String Amplitudes and Frame-like Formalism for Higher Spins

TL;DR

This paper explores the connection between string theory vertex operators and higher spin gauge fields, specifically spin 3, using a BRST framework to derive interactions and relate different formalisms.

Contribution

It introduces a BRST-based analysis of spin 3 gauge fields in string theory, connecting vertex operators with frame-like and Fronsdal formalisms, and computes cubic interactions.

Findings

Derived BRST constraints for spin 3 vertex operators

Established relations between frame-like and Fronsdal fields

Calculated cubic interaction vertices in the frame-like formalism

Abstract

We analyze open string vertex operators describing connection gauge fields for spin 3 in Vasiliev's frame-like formalism and perform their extended BRST analysis. Gauge symmetry transformations, generalized zero torsion constraints relating extra fields to the dynamical frame-like field and relation between dynamical frame-like field and fully symmetric Fronsdal's field for spin 3 are all realized in terms of BRST constraints on these vertex operators in string theory. Using the construction, we analyze the 3-point correlator for spin 3 field and calculate Chern-Simons type cubic interactions described by 3-derivative Berends-Burgers-van Dam (BBD) type vertex in the frame-like formalism.