Abstract
We consider an $O(d,d;\mathbb{Z})$ invariant massive deformation of double field theory at the level of free theory. We study Kaluza-Klein reduction on $R^{1,n-1} \times T^{d}$ and derive the diagonalized second order action for each helicity mode. Imposing the absence of ghosts and tachyons, we obtain a class of consistency conditions which include the well known weak constraint in double field theory as a special case. Consequently, we find two-parameter sets of $O(d,d;\mathbb{Z})$ invariant Fierz-Pauli massive gravity theories.
Highlights
Duality plays a central role in string theory, the most successful theory of quantum gravity
As a first step toward such a direction, we study massive deformations of Double field theory (DFT) within the free theory
We demonstrate that the standard weak constraint is picked up if we require in addition that the lightest massive spin 2 particle is lighter than the string scale
Summary
Duality plays a central role in string theory, the most successful theory of quantum gravity. [32], Hohm et al succeeded in making the strong constraint in type II DFT [31] mild and partially incorporated winding modes of the R-R fields without spoiling the gauge invariance. Note that the NS-NS (Neveu-Schwarz) two-form is massive in massive type IIA theory, so that gauge invariance associated to the two-form is spontaneously broken This motivates us to explore massive deformations of DFT as a bypass to phenomenology of winding modes: since massive theories do not have gauge invariance from the beginning, it might be technically possible to formulate a consistent interacting theory without imposing the strong constraint.
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