Abstract
We construct off-shell amplitudes in heterotic and type II string theories involving arbitrary combination of Ramond and Neveu-Schwarz sector external states. We also construct the equations of motion of a gauge invariant 1PI effective field theory which reproduces these off-shell amplitudes. Using this construction we prove that the renormalized physical masses do not depend on the choice of local coordinate system and locations of picture changing operators used in defining the off-shell amplitudes. We also use this formalism to examine the conditions under which space-time supersymmetry is unbroken in the quantum theory.
Highlights
Different levels and whose cohomology coincides with the usual BRST cohomology.1 There is an indirect argument from low energy effective field theory which goes as follows
If we did manage to write down a kinetic term for the R sector fields in a straightforward manner we could use it to write down a gauge invariant kinetic term for the RR 4-form field of type IIB string theory
The general string field configuration |Ψ is taken to be an element of the Hilbert space of matterghost conformal field theory with picture number −1 in the NS sector and picture number −1/2 in the R sector
Summary
We shall follow the notations of [1, 10]. We begin our discussion with heterotic string theory. The problem has its origin in the fact that in order to ensure that the off-shell amplitude leads to sensible definition of physical quantities — e.g. renormalized physical masses and S-matrix elements — we need to ensure that the choice of the integration cycle is gluing compatible To see what it means, recall that if we consider two Riemann surfaces Σ1 and Σ2, and pick one puncture on each of them with local coordinates z and w, we can construct a two parameter family of Riemann surfaces Σ by joining Σ1 and Σ2 using the plumbing fixture relation:. By construction Rg,m,n does not intersect the boundaries of Pg,m,n corresponding to separating type degenerations — they all arise from the s → ∞ limit of the plumbing fixture of two or more 1PI Riemann surfaces and lie in the 1PR region of the full integration cycle.
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