osp(1|32) and Extensions of super-AdS_5 X S^5 algebra

TL;DR

This paper investigates the relationship between osp(1|32) and super-AdS_5 X S^5 algebra, showing that the superconformal algebra is not a restriction of osp(1|32) and identifying limited U(1) extensions.

Contribution

It clarifies the algebraic relationship between osp(1|32) and super-AdS_5 X S^5, revealing that the superconformal algebra is not a subset of osp(1|32) and classifying possible U(1) extensions.

Findings

Super-AdS_5 X S^5 algebra is not a restriction of osp(1|32).

Only two types of U(1) extensions exist under bosonic covariance.

The results have implications for superstring theory algebraic structures.

Abstract

The super-AdS_5 X S^5 and the four-dimensional N=4 superconformal algebras play important roles in superstring theories. It is often discussed the roles of the osp(1|32) algebra as a maximal extension of the superalgebras in flat background. In this paper we show that the su(2,2|4), the super-AdS_5 X S^5 algebra or the superconformal algebra, is not a restriction of the osp(1|32) though the bosonic part of the former is a subgroup of the latter. There exist only two types of u(1) extension of the super-AdS_5 X S^5 algebra if the bosonic AdS_5 X S^5 covariance is imposed. Possible significance of the results is also discussed briefly.