) are not localized by this mechanism, as the zero-mode wavefunction vanishes in the limit m→0.
• The 3-form potential c^a_μνρ is non-localized on the brane when m - 2k ≤ 0, consistent with the requirement that only the gauge field mode is localized.
• The mechanism relies on a kink-like profile for the mass term, similar to fermion localization, ensuring the zero-mode wavefunction is normalizable and peaked at the brane.
• The failure to localize exactly massless modes is a subtle but potentially acceptable issue, as the discontinuity between massless and massive nonabelian theories appears only at the loop level, and small gluon masses are not ruled out experimentally.