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High Energy Physics - Theory, hep-th
Abstract:
We construct, in the closed bosonic string, the multiloop amplitude involving
$N$ tachyons and one massless particle with $26 -D$ compactified directions,
and we show that at least for $D>4$, the soft behaviors of the graviton and
dilaton satisfy the same soft theorems as at the tree level, up to one
additional term at the subsubleading order, which can only contribute to the
dilaton soft behavior and which we show is zero at least at one loop. This is
possible, since the infrared divergences due to the non-vanishing tachyon and
dilaton tadpoles do not depend on the number of external particles and are
therefore the same both in the amplitude with the soft particle and in the
amplitude without the soft particle. Therefore this leaves unchanged the soft
operator acting on the amplitude without the soft particle. The additional
infrared divergence appearing for $D \leq 4$ depend on the number of external
legs and must be understood on their own.
