TY - JOUR
T1 - Chiral de Rham Complex on Riemannian Manifolds and Special Holonomy
AU - Ekstrand, Joel
AU - Heluani, Reimundo
AU - Källén, Johan
AU - Zabzine, Maxim
PY - 2013/3
Y1 - 2013/3
N2 - Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically construct global sections of CDR from differential forms, and investigate the algebra of the sections corresponding to the covariantly constant forms associated with the special holonomy. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N = 2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau threefold and conjecture similar results for G2 manifolds. We also discuss quasi-classical limits of these algebras.
AB - Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically construct global sections of CDR from differential forms, and investigate the algebra of the sections corresponding to the covariantly constant forms associated with the special holonomy. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N = 2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau threefold and conjecture similar results for G2 manifolds. We also discuss quasi-classical limits of these algebras.
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U2 - 10.1007/s00220-013-1659-4
DO - 10.1007/s00220-013-1659-4
M3 - Article
AN - SCOPUS:84874561475
SN - 0010-3616
VL - 318
SP - 575
EP - 613
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -