TY - JOUR
T1 - 2D sigma models and differential Poisson algebras
AU - Arias, Cesar
AU - Boulanger, Nicolas
AU - Sundell, Per
AU - Torres-Gomez, Alexander
N1 - Funding Information:
We are thankful to Francisco Rojas, Ergin Sezgin and Brenno Vallilo for discussions. C.A. is supported by a UNAB PhD scholarship. N.B. is a Research Associate of the Fonds de la Recherche Scientifique-FNRS (Belgium). His work was partially supported by the contract ?Actions de Recherche concert?es -Communaut? francaise de Belgique? AUWB- 2010-10/15-UMONS-1. A.T.G. is supported by FONDECYT post-doctoral grant number 3130333. P.S. is supported by FONDECYT project number 1140296 and CONICYT project number DPI20140115.
Publisher Copyright:
© 2015, The Author(s).
PY - 2015/8/1
Y1 - 2015/8/1
N2 - Abstract: We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
AB - Abstract: We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
KW - Differential and Algebraic Geometry
KW - NonCommutative Geometry
KW - Topological Field Theories
KW - Topological Strings
UR - http://www.scopus.com/inward/record.url?scp=84958248860&partnerID=8YFLogxK
U2 - 10.1007/JHEP08(2015)095
DO - 10.1007/JHEP08(2015)095
M3 - Article
AN - SCOPUS:84958248860
VL - 2015
SP - 1
EP - 18
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 8
M1 - 95
ER -