On higher-order corrections in M theory

Abstract

A theoretical analysis of higher-order corrections to D=11 supergravity is given in a superspace framework. It is shown that any deformation of D=11 supergravity for which the lowest-dimensional component of the four-form $G_4$ vanishes is trivial. This implies that the equations of motion of D=11 supergravity are specified by an element of a certain spinorial cohomology group and generalises previous results obtained using spinorial or pure spinor cohomology to the fully non-linear theory. The first deformation of the theory is given by an element of a different spinorial cohomology group with coefficients which are local tensorial functions of the massless supergravity fields. The four-form Bianchi Identities are solved, to first order and at dimension $-1/2$, in the case that the lowest-dimensional component of $G_4$ is non-zero. Moreover, it is shown how one can calculate the first-order correction to the dimension-zero torsion and thus to the supergravity equations of motion given an explicit expression for this object in terms of the supergravity fields. The version of the theory with both a four-form and a seven-form is discussed in the presence of the five-brane anomaly-cancelling term. It is shown that the supersymmetric completion of this term exists and it is argued that it is the unique anomaly-cancelling invariant at this dimension which is at least quartic in the fields. This implies that the first deformation of the theory is completely determined by the anomaly term from which one can, in principle, read off the corrections to all of the superspace field strength tensors.

32 pages. v2: Two references added in the text; footnote added

References in corpus (26)

• Eleven Dimensional Origin of String/String Duality: A One Loop Test
• One loop in eleven dimensions
• Supersymmetry Constraints on Type IIB Supergravity
• R^4 Couplings in M and Type II Theories
• On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
• D-instantons, Strings and M-theory
• R^4 terms in 11 dimensions and conformal anomaly of (2,0) theory
• Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace
• Covariant Quantization of the Superparticle Using Pure Spinors
• Towards Covariant Quantization of the Supermembrane
• Spinorial cohomology and maximally supersymmetric theories
• The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections
• Sixteen-fermion and related terms in M-theory on T**2
• Component Actions from Curved Superspace: Normal Coordinates and Ectoplasm
• The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions
• Manifestly supersymmetric M-theory
• Weyl Superspace
• On Brane Actions and Superembeddings
• ON THE GENERALIZED ACTION PRINCIPLE FOR SUPERSTRINGS AND SUPERMEMBRANES
• D=10 Super-Yang-Mills at O(alpha'^2)
• On a supersymmetric completion of the R^4 term in IIB supergravity
• Type IIB $R^4{H}^{4g-4}$ Conjectures
• Duality in Supergravity Theories
• Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3
• Derivative corrections in 10-dimensional super-Maxwell theory
• A Note on Embedding of M-Theory Corrections into Eleven-Dimensional Superspace

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• Microscopic Black Hole Entropy in Theories with Higher Derivatives
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• Higher-derivative couplings in string theory: dualities and the B-field
• Covariant One-Loop Amplitudes in D=11
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• de Sitter Vacua in Type IIB String Theory: Classical Solutions and Quantum Corrections
• Higher order M theory corrections and the Kac-Moody algebra E10
• Supersymmetric Corrections to Eleven-Dimensional Supergravity
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• Pure spinor superfields -- an overview
• On BPS preons, generalized holonomies and D=11 supergravities
• Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry
• Invariants and divergences in half-maximal supergravity theories
• Enhanced Coset Symmetries and Higher Derivative Corrections
• Integral invariants in maximally supersymmetric Yang-Mills theories
• Curved 11D Supergeometry
• Duality Groups, Automorphic Forms and Higher Derivative Corrections
• Pure spinor superfields and Born-Infeld theory
• Higher Derivative Supergravities in Diverse Dimensions
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• Higher derivative effects for 4d AdS gravity
• IIA supergravity and M-theory on manifolds with SU(4) structure
• Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach
• Twisted Cohomotopy implies M5-brane anomaly cancellation
• The cohomology of superspace, pure spinors and invariant integrals
• D=10 supersymmetric Yang-Mills theory at alpha'^4
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• R^4 Corrections to Eleven Dimensional Supergravity via Supersymmetry
• Forms and algebras in (half-)maximal supergravity theories
• Type II and heterotic one loop string effective actions in four dimensions
• 11D supergravity at $\mathcal{O}(l^3)$
• Massive IIA supergravities
• Towards complete string effective actions beyond leading order
• Flux Quantization on 11-dimensional Superspace
• The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity
• 3d N=1 effective supergravity and F-theory from M-theory on fourfolds
• Adinkra Foundation of Component Decomposition and the Scan for Superconformal Multiplets in 11D, N = 1 Superspace
• Gauge field corrections to 11-dimensional supergravity via dimensional reduction
• Spin Cohomology
• Weyl Covariance, and Proposals for Superconformal Prepotentials in 10D Superspaces