Fat brane phenomena

Gravitons could permeate extra space dimensions inaccessible to all other particles, which would be confined to “branes”. We point out that these branes could be “fat” and have a non-vanishing width in the dimensions reserved for gravitons. In this case the other particles, confined within a finite width, should have “branon” excitations. Chiral fermions behave differently from bosons under dimensional reduction, and they may –or may not– be more localized than bosons. All these possibilities are in principle testable and distinguishable, they could yield spectacular signatures at colliders, such as the production of the first branon excitation of γ’s or Z’s, decaying into their ground state plus a quasi-continuum of graviton recurrences. We explore these ideas in the realm of a future lepton collider and we individuate a dimensiometer: an observable that would cleanly diagnose the number of large “extra” dimensions. February 1, 2008 [email protected] [email protected] [email protected] [email protected] No evidence counters the observation that we live in 3+1 dimensions. Yet, a large fraction of the current theoretical-physics literature deals with extra space dimensions. Clearly, new dimensions must be different from the “old” ones, the simplest possibility –of which the earliest milestone [1] is due to Kaluza and Klein– being to compactify them to a domain of minute size. The theoretical interest in extra-dimensional physics is kindled by successive “superstring revolutions”, which have ingrained the belief that there should be a total of 9 space dimensions. An interesting remark [2, 3] is that different particles may move in different spaces; in particular gravity could permeate dimensions into which quanta of other fields cannot propagate. It is not excluded that these latter dimensions be large enough for deviations from Newton’s law to be observable at submillimetre distances. It is also not excluded that the rest of the assumed 9 dimensions be compactified in manifolds of O(1) TeV size, which could make their effects testable at future colliders. These two remarks [4, 5, 6], however contrived, have led to a surge of phenomenological interest [7] in new dimensions much larger than the tiny, gravitationally “natural”, Planck length. We shall refer to the submillimetre and inverse-TeV dimensions as large and small, respectively. Theoretical descriptions of the possible phenomenological consequences of extra dimensions mix old concepts of compactification, such as towers of Kaluza–Klein (KK) excited particles, with novel ones, such as twisted sectors, D-branes, orientifolds, etc. We shall illustrate how some of the key assumptions in these constructions translate into observational tests, mainly in the form of selection rules. In Type I string theories, “Dirichlet p-branes” or D-branes, are defined as pdimensional spaces (p ≤ 9) to which the ends of open strings attach [8]. As an example, ordinary 3-space could be a 3-brane, to which all particles but (closedstring) gravitons would be confined by the aforementioned boundary conditions. The space spanned by the dimensions where only gravitons propagate is called the bulk, its dimensionality is δ = 6 in the above example. One can also choose δ < 6 extra large dimensions, by adopting a p-brane with p = 3 ordinary plus 6− δ small dimensions. Branes should be the vacua of some so far unresolved string dynamics [9]; they are hypersurfaces with a finite tension, f , and perhaps –like solitons– with a finite extension. The question of the extension or “width” of a brane (into the directions orthogonal to it) is obscured by the dualities of string dynamics: as for a monopole, what may look like a composite object in one realization of the theory may be more singular or “elementary” in a different one. Our intuition is that any of the objects that are solutions of a theory as non-singular as string theory ought to be nonsingular: branes should have –in an operational sense to be defined anon– a finite width L of the order of 1/f . The notion that branes are wide may be right or wrong, but it is testable in principle.