Gribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravity

We point out that averages of equivariant observables of 2D topological gravity are not globally defined forms on moduli space, when one uses the functional measure corresponding to the formulation of the theory as a 2D superconformal model. This is shown to be a consequence of the existence of the...

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Detalles Bibliográficos
Autores principales: Becchi, Carlo M., Imbimbo, Camillo
Lenguaje:eng
Publicado: 1995
Materias:
Acceso en línea:https://dx.doi.org/10.1016/0550-3213(95)00004-6
http://cds.cern.ch/record/288835
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author Becchi, Carlo M.
Imbimbo, Camillo
author_facet Becchi, Carlo M.
Imbimbo, Camillo
author_sort Becchi, Carlo M.
collection CERN
description We point out that averages of equivariant observables of 2D topological gravity are not globally defined forms on moduli space, when one uses the functional measure corresponding to the formulation of the theory as a 2D superconformal model. This is shown to be a consequence of the existence of the Gribov horizon {\it and} of the dependence of the observables on derivatives of the super-ghost field. By requiring the absence of global BRS anomalies, it is nevertheless possible to associate global forms to correlators of observables by resorting to the \v{C}ech-De Rham notion of form cohomology. To this end, we derive and solve the ``descent'' of local Ward identities which characterize the functional measure. We obtain in this way an explicit expression for the \v{C}ech-De Rham cocycles corresponding to arbitrary correlators of observables. This provides the way to compute and understand contact terms in string theory from first principles.
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spelling cern-2888352021-03-17T03:47:23Zdoi:10.1016/0550-3213(95)00004-6http://cds.cern.ch/record/288835engBecchi, Carlo M.Imbimbo, CamilloGribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravityParticle Physics - TheoryWe point out that averages of equivariant observables of 2D topological gravity are not globally defined forms on moduli space, when one uses the functional measure corresponding to the formulation of the theory as a 2D superconformal model. This is shown to be a consequence of the existence of the Gribov horizon {\it and} of the dependence of the observables on derivatives of the super-ghost field. By requiring the absence of global BRS anomalies, it is nevertheless possible to associate global forms to correlators of observables by resorting to the \v{C}ech-De Rham notion of form cohomology. To this end, we derive and solve the ``descent'' of local Ward identities which characterize the functional measure. We obtain in this way an explicit expression for the \v{C}ech-De Rham cocycles corresponding to arbitrary correlators of observables. This provides the way to compute and understand contact terms in string theory from first principles.We point out that averages of equivariant observables of 2D topological gravity are not globally defined forms on moduli space, when one uses the functional measure corresponding to the formulation of the theory as a 2D superconformal model. This is shown to be a consequence of the existence of the Gribov horizon {\it and} of the dependence of the observables on derivatives of the super-ghost field. By requiring the absence of global BRS anomalies, it is nevertheless possible to associate global forms to correlators of observables by resorting to the \v{C}ech-De Rham notion of form cohomology. To this end, we derive and solve the ``descent'' of local Ward identities which characterize the functional measure. We obtain in this way an explicit expression for the \v{C}ech-De Rham cocycles corresponding to arbitrary correlators of observables. This provides the way to compute and understand contact terms in string theory from first principles.We point out that averages of equivariant observables of 2D topological gravity are not globally defined forms on moduli space, when one uses the functional measure corresponding to the formulation of the theory as a 2D superconformal model. This is shown to be a consequence of the existence of the Gribov horizon and of the dependence of the observables on derivatives of the super-ghost field. By requiring the absence of global BRS anomalies, it is nevertheless possible to associate global forms to correlators of observables by resorting to the Čech-De Rham cohomology. To this end, we derive and solve the “descent” of local Ward identities which characterize the functional measure. We obtain in this way an explicit expression for the Čech-De Rham cocycles corresponding to arbitrary correlators of observables. This provides the way to compute and understand contact terms in string theory from first principles.hep-th/9510003CERN-TH-95-242GEF-TH-95-8CERN-TH-95-242GEF-TH-95-8oai:cds.cern.ch:2888351995-10-02
spellingShingle Particle Physics - Theory
Becchi, Carlo M.
Imbimbo, Camillo
Gribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravity
title Gribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravity
title_full Gribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravity
title_fullStr Gribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravity
title_full_unstemmed Gribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravity
title_short Gribov problem, contact terms and Cech-de Rham cohomology in 2D topological gravity
title_sort gribov problem, contact terms and cech-de rham cohomology in 2d topological gravity
topic Particle Physics - Theory
url https://dx.doi.org/10.1016/0550-3213(95)00004-6
http://cds.cern.ch/record/288835
work_keys_str_mv AT becchicarlom gribovproblemcontacttermsandcechderhamcohomologyin2dtopologicalgravity
AT imbimbocamillo gribovproblemcontacttermsandcechderhamcohomologyin2dtopologicalgravity