Quantum corrections toAdS5×S5left-invariant superstring current algebra

Abstract

In this work the pure spinor formulation of the superstring is used to study quantum corrections to the left current OPE algebra of the coset P SU (2, 2|4)/SO(4, 1) × SO(5) sigma model, which describes the superstring dynamics in the AdS 5 × S 5 background. In particular, the one loop corrections to the simple poles of the bosonic currents are computed. Unlike the case of the double poles, we show that the simple poles suffer corrections, which are important since the simple poles contribute to the four point amplitudes. We show that the only contribution to the simple poles comes from the pure spinor Lorentz currents. * 1 The classical integrability of the AdS 5 × S 5 sigma model was established in the paper [7] for Green-Schwarz-Metsaev-Tseytlin action and in [8] for the pure spinor description. Using cohomological and algebraic renormalization techniques, Berkovits argued that the sigma model still has an infinite number of conserved charges when quantum effects are taken into account [3]. A detailed study of the transfer matrix of the worldsheet was done in [9], where it was shown to be a well defined operator in quantum theory. The literature on this subject is very large, and we did not attempt to give a list of references.The reader can see a list of references in [10,11].

AdS 5 × S5 supergravity vertex operators

“…Another way of trying to construct the massive vertex operators is by generalizing the techniques developed in [95]. It will be also very interesting to better understand the current algebra of the model at the quantum level, see [29,96] for progresses. Notice that the BRST operator is a pure spinor times a fermionic current.…”

$AdS_5 \times S^5$ supergravity vertex operators

“…Another way of trying to construct the massive vertex operators is by generalizing the techniques developed in [94]. It will be also very interesting to better understand the current algebra of the model at the quantum level, see [28,95] for progresses. Notice that the BRST operator is a pure spinor times a fermionic current.…”