Moduli Stabilization in Warped Compactifications at One Loop

We review the moduli stabilization mechanism found in Garriga et al. (Garriga, J., Pujolas, O., and Tanaka, T. (2000). Preprint hep-th/0111277.) for a class of five-dimensional warped brane-world scenarios. Specifically, we consider solutions with a power-law warp factor and a bulk dilaton with logarithmic profile in terms of the proper distance in the extra dimension. This includes the Heterotic M-theory brane-world of Lukas et al. (Lukas, A., Ovrut, B. A., Stelle, K. S., and Waldram, D. (1999). Physical Review D59, 086001.) and Khoury et al. (Khoury, J., Ovrut, B. A., Steinhardt, P. J., and Turok, N. (2001). Preprint hep-th/0103239.) and the Randall–Sundrum (RS) model as a limiting case. In general, there are two moduli fields y±, corresponding to the “positions” of two branes. Classically, the moduli are massless due to a scaling symmetry of the action. However, in the absence of supersymmetry, they develop an effective potential at one loop. Local terms proportional to some powers of the local curvature scale at the location of the corresponding brane are needed in order to remove the divergences in the effective potential. Such terms break the scaling symmetry and therefore act as stabilizers for the moduli. Moreover, for q ≳ 10, the observed hierarchy can be naturally generated by this potential, and the lightest modulus mass is of order m− ≲ TeV.