On possible generalization of the superstring action to eleven dimensions

TL;DR

This paper proposes a novel eleven-dimensional superstring action with free dynamics and only second class fermionic constraints, challenging the necessity of kappa-symmetry and broadening the scope of superstring theories.

Contribution

It introduces a superstring action in eleven dimensions that avoids kappa-symmetry, using only second class fermionic constraints, enabling classical existence in any spacetime dimension.

Findings

Superstring action with free dynamics in 11D

Elimination of kappa-symmetry requirement

Potential to revisit brane-scan in superstring theory

Abstract

We suggest a D=11 super Poincar\'e invariant action for the superstring which has free dynamics in the physical variables sector. Instead of the standard approach based on the searching for an action with local $\kappa$-symmetry (or, equivalently, with corresponding first class constraints), we propose a theory with fermionic constraints of second class only. Then the $\kappa$-symmetry and the well known $\Gamma$-matrix identities are not necessary for the construction. Thus, at the classical level, the superstring action of the type described can exist in any spacetime dimensions and the known brane-scan can be revisited.