More Stringy Effects in Target Space from Double Field Theory

TL;DR

This paper explores additional stringy effects in Double Field Theory, focusing on massive states with non-zero momenta and windings, revealing new gauge invariances and mass terms not seen in simpler models.

Contribution

It introduces a quadratic action for doubled fields with non-zero momenta and windings, revealing a new mass term and gauge invariance generalization in Double Field Theory.

Findings

A new mass term for symmetric traceless tensor fields due to stringy effects.

Generalized gauge transformations involving extended constraints.

The stringy effect disappears with only one compact doubled dimension.

Abstract

In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to $N_L+N_R-2$. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with $(N_L=1, N_R=1)$ such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states $(N_L=2, N_R=0)$ and $(N_L=0, N_R=2)$ which are massive in the lower-dimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states $(N_L=1, N_R=1)$. A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension.