The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity
arXiv:1612.02021 · doi:10.1103/PhysRevD.95.026013
Abstract
We develop computational tools for calculating supersymmetric higher-order derivative corrections to eleven-dimensional supergravity using the action principle approach. We show that, provided the superspace Bianchi identities admit a perturbative solution in the derivative expansion, there are at least two independent superinvariants at the eight-derivative order of eleven-dimensional supergravity. Assuming the twelve-superforms associated to certain anomalous Chern-Simons terms are Weil-trivial, there will be a third independent superinvariant at this order. Under certain conditions, at least two superinvariants will survive to all orders in the derivative expansion. However only one of them will be present in the quantum theory: the supersymmetrization of the Chern-Simons terms of eleven dimensional supergravity required for the cancellation of the M5-brane gravitational anomaly by inflow. This superinvariant can be shown to be unique at the eight-derivative order, assuming it is quartic in the fields. On the other hand, a necessary condition for the superinvariant to be quartic is the exactness, in tau-cohomology, of X0,8 -the purely spinorial component of the eight-superform related by descent to the M5-brane anomaly polynomial. In that case it can also be shown that the solution of the Weil-triviality condition of the corresponding twelve-form, which is a prerequisite for the explicit construction of the superinvariant, is guaranteed to exist. We prove that certain highly non-trivial necessary conditions for the tau-exactness of X0,8 are satisfied. Moreover any potential superinvariant associated to anomalous Chern-Simons terms at the eight-derivative order must necessarily contain terms cubic or lower in the fields.
arXiv comment45 pages ; v2: added references
References in corpus (43)
- String Theory Dynamics In Various Dimensions
- Eleven Dimensional Origin of String/String Duality: A One Loop Test
- One loop in eleven dimensions
- A One-Loop Test Of String Duality
- Two loops in eleven dimensions
- Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace
- R^4, purified
- Higher-derivative couplings in string theory: dualities and the B-field
- Towards Covariant Quantization of the Supermembrane
- Spinorial cohomology and maximally supersymmetric theories
- The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections
- The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions
- Component Actions from Curved Superspace: Normal Coordinates and Ectoplasm
- GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions
- On Brane Actions and Superembeddings
- ON THE GENERALIZED ACTION PRINCIPLE FOR SUPERSTRINGS AND SUPERMEMBRANES
- D=10 Super-Yang-Mills at O(alpha'^2)
- Supersymmetric Corrections to Eleven-Dimensional Supergravity
- The One-Loop Five-Graviton Amplitude and the Effective Action
- Chiral splitting and world-sheet gravitinos in higher-derivative string amplitudes
- Counterterms/M-theory Corrections to D=11 Supergravity
- Duality in Supergravity Theories
- Tree Amplitudes and Two-loop Counterterms in D=11 Supergravity
- On higher-order corrections in M theory
- Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry
- Toward the Determination of R^3F^2 Terms in M-theory
- Conformal supergravities as Chern-Simons theories revisited
- Curved 11D Supergeometry
- Higher-derivative gauge field terms in the M-theory action
- Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
- Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3
- The cohomology of superspace, pure spinors and invariant integrals
- The One-Loop H^2R^3 and H^2(DH)^2R Terms in the Effective Action
- R^4 Corrections to Eleven Dimensional Supergravity via Supersymmetry
- Supersymmetry algebra cohomology III: Primitive elements in four and five dimensions
- On supersymmetric Chern-Simons-type theories in five dimensions
- The deformed M2-brane
- Graviton-Form Invariants in D=11 Supergravity
- 11D supergravity at
- Supersymmetry algebra cohomology II: Primitive elements in 2 and 3 dimensions
- Deformations with Maximal Supersymmetries Part 1: On-shell Formulation
- Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D=4 to D=11
- Supersymmetry algebra cohomology I: Definition and general structure