Abstract
In this work we propose a systematic way to compute the logarithmic divergences of composite operators in the pure spinor description of the $AdS_5\times S^5$ superstring. The computations of these divergences can be summarized in terms of a dilatation operator acting on the local operators. We check our results with some important composite operators of the formalism.
Highlights
All physical vertex operators and their correlation functions
Since the pure spinor formalism is based on BRST quantization, physical vertex operators should be in the cohomology of the BRST charge
In this paper we outlined a general method to compute the logarithmic divergences of local operators of the pure spinor string in an AdS5 × S5 background
Summary
The purpose of this section is to review the computation of logarithmic divergences of operators in principal chiral models using the background field method. This is standard knowledge, the approach taken here is somewhat unorthodox so we include it for the sake of completeness. At one loop order only quadratic terms in the quantum field expansion contribute and, as usual, linear terms cancel by the use of the background equation of motion. This means that we can separate the relevant terms action. We begin with a review of the pure spinor description, pointing out the differences between this model and the principal chiral model, and describe the main steps of the computation
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