Born reciprocity in string theory and the nature of spacetime

Laurent Freidel,Robert G Leigh,Djordje Minic

doi:10.1016/j.physletb.2014.01.067

Laurent Freidel, Robert G Leigh + Show 1 more

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https://doi.org/10.1016/j.physletb.2014.01.067

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Abstract

After many years, the deep nature of spacetime in string theory remains an enigma. In this Letter we incorporate the concept of Born reciprocity in order to provide a new point of view on string theory in which spacetime is a derived dynamical concept. This viewpoint may be thought of as a dynamical chiral phase space formulation of string theory, in which Born reciprocity is implemented as a choice of a Lagrangian submanifold of the phase space, and amounts to a generalization of T-duality. In this approach the fundamental symmetry of string theory contains phase space diffeomorphism invariance and the underlying string geometry should be understood in terms of dynamical bi-Lagrangian manifolds and an apparently new geometric structure, somewhat reminiscent of para-quaternionic geometry, which we call Born geometry.

Highlights

String theory is a remarkable model that aims to be a description of the quantum nature of spacetime
In this approach the fundamental symmetry of string theory contains phase space diffeomorphism invariance and the underlying string geometry should be understood in terms of dynamical bi-Lagrangian manifolds and an apparently new geometric structure, somewhat reminiscent of para-quaternionic geometry, which we call Born geometry
The Born reciprocity principle states that the validity of quantum mechanics implies a fundamental symmetry between space and momentum space

Summary

Born Reciprocity in String Theory and the Nature of Spacetime

Perhaps one of the simplest is the concept of T-duality on flat compact target spaces, one of the hallmarks of perturbative string theory [5]. We will emphasize that some of the structure of traditional string perturbation theory is dictated not by general principles of quantization and consistency, but by auxiliary ad hoc requirements, including locality Relaxing these auxiliary requirements and letting the string take its fullest extension will allow a reformulation that implements quantum mechanical Born reciprocity. What matters here is not that string theory possesses or not a geometrical interpretation but whether it can be defined consistently This is no different than the usual CFT perspective, in which there are only a few conditions coming from quantization that must be imposed; a realization of a target spacetime is another independent concept.

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Conclusion