Anomalies in Instanton Calculus

Abstract

I develop a formalism for solving topological field theories explicitly, in the case when the explicit expression of the instantons is known. I solve topological Yang-Mills theory with the $k=1$ Belavin {\sl et al.} instanton and topological gravity with the Eguchi-Hanson instanton. It turns out that naively empty theories are indeed nontrivial. Many unexpected interesting hidden quantities (punctures, contact terms, nonperturbative anomalies with or without gravity) are revealed. Topological Yang-Mills theory with $G=SU(2)$ is not just Donaldson theory, but contains a certain {\sl link} theory. Indeed, local and non-local observables have the property of {\sl marking} cycles. From topological gravity one learns that an object can be considered BRST exact only if it is so all over the moduli space $\mathcal{M}$, boundary included. Being BRST exact in any interior point of $\mathcal{M}$ is not sufficient to make an amplitude vanish. Presumably, recursion relations and hierarchies can be found to solve topological field theories in four dimensions, in particular topological Yang-Mills theory with $G=SU(2)$ on ${\mathbf{R}}^4$ and topological gravity on ALE manifolds.

34 pages, latex, no figures

References in corpus (10)

• Holomorphic Anomalies in Topological Field Theories
• Twisted N=2 Supergravity as Topological Gravity in Four Dimensions
• ALE manifolds and Conformal Field Theory
• Topological Sigma-Models in Four Dimensions and Triholomorphic Maps
• Predictivity and Nonrenormalizability
• ALE Instantons in String Effective Theory
• Topological 2-form Gravity in Four Dimensions
• Topological Conformal Gravity in Four Dimensions
• Constrained Topological Field Theory
• Constrained Topological Gravity from Twisted N=2 Liouville Theory

Cited by in corpus (10)

• Gauged Hyperinstantons and Monopole Equations
• Topological field theory and physics
• Topological Gravity versus Supergravity on Manifolds with Special Holonomy
• Topological Yang-Mills cohomology in pure Yang-Mills Theory
• Gauge dependence in topological gauge theories
• Super Background Field Method for N=2 SYM
• On field theory quantization around instantons
• Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding
• Topological Yang-Mills Theory with Two Fermionic Charges. A Superfield Approach on Kähler Manifolds
• The ADHM Construction and Anselmi's Topological Anomalies