The cohomology of superspace, pure spinors and invariant integrals

Abstract

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to $\a'^3$. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.

24 pages. Minor changes; added references

References in corpus (5)

• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• Covariant One-Loop Amplitudes in D=11
• Pure Spinors, Free Differential Algebras, and the Supermembrane
• Kappa-symmetric Derivative Corrections to D-brane Dynamics
• Kappa-symmetric deformations of M5-brane dynamics

Cited by in corpus (17)

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• Topologically gauged superconformal Chern-Simons matter theories
• Integral invariants in maximally supersymmetric Yang-Mills theories
• Higher Derivative Supergravities in Diverse Dimensions
• Maximal supergravity in three dimensions: supergeometry and differential forms
• Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
• Half-maximal supergravity in three dimensions: supergeometry, differential forms and algebraic structure
• Forms and algebras in (half-)maximal supergravity theories
• Maximal supergravity in D=10: forms, Borcherds algebras and superspace cohomology
• Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories
• Ectoplasm with an Edge
• Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
• All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies
• Off-Shell Scalar Supermultiplet in the Unfolded Dynamics Approach
• The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity
• Superfield Component Decompositions and the Scan for Prepotential Supermultiplets in 10D Superspaces