The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of classes in degree-(2k + 2) differential cohomology. We first refine this statement from the moduli space to the full higher smooth moduli stack of fields, to which the higher-order-ghost BRST complex is the infinitesimal approximation. Then we generalize the refined formulation to cup product Chern-Simons theories of nonabelian and higher nonabelian gauge fields, such as the nonabelian String(c)-2-connections appearing in quantum-corrected 11-dimensional supergravity and M-branes. We discuss aspects of the off-shell extended geometric prequantization (in the sense of extended or multi-tiered QFT) of these theories, where there is a prequantum U(1)-k-bundle (equivalently: a U(1)-(k 1)-bundle gerbe) in each codimension k. Examples we find include moduli stacks for differential T-duality structures as well as the anomaly line bundles of higher electric/magnetic charges, such as the 5-brane charges appearing in heterotic supergravity, appearing as line bundles with connection on the smooth higher moduli stacks of field configurations. (C) 2013 Elsevier B.V. All rights reserved.

Extended higher cup-product Chern-Simons theories / Fiorenza, Domenico; Hisham, Sati; Urs, Schreiber. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - STAMPA. - 74(2013), pp. 130-163. [10.1016/j.geomphys.2013.07.011]

Extended higher cup-product Chern-Simons theories

FIORENZA, DOMENICO;
2013

Abstract

The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of classes in degree-(2k + 2) differential cohomology. We first refine this statement from the moduli space to the full higher smooth moduli stack of fields, to which the higher-order-ghost BRST complex is the infinitesimal approximation. Then we generalize the refined formulation to cup product Chern-Simons theories of nonabelian and higher nonabelian gauge fields, such as the nonabelian String(c)-2-connections appearing in quantum-corrected 11-dimensional supergravity and M-branes. We discuss aspects of the off-shell extended geometric prequantization (in the sense of extended or multi-tiered QFT) of these theories, where there is a prequantum U(1)-k-bundle (equivalently: a U(1)-(k 1)-bundle gerbe) in each codimension k. Examples we find include moduli stacks for differential T-duality structures as well as the anomaly line bundles of higher electric/magnetic charges, such as the 5-brane charges appearing in heterotic supergravity, appearing as line bundles with connection on the smooth higher moduli stacks of field configurations. (C) 2013 Elsevier B.V. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/525955
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