The OSp(32|1) versus OSp(8|2) supersymmetric M-brane action from self-dual (2,2) strings

TL;DR

This paper explores the extension of (2,2) string theory to a supersymmetric M-brane framework in higher dimensions, proposing a new action that unifies string and membrane theories with potential implications for fundamental physics.

Contribution

It introduces an OSp(32|1) supersymmetric action for M-branes derived from (2,2) string theory, extending to higher dimensions and providing a pre-geometrical formulation relevant for F&M theory.

Findings

Proposes a Kähler-Chern-Simons-type action for self-dual gravity in 2+2 dimensions.

Extends supersymmetry to 2+10 dimensions for M-brane target space.

Introduces an OSp(32|1) supersymmetric action as a pre-geometrical M-brane description.

Abstract

Taking the (2,2) strings as a starting point, we discuss the equivalent integrable field theories and analyze their symmetry structure in 2+2 dimensions from the viewpoint of string/membrane unification. Requiring the Lorentz invariance and supersymmetry in the (2,2) string target space leads to an extension of the (2,2) string theory to a theory of 2+2 dimensional supermembranes (M-branes) propagating in a higher dimensional target space. The origin of the hidden target space dimensions of the M-brane is related to the maximally extended supersymmetry implied by the Lorentz covariance and dimensional reasons. The K"ahler-Chern-Simons-type action describing the self-dual gravity in 2+2 dimensions is proposed. Its maximal supersymmetric extension (of the Green-Schwarz-type) naturally leads to the 2+10 (or higher) dimensions for the M-brane target space. The proposed OSp(32|1) supersymmetric action gives the pre-geometrical description of M-branes, which may be useful for a fundamental formulation of F&M theory.