Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Superfield Theories in Tensorial Superspaces and the Dynamics of Higher Spin Fields

Igor Bandos, Paolo Pasti, Dmitri Sorokin, Mario Tonin

TL;DR

The paper develops a superfield formulation of free higher spin equations in tensorial superspaces and analyzes tensorial supergravities with GL(n) and SL(n) holonomy as a route to non-linear higher spin theories. It finds that the general solution to tensorial supergravity constraints corresponds to geometries that are conformally flat or related to the supergroup manifold OS p(1|n), and that, due to generalized Weyl invariance, these backgrounds render higher spin dynamics effectively free and decoupled from the geometry. Consequently, minimal couplings or interacting higher spin dynamics do not arise within this framework, unless the tensorial space is extended with additional coordinates such as twistor-like spinors. The work provides a geometrical basis and clear no-go result, motivating future models that incorporate extra auxiliary variables to realize nontrivial higher spin interactions, potentially via spontaneous breaking of superconformal symmetry and larger symmetry algebras.

Abstract

We present the superfield generalization of free higher spin equations in tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n) holonomy as a possible framework for the construction of a non-linear higher spin field theory. Surprisingly enough, we find that the most general solution of the supergravity constraints is given by a class of superconformally flat and OSp(1|n)-related geometries. Because of the conformal symmetry of the supergravity constraints and of the higher spin field equations such geometries turn out to be trivial in the sense that they cannot generate a `minimal' coupling of higher spin fields to their potentials even in curved backgrounds with a non-zero cosmological constant. This suggests that the construction of interacting higher spin theories in this framework might require an extension of the tensorial superspace with additional coordinates such as twistor-like spinor variables which are used to construct the OSp(1|2n) invariant (`preonic') superparticle action in tensorial superspace.

Superfield Theories in Tensorial Superspaces and the Dynamics of Higher Spin Fields

TL;DR

The paper develops a superfield formulation of free higher spin equations in tensorial superspaces and analyzes tensorial supergravities with GL(n) and SL(n) holonomy as a route to non-linear higher spin theories. It finds that the general solution to tensorial supergravity constraints corresponds to geometries that are conformally flat or related to the supergroup manifold OS p(1|n), and that, due to generalized Weyl invariance, these backgrounds render higher spin dynamics effectively free and decoupled from the geometry. Consequently, minimal couplings or interacting higher spin dynamics do not arise within this framework, unless the tensorial space is extended with additional coordinates such as twistor-like spinors. The work provides a geometrical basis and clear no-go result, motivating future models that incorporate extra auxiliary variables to realize nontrivial higher spin interactions, potentially via spontaneous breaking of superconformal symmetry and larger symmetry algebras.

Abstract

We present the superfield generalization of free higher spin equations in tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n) holonomy as a possible framework for the construction of a non-linear higher spin field theory. Surprisingly enough, we find that the most general solution of the supergravity constraints is given by a class of superconformally flat and OSp(1|n)-related geometries. Because of the conformal symmetry of the supergravity constraints and of the higher spin field equations such geometries turn out to be trivial in the sense that they cannot generate a `minimal' coupling of higher spin fields to their potentials even in curved backgrounds with a non-zero cosmological constant. This suggests that the construction of interacting higher spin theories in this framework might require an extension of the tensorial superspace with additional coordinates such as twistor-like spinor variables which are used to construct the OSp(1|2n) invariant (`preonic') superparticle action in tensorial superspace.

Paper Structure

This paper contains 17 sections, 138 equations.

Table of Contents

  1. Introduction
  2. Superfield generalization of the massless higher spin equations
  3. Scalar superfield equations in flat tensorial superspace
  4. Scalar superfield equations on OSp(1$|$n)
  5. Geometry of tensorial superspace
  6. The definition of tensorial supergeometry
  7. The massless superparticle in curved tensorial superspace.
  8. Superparticle action, $\kappa$--symmetry and the basic torsion constraint in tensorial superspace
  9. On the freedom in superfield redefinitions and conventional constraints
  10. The Bianchi identities and the complete set of the constraints in the tensorial superspace with the structure group $GL(n)$
  11. Tensorial superspace with the holonomy group $SL(n)$
  12. The scalar superfield equation in a tensorial supergravity background
  13. Generalized Weyl invariance of the tensorial supergravity constraints and conformally related supermanifolds
  14. Decoupling of higher spin field dynamics from superconformal geometry
  15. The general solution of the tensorial supergravity constraints
  16. ...and 2 more sections