Abstract
We show that 4-point vector boson one-loop amplitudes, computed in ref.[1] in the RNS formalism, around vacuum configurations with open unoriented strings, preserving at least N=1 SUSY in D=4, satisfy the correct supersymmetry Ward identities, in that they vanish for non MHV configurations (++++) and (-+++). In the MHV case (--++) we drastically simplify their expressions. We then study factorisation and the limiting IR and UV behaviour and find some unexpected results. In particular no massless poles are exposed at generic values of the modular parameter. Relying on the supersymmetric properties of our bosonic amplitudes, we extend them to manifestly supersymmetric super-amplitudes and compare our results with those obtained in the D=4 hybrid formalism, pointing out difficulties in reconciling the two approaches for contributions from N=1,2 sectors.
Highlights
There is a revival of interest in superstring loop amplitudes from different perspectives [1,2,3,4,5,6,7]
We show that 4-point vector boson one-loop amplitudes, computed in [1] in the RNS formalism, around vacuum configurations with open unoriented strings, preserving at least N = 1 SUSY in D = 4, satisfy the correct supersymmetry Ward identities, in that they vanish for non Maximally Helicity Violating (MHV) configurations (++++) and (−+++)
Relying on the supersymmetric properties of our bosonic amplitudes, we extend them to manifestly supersymmetric superamplitudes and compare our results with those obtained in the D = 4 hybrid formalism, pointing out difficulties in reconciling the two approaches for contributions from N = 1, 2 sectors
Summary
There is a revival of interest in superstring loop amplitudes from different perspectives [1,2,3,4,5,6,7]. The main difference is that despite vector boson vertex operators are compactification independent, i.e. they are proportional to the identity operator of the internal SCFT, only in the N = 4 sector one has a complete factorisation of the space-time and internal part, encoded in the sum of KK momenta or alike. We show that they satisfy the correct Ward identities, in that, for instance, 3-point amplitudes with 3 positive helicity vector bosons vanish, and identify their divergences. The results of [1] for 4-point amplitudes are reviewed in section 4 and systematically simplified, where we show that only MHV amplitudes are non-vanishing.
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