Abstract
We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing Operators, analogous to the one introduced in String Theory. As an application, we construct a geometric action principle for N = 1 D = 3 super-Chern-Simons theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Catenacci, M. Debernardi, P.A. Grassi and D. Matessi, Cech and de Rham cohomology of integral forms, J. Geom. Phys. 62 (2012) 890 [arXiv:1003.2506] [INSPIRE].
L. Castellani, R. Catenacci and P.A. Grassi, Supergravity Actions with Integral Forms, Nucl. Phys. B 889 (2014) 419 [arXiv:1409.0192] [INSPIRE].
T. Voronov and A. Zorich, Integral transformations of pseudodifferential forms, Usp. Mat. Nauk. 41 (1986) 167.
T. Voronov and A. Zorich, Complex of forms on a supermanifold, Funkt. Anal. i Pril. 20 (1986) 58.
T. Voronov and A. Zorich, Theory of bordisms and homotopy properties of supermanifolds, Funkt. Anal. i Pril. 21 .(1987) 77
T. Voronov and A. Zorich, Cohomology of supermanifolds, and integral geometry, Sov. Math. Dokl. 37 (1988) 96.
A. Belopolsky, New geometrical approach to superstrings, hep-th/9703183 [INSPIRE].
A. Belopolsky, Picture changing operators in supergeometry and superstring theory, hep-th/9706033 [INSPIRE].
E. Witten, Notes on supermanifolds and integration, arXiv:1209.2199 [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, JHEP 09 (2004) 047 [hep-th/0406055] [INSPIRE].
P.A. Grassi and G. Policastro, Super-Chern-Simons theory as superstring theory, hep-th/0412272 [INSPIRE].
H. Nishino and S.J. Gates, Jr., Chern-Simons theories with supersymmetries in three-dimensions, Int. J. Mod. Phys. A 8 (1993) 3371 [INSPIRE].
L. Castellani, R. D’Auria and P. Fré, Supergravity and superstrings: a geometric perspective, World Scientific, Singapore (1991).
L. Castellani, R. Catenacci and P.A. Grassi, Hodge dualities on supermanifolds, Nucl. Phys. B 899 (2015) 570 [arXiv:1507.01421] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, Resolving Witten’s superstring field theory, JHEP 04 (2014) 150 [arXiv:1312.2948] [INSPIRE].
C.R. Preitschopf, C.B. Thorn and S.A. Yost, Superstring field theory, Nucl. Phys. B 337 (1990) 363 [INSPIRE].
I.Ya. Arefeva, P.B. Medvedev and A.P. Zubarev, New representation for string field solves the consistency problem for open superstring field theory, Nucl. Phys. B 341 (1990) 464 [INSPIRE].
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).
L. Castellani, R. Catenacci and P.A. Grassi, The geometry of supermanifolds and new supersymmetric actions, Nucl. Phys. B 899 (2015) 112 [arXiv:1503.07886] [INSPIRE].
D. Fabbri, P. Fré, L. Gualtieri and P. Termonia, Osp(N |4) supermultiplets as conformal superfields on partial AdS 4 and the generic form of N = 2, D = 3 gauge theories, Class. Quant. Grav. 17 (2000) 55 [hep-th/9905134] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1606.06609
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Grassi, P.A., Maccaferri, C. Chern-Simons theory on supermanifolds. J. High Energ. Phys. 2016, 170 (2016). https://doi.org/10.1007/JHEP09(2016)170
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2016)170