Abstract
Abstract Relation between semiclassical analyses of Green-Schwarz and pure spinor formalisms in an AdS 5 × S 5 background is clarified. It is shown that the two formalisms have identical semiclassical partition functions for a simple family of classical solutions. It is also shown that, when the classical string is furthermore rigid, this in turn implies that the two formalisms predict the same one-loop corrections to spacetime energies.
Highlights
Basic picture laid in [4,5,6], matching quantum corrections to string energies to anomalous dimensions of gauge invariant operators in the N = 4 super Yang-Mills theory
Using the pure spinor formalism we perform a semiclassical analysis around a simple family of classical solutions in an AdS5 × S5 background and show that the formalism reproduces the one-loop anomalous dimensions known from the Green-Schwarz formalism
Pure spinor formalism in a flat background is defined as a worldsheet conformal field theory with a BRST symmetry and it allows one to quantize a string in a super-Poincare covariant manner
Summary
In contrast to conventional approaches to string theory, the pure spinor formalism in a trivial background starts off by postulating a quadratic worldsheet action with a BRST symmetry [8]. Works taking a conventional viewpoint have explained how the BRST structure arises from the classical Green-Schwarz superstring [16, 17]. In these approaches, pure spinor “ghosts” in the BRST operator are literally interpreted as the BRST ghosts for the kappa symmetry of the classical Green-Schwarz action. The combination of the free field action of (2.1) and the BRST symmetry of (2.4) is arguably much simpler than the classical Green-Schwarz formalism with the troublesome kappa symmetry, and the pure spinor formalism has been proved very useful for computing amplitudes in a flat spacetime The combination of the free field action of (2.1) and the BRST symmetry of (2.4) is arguably much simpler than the classical Green-Schwarz formalism with the troublesome kappa symmetry, and the pure spinor formalism has been proved very useful for computing amplitudes in a flat spacetime (see e.g. [14, 15] and references therein)
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