T-duality and T-folds for point particles

Abstract

We argue that the T-duality phenomenon is not exclusively a stringy effect but it is relevant also in the context of the standard point particle dynamics. To illustrate the point, we construct a four-parametric family of four-dimensional electro-gravitational backgrounds such that the dynamics of a charged point particle in those backgrounds is insensitive to a particular permutation of the parameters although this very permutation does alter the background geometry. In particular, we find that a direct product of the Euclidean plane with the two-dimensional Euclidean black hole admits a point-particle T-dual with asymptotically negative curvature. For neutral particles, this point-particle T-duality picture gets slightly modified because the T-duality map is no longer defined everywhere but only on a dense open domain of the space of states. We suggest a possible interpretation of this phenomenon in terms of a point particle T-fold.

arXiv comment11 pages, a discussion of consistency conditions for the definition of T-folds is added

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Cited by in corpus (3)

• Brief lectures on duality, integrability and deformations
• Supergravity solution-generating techniques and canonical transformations of $\sigma$-models from $O(D,D)$
• Superintegrability, symmetry and point particle T-duality