Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism

TL;DR

This paper simplifies the pure spinor formalism for the AdS_5xS^5 background, revealing new geometric and topological features that connect to free super-Yang-Mills theory and unbroken superstring phases.

Contribution

It introduces a topological version of the AdS_5xS^5 pure spinor formalism via gauge fixing a G/G model, linking to the zero radius limit and free super-Yang-Mills.

Findings

Pure spinor formalism is simpler in AdS_5xS^5 background.

A topological model describes the zero radius limit dual to free N=4 super-Yang-Mills.

The topological model can be viewed as an unbroken phase of superstring theory.

Abstract

Although the AdS_5xS^5 worldsheet action is not quadratic, some features of the pure spinor formalism are simpler in an AdS_5xS^5 background than in a flat background. The BRST operator acts geometrically, the left and right-moving pure spinor ghosts can be treated as complex conjugates, the zero mode measure factor is trivial, and the b ghost does not require non-minimal fields. Furthermore, a topological version of the AdS_5xS^5 action with the same worldsheet variables and BRST operator can be constructed by gauge-fixing a G/G principal chiral model where G=PSU(2,2|4). This topological model is argued to describe the zero radius limit that is dual to free N=4 super-Yang-Mills and can also be interpreted as an "unbroken phase" of superstring theory.