Abstract
We study Fayet-Iliopoulos (FI) terms of 5-dimensional supersymmetric $U(1)$ gauge theory compactified on $S^1/Z_2$. In this model, loop diagrams including matter hypermultiplets and brane chiral multiplets induce FI-terms localized at the fixed points. Localized FI-terms lead instabilities of bulk modes. The form of the induced FI-terms strictly depends on wave function profiles of matter multiplets. It is a non-trivial question whether the vacuum of 1-loop corrected potential is stable under radiative corrections. We investigate this issue and it is found that the stable configuration is obtained when the bulk zero modes shield the brane charge completely.
Highlights
Supersymmetric gauge theories in higher dimensions have been studied for a long time
We have studied quantum corrections to Fayet-Iliopoulos term (FI-term) in 5 dimensional SUSY Abelian gauge theory compactified on the S1=Z2 orbifold
If there is a matter field which is charged under the Uð1Þ symmetry, the localized FI-term is induced by quantum corrections
Summary
Supersymmetric gauge theories in higher dimensions have been studied for a long time. The localized FI-term generates a local potential of the real scalar component of bulk vector multiplet Σ, and Σ develops its vacuum expectation value (VEV), which corresponds to a kink mass on the compact space It leads instabilities of bulk fields, especially localization of bulk zero modes at the fixed points in the S1=Z2 orbifold [9,11,12,13] and the T2=Z2 orbifold [14]. We find that stability of 1-loop corrected hΣi background depends on configuration of the brane charges and zero mode profiles It is necessary for the stable configuration that the zero modes are localized at the fixed points and they shield the brane charges completely, otherwise induced FI-term shifts the hΣi background again. In the Appendix, we study wave function profiles of parity odd modes and summation of massive mode wave functions explicitly
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