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One loop gauge couplings in AdS5

Kiwoon Choi, Ian-Woo Kim

TL;DR

This work computes the full 1-loop corrections to the low-energy gauge couplings of bulk gauge fields in a slice of AdS5, induced by generic 5D scalars, fermions, and vectors with arbitrary Z2×Z2' orbifold boundary conditions. Using the background-field method with dimensional regularization, it derives regulator-independent expressions for the 1-loop corrections, encoded through N-functions that capture the KK spectrum. In the SUSY limit, the results are shown to reproduce the corresponding 4D supergravity expressions for gauge couplings, providing a nontrivial cross-check. The analysis clarifies the warp-factor–dependent subtraction scheme and establishes consistency between 5D EFT results and 4D effective theories, with implications for gauge coupling unification in warped extra-dimensional models.

Abstract

We calculate the full 1-loop corrections to the low energy coupling of bulk gauge boson in a slice of AdS5 which are induced by generic 5-dimensional scalar, Dirac fermion, and vector fields with arbitrary Z_2 times Z_2' orbifold boundary conditions. In supersymmetric limit, our results correctly reproduce the results obtained by an independent method based on 4-dimensional effective supergravity. This provides a nontrivial check of our results and assures the regularization scheme-independence of the results.

One loop gauge couplings in AdS5

TL;DR

This work computes the full 1-loop corrections to the low-energy gauge couplings of bulk gauge fields in a slice of AdS5, induced by generic 5D scalars, fermions, and vectors with arbitrary Z2×Z2' orbifold boundary conditions. Using the background-field method with dimensional regularization, it derives regulator-independent expressions for the 1-loop corrections, encoded through N-functions that capture the KK spectrum. In the SUSY limit, the results are shown to reproduce the corresponding 4D supergravity expressions for gauge couplings, providing a nontrivial cross-check. The analysis clarifies the warp-factor–dependent subtraction scheme and establishes consistency between 5D EFT results and 4D effective theories, with implications for gauge coupling unification in warped extra-dimensional models.

Abstract

We calculate the full 1-loop corrections to the low energy coupling of bulk gauge boson in a slice of AdS5 which are induced by generic 5-dimensional scalar, Dirac fermion, and vector fields with arbitrary Z_2 times Z_2' orbifold boundary conditions. In supersymmetric limit, our results correctly reproduce the results obtained by an independent method based on 4-dimensional effective supergravity. This provides a nontrivial check of our results and assures the regularization scheme-independence of the results.

Paper Structure

This paper contains 5 sections, 91 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Gauge theory on a slice of ${\rm AdS}_5$
  3. one loop effective couplings
  4. 4d supergravity calculation
  5. conclusion

Figures (2)

  • Figure 1: Contour $\leftrightharpoons$ in the complex $q$-plane. Bold dots represent the mass poles.
  • Figure 2: For the contribution from $\tilde{P}(q)$, the contour $\leftharpoonup$ can be deformed to the contour $C$ represented by the bold line since the contribution vanishes on the dotted infinite half circle. Hatched lines on the imaginary axis are logarithmic branch-cuts. After integrating by parts, the point x where the branch-cut starts becomes a simple pole. Then the integral along $C$ is given by the values of integrand at the boundary of $C$ at infinity and the residue value at the point x. The integral along $\rightharpoondown$ can be similarly treated in the lower half plane.