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Infrared limit of left-handed string at genus one
We extend the left-handed string formalism at one-loop level to focus on only
the infrared limit, where the Green's function for the left-handed string is
expanded around the cusp of the modular parameter. This expansion leads to the
separating degeneration limit of a Riemann surface corresponding to a sphere
and a torus connected by a long tube. The well-behaved short-distance behavior
of the Green's function requires all marked points to be inserted on the
sphere. Analogous to the tree-level calculations, we obtain Dirac
-functions by integrating out the anti-holomorphic variables. The
constraints embedded in these -functions, associated with the marked
points on the sphere part of the Riemann surface, are the same Scattering
Equations at the tree-level. After the integration over the modular parameter,
we observe the expected pattern of the infrared divergence, consistent with the
one-loop results from the box diagram calculations in field theory
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