Warped brane worlds in six dimensional supergravity

Abstract

We present warped compactification solutions of six-dimensional supergravity, which are generalizations of the Randall-Sundrum (RS) warped brane world to codimension two and to a supersymmetric context. In these solutions the dilaton varies over the extra dimensions, and this makes the electroweak hierarchy only power-law sensitive to the proper radius of the extra dimensions (as opposed to being exponentially sensitive as in the RS model). Warping changes the phenomenology of these models because the Kaluza-Klein gap can be much larger than the internal space's inverse proper radius. We provide examples both for Romans' nonchiral supergravity and Salam-Sezgin chiral supergravity, and in both cases the solutions break all of the supersymmetries of the models. We interpret the solution as describing the fields sourced by a 3-brane and a boundary 4-brane (Romans' supergravity) or by one or two 3-branes (Salam-Sezgin supergravity), and we identify the topological constraints which are required by this interpretation. For both types of solutions the 3-branes are flat for all topologically-allowed values of the brane tensions. We identify the general mechanism for and limitations of the self-tuning of the effective 4D cosmological constant in higher-dimensional supergravity which these models illustrate.Keywords: brane-world, supergravity, warped geometries. 42 7. Appendix: Explicit Solution with λ 4 = −ζ 4 = 1 2 44 -1 - 4 We are outlining the calculation for the case where the vacuum expectation value of the gauge field lies in the U (1) subgroup, but the result is the same in the case that it lies in SU (2). 5 If b 2 = 0, such as when A = 0, then instead one finds r 2 3 = B/b 1 .

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“…We find the moduli of such spaces can stabilise at sufficiently anisotropic shapes to allow the size, L, of the base to be of sub-millimetre size. Thus the low-energy limit is described by a 6-dimensional effective field theory (EFT), comprising a stringy derivation of the supersymmetric large-volume scenario [1,2,[11][12][13]. The crucial ingredient for obtaining this is the use of poly-instanton corrections to the superpotential [25].…”

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