Kodaira-Spencer Anomalies with Stora-Zumino Method

Abstract

Holomorphic diffeomorphism anomalies of $2n$-dimensional gravitational theories in Beltrami parametrisation (Kodaira-Spencer anomalies) are computed in the BRST framework, using an extension of the Stora-Zumino method. This method, which allows to compute anomalies in a very concise way, makes manifest the topological origin of anomalies. They have a clear geometric interpretation, since they are expressed in terms of Chern polynomials and Pontryagin invariants. The key ingredient is the formulation of the BRST transformations in terms of polyforms, whose total degree is the sum of the form degree and of the ghost number. This approach simplifies significantly the analysis available in literature and it allows to compute many other solutions. Namely, an anomaly, which was computed using different methods, is proved to be a consistent BRST anomaly, thereby supplementing a conclusion in a previous analysis.

arXiv commentPublished version

References in corpus (26)

• The Holographic Weyl anomaly
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Holomorphic Anomalies in Topological Field Theories
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• Algebraic characterization of the Wess-Zumino consistency conditions in gauge theories
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• Theory of Kähler Gravity
• Equivariant localization in supergravity
• Chiral Lagrangians, Anomalies, Supersymmetry, and Holomorphy
• Equivariant localization and holography
• A Closed form for Consistent Anomalies in Gauge Theories
• Type B Topological Matter, Kodaira-Spencer Theory, and Mirror Symmetry
• Equivariant localization for AdS/CFT
• Localization and Attraction
• The BRST--antibracket cohomology of $2d$ gravity conformally coupled to scalar matter
• Supersymmetric Structure of the Bosonic String Theory in the Beltrami Parametrization
• Diffeomorphism Cohomology in Beltrami Parametrization II : The 1-Forms
• The Coupling of Chern-Simons Theory to Topological Gravity
• Anomalies in Covariant Fracton Theories
• Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity
• Kodaira-Spencer deformation of complex structures and Lagrangian field theory
• Superconformal anomalies from superconformal Chern-Simons polynomials
• BRST cohomology in Beltrami parametrization
• Deformations of Supergravity and Supersymmetry Anomalies
• The Holomorphic Anomaly of Topological Strings