Higher-Spin Theories and $Sp(2M)$ Invariant Space--Time

TL;DR

This work develops a framework for higher-spin (HS) gauge theories using unfolded dynamics in a spacetime ${ m extcal M}_M$ with $Sp(2M)$-invariant structure. Massless 4d conformal fields are encoded by a Fock-space generating function $C(b,ar b|x)$, obeying the unfolded equation $D_0| ext{Φ}(x) angle=0$, and exhibit an extended symmetry from $su(2,2)$ to $sp(8)$ (and beyond to $Sp(2M)$). The sigma-minus cohomology identifies dynamical content, with scalar $b(X)$ and spinor $f_A(X)$ as fundamental fields on ${ m extcal M}_M$, leading to Klein–Gordon and Dirac-type equations generalized to $M$-dependent coordinates. Time and locality are recast via generalized light-like directions and Clifford-algebra coordinates, yielding a global notion of causality and a geometric emergence of the metric from algebraic structure. The results point to a novel spacetime geometry and a path toward manifestly $Sp(2M)$-symmetric nonlinear HS theories, potentially informing unification of gravity and quantum mechanics.

Abstract

Some methods of the ``unfolded dynamics'' machinery particularly useful for the analysis of higher spin gauge theories are summarized. A formulation of 4d conformal higher spin theories in Sp(8) invariant space-time with matrix coordinates and its extension to Sp(2M) invariant space-times are discussed. A new result on the global characterizaton of causality of physical events in the Sp(2M) invariant space-time is announced.