In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.
Gradient flow exact renormalization group
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abstract
The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang--Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.
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Towards gauge independence in asymptotically safe quantum gravity
In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.