Abstract
We have studied supersymmetric and super Poincaré invariant deformations of maximally supersymmetric gauge theories, in particular, of ten-dimensional super Yang-Mills theory and of its reduction to a point. We have described all infinitesimal super Poincaré invariant deformations of equations of motion and proved that all of them are Lagrangian deformations and all of them can be extended to formal deformations. Our methods are based on homological algebra, in particular, on the theory of L-infinity and A-infinity algebras. In this paper we formulate some of the results we have obtained, but skip all proofs. However, we describe (in Sects. 2 and 3) the results of the theory of L-infinity and A-infinity algebras that serve as the main tool in our calculations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. Berkovits, Explaining the pure spinor formalism for the superstring. JHEP0801:065, arXiv:0712.0324 (2008)
D. Burghelea, Z. Fiedorowicz, W. Gajda, Adams operations in Hochschild and cyclic homology of de Rham algebra and free loop spaces. K-Theory 4(3), 269–287 (1991)
B.L. Feigin, B.L. Tsygan, in Cyclic Homology of Algebras with Quadratic Relations, Universal Enveloping Algebras and Group Algebras. K-Theory, Arithmetic and Geometry (Moscow, 1984–1986). Lecture Notes in Mathematics, vol. 1289 (Springer, Berlin, 1987), pp. 210–239
B. Keller, Invariance and localization for cyclic homology of DG algebras. J. Pure Appl. Algebra 123(1–3), 223–273 (1998)
B. Keller, Derived invariance of higher structures on the Hochschild complex. Preprint available at http://people.math.jussieu.fr/keller/publ/dih.pdf
M. Kontsevich, private communication
J.-L. Loday, in Cyclic Homology. Grundlehren der Mathematischen Wissenschaften, vol. 301 (Springer, Berlin, 1998)
M. Movshev, Cohomology of Yang-Mills algebras. J. Noncommut. Geom. 2(3), 353–404 (2008)
M. Movshev, Deformation of maximally supersymmetric Yang-Mills theory in dimensions 10. An algebraic approach. arXiv:hep-th/0601010v1
M. Movshev, Deformation of maximally supersymmetric Yang-Mills theory in dimensions 10. An algebraic approach. hep-th/0601010
M. Movshev, Yang-Mills theories in dimensions 3, 4, 6, 10 and Bar-duality. hep-th/0503165
M. Movshev, A. Schwarz, Algebraic structure of Yang-Mills theory. hep-th/0404183
M. Movshev, A. Schwarz, On maximally supersymmetric Yang-Mills theories. hep-th/0311132
M. Movshev, A. Schwarz, Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories. I
M. Penkava, A. Schwarz, A ∞ algebras and the cohomology of moduli spaces. Am. Math. Soc. Transl. Ser. 2, 169 (1995). hep-th/9408064
A. Schwarz, Semiclassical approximation in Batalin-Vilkovisky formalism. Commun. Math. Phys. 158, 373–396 (1993)
Acknowledgements
The work of both authors was partially supported by NSF grant No. DMS 0505735 and by grants DE-FG02-90ER40542 and PHY99-0794.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Movshev, M.V., Schwarz, A. (2011). Maximal Supersymmetry. In: Ferrara, S., Fioresi, R., Varadarajan, V. (eds) Supersymmetry in Mathematics and Physics. Lecture Notes in Mathematics(), vol 2027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21744-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-21744-9_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21743-2
Online ISBN: 978-3-642-21744-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)