Abstract
We construct gauge invariant 1PI effective action for the NS sector of type II and heterotic string field theory. By construction, zero eigenvalues of the kinetic operator of this action determine the renormalized physical masses, and tree level amplitudes computed from this action (after gauge fixing) give the loop corrected S-matrix elements. Using this formalism we can give a simple proof of the result 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 amplitude. We also eliminate the need for an infrared regulator in dealing with tadpoles of massless fields.
Highlights
Zero eigenvalues of the kinetic operator of this action determine the renormalized physical masses, and tree level amplitudes computed from this action give the loop corrected S-matrix elements
Using this formalism we can give a simple proof of the result 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 amplitude
In particular we give a simple argument showing that the renormalized physical mass and the S-matrix elements in perturbative vacuum are independent of the choice of local coordinate system and the PCO locations used to construct the 1PI action. This argument can be extended to the shifted vacuum when the latter is the correct ground state, in appendix A we extend the analysis of section 3.4 to show that even when we consider two choices of PCO locations which differ in their vertical segment, there is a field redeinition that relates the corresponding 1PI actions
Summary
We shall review some of the background material that goes into the construction of the 1PI effective action of string field theory. Rg,n can (and does) contain boundaries corresponding to non-separating type degenerations where two punctures on the same Riemann surface are connected by a long handle Once these different regions have been identified, we define the genus g, n-point off-shell amplitude with external states |Φ1 , · · · |Φn to be the integral of Ω6(gg,−n)6+2n(|Φ1 , · · · |Φn ) over the subspace Sg,n. If we take the Vg,n’s of [47] and glue them together in all possible ways using (2.8) including configuration with loops, but not allowing those configurations where by taking the parameter s associated with one of the plumbing fixture relations to infinity we reach a separating type degeneration, we get possible candidates for Rg,n (without the PCO data) This is precisely analogous to the construction of 1PI amplitudes using Feynman diagrams of a quantum field theory.
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