Large Mass Hierarchy from a Small Extra Dimension

Abstract

We propose a new higher-dimensional mechanism for solving the hierarchy problem. The weak scale is generated from a large scale of order the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of AdS 5 spacetime). This mechanism relies on the existence of only a single additional dimension. We demonstrate a simple explicit example of this mechanism with two three-branes, one of which contains the Standard Model fields. The experimental consequences of this scenario are new and dramatic. There are fundamental spin-2 excitations with mass of weak scale order, which are coupled with weak scale as opposed to gravitational strength to the standard model particles. The phenomenology of these models is quite distinct from that of large extra dimension scenarios; none of the current constraints on theories with very large extra dimensions apply.

On the one-loop Kähler potential in five-dimensional brane-world supergravity

“…and so the gravitational background in this set-up is precisely that of the Randall-Sundrum model [17]. In absence of brane matter the second term vanishes.…”

“…The Kähler potential that reproduces the kinetic terms (16), (17) and (19) is given by K = −3 log Ω where…”

Null deformed domain wall

“…As a general fact in supergravity, the potential is given by the sum of "squares of the fermionic shifts" (the scalar expressions in the above transformations of the fermions): 19) where C AB is the (antisymmetric) symplectic metric of USp(2n H ).…”

“…As solutions of gauged supergravity these are conjectured to be dual to the Renormalization Group (RG) flows of field theory couplings [7,8,9,10,11,12,13]. Domain Walls are also a key ingredient of Brane world construction [14,15,16,17,18,19]. More recently, in four dimensions, these solitons have been used as a laboratory for the comprehension of mirror symmetry in flux/generalized geometry compactifications [20,21,22] and to explore transitions between the different cosmological vacua of the Landscape [23].…”

“…19 The Lie algebra of sp(2, 1) can be split into a compact (anti-Hermitian) and non-compact (Hermitian) part :…”