Abstract
We consider time-dependent orbifolds in String Theory and we show that divergences are not associated with a gravitational backreaction since they appear in the open string sector too. They are related to the non existence of the underlying effective field theory as in several cases fourth and higher order contact terms do not exist. Since contact terms may arise from the exchange of string massive states, we investigate and show that some three points amplitudes with one massive state in the open string sector are divergent on the time-dependent orbifolds. To check that divergences are associated with the existence of a discrete zero eigenvalue of the Laplacian of the subspace with vanishing volume, we construct the Generalized Null Boost Orbifold where this phenomenon can be turned on and off.
Highlights
A number of reasons are cited in the literature for the existence of these singularities
We consider time-dependent orbifolds in String Theory and we show that divergences are not associated with a gravitational backreaction since they appear in the open string sector too
Since contact terms may arise from the exchange of string massive states, we investigate and show that some three points amplitudes with one massive state in the open string sector are divergent on the time-dependent orbifolds
Summary
As we discussed in the Introduction, the four open string tachyons amplitude diverges in the NBO. Given the suggestion in the literature [4] that this can be cured by the eikonal resummation, we would like to consider the scalar QED on the NBO. Another reason is that all eigenmodes can be written using elementary functions making the issues more transparent. We reserve small letters for quantities defined on the orbifold and capital ones for those defined in Minkowski. We will construct directly both the scalar and the spin-1 eigenfunctions which we can use as a starting point for the perturbative computations
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