Gravitational null rays are quantized in a diffeomorphism-covariant way using the gravitational dressing time as quantum reference frame, producing a Virasoro crossed-product algebra of gauge-invariant observables.
The Operator Product Expansion in Quantum Field Theory
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abstract
Operator product expansions (OPEs) in quantum field theory (QFT) provide an asymptotic relation between products of local fields defined at points $x_1, \dots, x_n$ and local fields at point $y$ in the limit $x_1, \dots, x_n \to y$. They thereby capture in a precise way the singular behavior of products of quantum fields at a point as well as their ``finite trends.'' In this article, we shall review the fundamental properties of OPEs and their role in the formulation of interacting QFT in curved spacetime, the ``flow relations'' in coupling parameters satisfied by the OPE coefficients, the role of OPEs in conformal field theories, and the manner in which general theorems -- specifically, the PCT theorem -- can be formulated using OPEs in a curved spacetime setting.
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Extends celestial RSVW formalism to minitwistor superspace to build tree-level N^k-MHV leaf amplitudes in planar N=4 SYM and gives dynamical realizations via Wilson operators on algebraic cycles and a minitwistor sigma model.
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
Proves sine-Gordon OPEs for derivative fields develop log singularities and generate Wick exponentials using Onsager-type inequalities and GFF moment bounds.
Derives universal first-order ODEs governing the RG flow of boundary operator data (scaling dimensions, OPE and BOE coefficients) for 2D QFTs on hyperbolic space.
Generalizes flow ODEs for QFT data in AdS3/AdS4, capturing operator merger-annihilation and level repulsion, with efficiency gains from crossing equations and Padé approximants.
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Operator product expansions of derivative fields in the sine-Gordon model
Proves sine-Gordon OPEs for derivative fields develop log singularities and generate Wick exponentials using Onsager-type inequalities and GFF moment bounds.