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Nonrenormalization and Operator Mixing via On-Shell Methods.
Phys Rev Lett
February 2020
Mani L. Bhaumik Institute for Theoretical Physics, UCLA Department of Physics and Astronomy, Los Angeles, California 90095, USA.
Using on-shell methods, we present a new perturbative nonrenormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions, we show that longer operators are often restricted from renormalizing shorter operators at the first order where Feynman diagrams exist. The theorem applies quite generally and depends only on the field content of the operators involved.
View Article and Find Full Text PDFNonrenormalization Theorems without Supersymmetry.
Phys Rev Lett
August 2015
Walter Burke Institute for Theoretical Physics California Institute of Technology, Pasadena, California 91125, USA.
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations.
View Article and Find Full Text PDFTopological field theory of dynamical systems.
Chaos
September 2012
Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, California 90095-1594, USA.
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry).
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