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Integral invariants in flat superspace. (English) Zbl 1323.81093

Summary: We are solving for the case of flat superspace some homological problems that were formulated by Berkovits and Howe. (Our considerations can be applied also to the case of supertorus.) These problems arise in the attempt to construct integrals invariant with respect to supersymmetry. They appear also in other situations, in particular, in the pure spinor formalism in supergravity.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
17B55 Homological methods in Lie (super)algebras
83E50 Supergravity

Software:

Macaulay2

References:

[1] Berkovits, N.; Howe, P. S., The cohomology of superspace, pure spinors and invariant integrals, J. High Energy Phys., 0806, 046 (2008)
[2] Berkovits, N., Covariant quantization of the superparticle using pure spinors, J. High Energy Phys., 0109, 016 (2001)
[3] Berkovits, N., Towards covariant quantization of the supermembrane, J. High Energy Phys., 0209, 051 (2002)
[4] Cederwall, M.; Nilsson, B. E.W.; Tsimpis, D., The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections, J. High Energy Phys., 0106 (2001), 034
[5] Cederwall, M.; Nilsson, B. E.W.; Tsimpis, D., Spinorial cohomology and maximally supersymmetric theories, J. High Energy Phys., 0202, 009 (2002)
[6] Howe, P. S.; Tsimpis, D., On higher-order corrections in M theory, J. High Energy Phys., 0309 (2003), 038
[7] Movshev, M. V.; Schwarz, A.; Xu, Renjun, Homology of Lie algebra of supersymmetries · Zbl 1229.81117
[8] Movshev, M. V., Geometry of a desingularization of eleven-dimensional gravitational spinors
[9] Grayson, Daniel R.; Stillman, Michael E., Macaulay 2, a software system for research in algebraic geometry
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