We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such nonultralocal operators, whose computational cost is volume independent at fixed accuracy, and only grows logarithmically as this accuracy approaches zero. This makes computation of useful operators, such as overlap-based topological density, practical. The key notion underlying these features is that of exponential insensitivity to distant fields, made rigorous by introducing the procedure of statistical regularization. The scales associated with insensitivity property are useful characteristics of nonlocal continuum operators.
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A. A. is supported in part by the National Science Foundation CAREER Grant No. PHY-1151648 and Department of Energy Grant No. DE-FG02-95ER-40907.
Alexandru, Andrei and Horváth, Ivan, "Locality and Efficient Evaluation of Lattice Composite Fields: Overlap-Based Gauge Operators" (2017). Physics and Astronomy Faculty Publications. 544.