Extra Dimensions in Superstring Theory

TL;DR

This paper explores the connection between superstring variables and higher-dimensional theories, suggesting an interpretation of certain spinor variables as momentum in an extra dimension, revealing underlying SO(10,2) and SO(9,1) x SO(2,1) structures.

Contribution

It introduces a novel interpretation of superstring spinor variables as momentum in an eleventh dimension, linking superstring theory to higher-dimensional frameworks.

Findings

Identification of spinor variables with eleventh-dimensional momentum.

Evidence from zero-momentum vertex operators and D0-branes supports the interpretation.

Discovery of SO(10,2) and SO(9,1) x SO(2,1) structures in superstring theories.

Abstract

It was earlier shown that an SO(9,1) $\theta^\a$ spinor variable can be constructed from RNS matter and ghost fields. $\theta^\a$ has a bosonic worldsheet super-partner $\lambda^\a$ which plays the role of a twistor variable, satisfying $\lambda\Gamma^\mu\lambda = \partial x^\mu +i\theta\Gamma^\mu \partial\theta$. For Type IIA superstrings, the left-moving $[\theta_L^\a,\lambda_L^\a]$ and right-moving $[\theta_{R\a},\lambda_{R\a}]$ can be combined into 32-component SO(10,1) spinors $[\theta^A,\lambda^A]$. This suggests that $\lambda^A \Gamma^{11}_{AB}\lambda^B= 2\lambda_L^\a \lambda_{R\a}$ can be interpreted as momentum in the eleventh direction. Evidence for this interpretation comes from the zero-momentum vertex operators of the Type IIA superstring and from consideration of $D_0$-branes. As in the work of Bars, one finds an SO(10,2) structure for the Type IIA superstring and an SO(9,1) x SO(2,1) structure for the Type IIB superstring.