Elsevier

Physics Letters B

Volume 436, Issues 3–4, 24 September 1998, Pages 257-263
Physics Letters B

New dimensions at a millimeter to a fermi and superstrings at a TeV

https://doi.org/10.1016/S0370-2693(98)00860-0Get rights and content

Abstract

Recently, a new framework for solving the hierarchy problem has been proposed which does not rely on low energy supersymmetry or technicolor. The gravitational and gauge interactions unite at the electroweak scale, and the observed weakness of gravity at long distances is due the existence of large new spatial dimensions. In this letter, we show that this framework can be embedded in string theory. These models have a perturbative description in the context of type I string theory. The gravitational sector consists of closed strings propagating in the higher-dimensional bulk, while ordinary matter consists of open strings living on D3-branes. This scenario raises the exciting possibility that the LHC and NLC will experimentally study ordinary aspects of string physics such as the production of narrow Regge-excitations of all standard model particles, as well more exotic phenomena involving strong gravity such as the production of black holes. The new dimensions can be probed by events with large missing energy carried off by gravitons escaping into the bulk. We finally discuss some important issues of model building, such as proton stability, gauge coupling unification and supersymmetry breaking.

Introduction

In a recent paper [1], a general framework for solving the hierarchy problem was proposed not relying on low-energy supersymmetry or technicolor. The hierarchy problem is solved by nullification: in this scenario, gravity becomes unified with the gauge interactions at the weak scale and there is no large disparity between the size of different short distance scales in the theory. As argued in [1], the observed weakness of gravity is then due to the existence of new spatial dimensions much larger than the weak scale, perhaps as large as a millimeter for the case of two extra dimensions. The success of the Standard Model (SM) then implies that, while gravity is free to propagate in the bulk of the extra dimensions, the SM fields must be localised to a 3 spatial dimensional wall at energies beneath the weak scale. While field-theoretic mechanisms for localising the SM fields on a topological defect were suggested, the nature of the theory of gravity above the weak scale was left unspecified in the general framework of [1].

In this letter, we show that the above scenario can be embedded within string theory, which at present offers the only hope for a consistent theory of gravity. The traditional line of thought has been that string theory becomes relevant only at very short distances of order of the Planck length ∼10−33 cm. However various arguments involving unification, supersymmetry breaking or the gauge hierarchy, suggest that it may be relevant at even larger distances. For instance, compatibility of string unification with gauge coupling unification within the minimal supersymmetric standard model [2]implies that the string (or M-theory) scale should be of the order MGUT∼1016 GeV, while additional dimensions would show up at even lower energies ≲1015 GeV 3, 4. As another example, low energy supersymmetry breaking within perturbative string theory implies the existence of a large internal dimension whose size determines the breaking scale [5]. The possibility that the string scale is close to the electroweak scale was mentioned in, for example 6, 7, 4. This is certainly a requirement for a string realization of the scenario proposed in [1].

In this work we show that the only perturbative string theory with weak scale string tension must be a type I theory of open and closed strings with (a) new dimensions much larger than the weak scale ranging from a fermi to a millimeter (b) an O(1) string coupling and (c) SM fields identified with open strings localized on a 3-brane. Aside from providing a specific realization of the considerations of [1], this construction has the immediate advantage that the localisation of non-gravitational fields to a three dimensional submanifold is automatic and natural. Moreover, our explicit realization will allow us to address a certain number of important theoretical questions arising from this idea, while simultaneously it offers a calculable framework for studying its phenomenological implications.

Section snippets

String embedding

Any perturbative description of string theory has two fundamental parameters: the string scale M and a dimensionless coupling λ which controls the loop expansion1. Upon compactification to D=4 dimensions, these parameters can be expressed in terms of the 4D Planck mass Mp, the gauge coupling αG at the string scale and the compactification volume (2π)6V of the internal six-dimensional manifold. Imposing the string

Accelerator signals and constraints

There are two distinct classes of novel phenomena that occur at a TeV in our framework3:

  • 1.

    Production of Regge-excitations

  • 2.

    Emission of (4+n)-dimensional gravitons into the extra dimensions.

The existence of Regge-excitations (RE) for all the elementary particles of the standard model is a consequence of having a string theory at a TeV and does not per-se

Conclusions

As will be discussed in greater detail in [10], the scenario we propose is not experimentally excluded by any lab or astrophysical constraint we are aware of. We briefly discussed some issues of model building such as stabilising the proton through discrete gauge symmetries, SUSY breaking and gauge coupling unification at the weak scale, but it is clear that much work remains to be done to construct a completely realistic model. In particular, the most pressing theoretical issue is to

Acknowledgements

We wish to thank Petr Horava for valuable correspondence. I.A. and G.D. would like to thank the Institute of Theoretical Physics at Stanford for their hospitality. NAH is supported by the Department of Energy under contract DE-AC03-76SF00515. SD is supported by NSF grant PHY-9219345-004. IA and GD are supported partially by the European Community under the TMR contract ERBFMRX-CT96-0090.

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