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PP-wave Green-Schwarz superstring, polygon divergent structure and conformal field theory

Mark A. Walton·Jian-Ge Zhou
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Abstract

In the semi-light cone gauge $g_{ab}=e^{2ϕ}δ_{ab}$, $\barγ^+θ=0$, we evaluate the $ϕ$-dependent effective action for the pp-wave Green-Schwarz (GS) superstring in both harmonic and group coordinates. When we compute the fermionic $ϕ$-dependent effective action in harmonic coordinates, we find a new triangular one-loop Feynman diagram. We show that the bosonic $ϕ$-dependent effective action cancels with the fermionic one, indicating that the pp-wave GS superstring is a conformal field theory. We introduce the group coordinates preserving $SO(4)\times SO(4)$ and conformal symmetry. Group coordinates are interesting because vertex operators take simple forms in them. The new feature in group coordinates is that there are logarithmic divergences from n-gons, so that the divergent structure is more complicated than in harmonic coordinates. After summing over all contributions from n-gons, we show that in group coordinates, the GS superstring on pp-wave RR background is still a conformal field theory.

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Mark A. Walton, Jian-Ge Zhou. 2003-07-25. PP-wave Green-Schwarz superstring, polygon divergent structure and conformal field theory. https://doi.org/10.1103/physrevd.68.066004

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