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

Abstract

In the semi-light cone gauge $g_{ab}=e^{2\varphi }{\delta }_{ab}$, ${\bar{\gamma }}^{+}\theta =0$, we evaluate the $\varphi$-dependent effective action for the pp-wave Green-Schwarz (GS) superstring in both harmonic and group coordinates. When we compute the fermionic $\varphi$-dependent effective action in harmonic coordinates, we find a new triangular one-loop Feynman diagram. We show that the bosonic $\varphi$-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.

arXiv comment24 pages, 8 figures, minor changes made

References in corpus (13)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Exactly solvable model of superstring in Ramond-Ramond plane wave background
• A new maximally supersymmetric background of IIB superstring theory
• A class of exact pp-wave string models with interacting light-cone gauge actions
• Super 0-brane and GS Superstring Actions on AdS_2 \times S^2
• Conformal Field Theory for the Superstring in a Ramond-Ramond Plane Wave Background
• PP-Waves and Holography
• PP-wave String Interactions from String Bit Model
• Strings in Plane Wave Backgrounds Revisited
• N=2 Superconformal Description of Superstring in Ramond-Ramond Plane Wave Backgrounds
• Killing gauge for the 0-brane on $Ad{S}_2\times S^2$ coset superspace
• A Comment on Masses, Quantum Affine Symmetries and PP-Wave Backgrounds

Cited by in corpus (2)

• Strings in plane wave backgrounds
• Dynamical supersymmetry analysis of conformal invariance for superstrings in type IIB R-R plane-wave