Supersymmetric corrections to eleven-dimensional supergravity

Abstract

In this paper we study eleven-dimensional supergravity in its most general form. This is done by implementing manifest supersymmetry (and Lorentz invariance) through the use of the geometric (torsion and curvature) superspace Bianchi identities. These identities are solved to linear order in a deformation parameter introduced via the dimension zero supertorsion given in its most general form. The theory so obtained is referred to as the deformed theory (to avoid the previously used term "off-shell"). An important by-product of this result is that any higher derivative correction to ordinary supergravity of the same dimension as R 4 , but not necessarily containing it, derived e.g. from M-theory, must appear in a form compatible with the equations obtained here. Unfortunately we have not yet much to say about the explicit structure of these corrections in terms of the fields in the massless supermultiplet. Our results are potentially powerful since if the dimension zero torsion could be derived by other means, our reformulation of the Bianchi identities as a number of algebraic relations implies that the full theory would be known to first order in the deformation, including the dynamics. We mention briefly some methods to derive the information needed to obtain explicit answers both in the context of supergravity and ten-dimensional super-Yang-Mills where the situation is better understood. Other relevant aspects like spinorial cohomology, the role of the 3-and 6-form potentials and the connection of these results to M2 and M5 branes are also commented upon.

The Rational Higher Structure of M‐theory

“…3]) imply that vanishing of the super torsion tensor τ is equivalent to space‐time super geometry being equivalent to that of super Minkowski space‐time on the first order infinitesimal neighborhood of every space‐time point (Figure ). Remarkably, for and this condition is equivalent to the equations of motion of 11‐dimensional supergravity () subject to the constraint of vanishing bosonic 4‐form flux () (see [, Sec. 2.4]).…”

“…In particular, by the classical result of [], the condition that the global supergravity geometry coincides with that of super Minkowski space‐time on the infinitesimal neighborhood of each point is equivalently the condition that the super torsion tensor vanishes . Moreover, by the striking result of [] (see [, Sec. 2.4]) in , the vanishing of the bosonic components of the supertorsion tensor () is already equivalent to the equations of motion of 11‐dimensional supergravity, which implies that the full vanishing of the super torsion tensor (also ) is equivalent to 11‐dimensional supergravity with vanishing bosonic 4‐form flux.…”

Operators on Pure Spinor Spaces

“…The fact that pure spinors had a rôle to play in maximally supersymmetric models was recognised early by Nilsson [1] and Howe [2,3]. Pure spinor superfields were developed with the purpose of covariant quantisation of superstrings by Berkovits [4,5,6,7] and the cohomological structure was independently discovered in supersymmetric field theory and supergravity, originally in the context of higher-derivative deformations [8,9,10,11,12,13,14,15]. The present lecture only deals with pure spinors for maximally supersymmetric field theory.…”

“…Take for example the pure spinors in D = 11 relevant for supergravity. They fulfil (λ γ a λ ) = 0, while (λ γ ab λ ) and (λ γ abcde λ ) remain unconstrained [10], [13], [14]. In this case, there are several irreducible representations at a given power of λ which are outside the ideal.…”

Pure spinor superspace action for D = 6, N = 1 super-Yang-Mills theory

“…[1] and references therein) have been used in the construction of actions for maximally supersymmetric theories [2][3][4][5][6][7][8][9][10][11][12][13]. It is there that the formalism, originating in superstring theory [14][15][16][17] and in the deformation theory for maximally supersymmetric super-Yang-Mills theory (SYM) and supergravity [18][19][20][21][22][23][24][25], has its greatest power. The superspace constraints, turned into a relation of the form "QΨ + .…”