**Authors:**

(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);

(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp).

## Table of Links

2 U(1) gauge theory on a warped background

3 Gauge-Higgs inflation on a warped background

4 Conclusions and discussions, Acknowledgements, and References

## 2 U(1) gauge theory on a warped background

### 2.1 Randall-Sundrum metric and action integral

The spacetime is assumed to be 5d one with the RS metric given by [8, 9]

### 2.2 Conjugate boundary conditions

where β is a constant called a twisted phase, the superscript C denotes a 4d charge conjugation, θC is a real number, and the asterisk means the complex conjugation. Then, the covariant derivatives obey the relations:

### 2.3 Mass spectrum

Then, the action integral is rewritten as

### 2.4 Effective potential

Let us derive the effective potential for the Wilson line phase θ(= θ(x)). Taking the standard procedure, a d-dimensional effective potential involving one degree of freedom at the one-loop level is given b

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[3] We introduce both Mψ and cσ′ (y) in a general standpoint, and we will see that cσ′ (y) is forbidden by imposing specific boundary conditions on fields in the next subsection.