A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
On the Connection Between Momentum Cutoff and Operator Cutoff Regularizations
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abstract
Operator cutoff regularization based on the original Schwinger's proper-time formalism is examined. By constructing a regulating smearing function for the proper-time integration, we show how this regularization scheme simulates the usual momentum cutoff prescription yet preserves gauge symmetry even in the presence of the cutoff scales. Similarity between the operator cutoff regularization and the method of higher (covariant) derivatives is also observed. The invariant nature of the operator cutoff regularization makes it a promising tool for exploring the renormalization group flow of gauge theories in the spirit of Wilson-Kadanoff blocking transformation.
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A hard-cutoff scheme for scalar and fermionic QED is constructed that preserves gauge invariance and reproduces the standard Euler-Heisenberg effective action up to cutoff-suppressed periodic corrections.
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
citing papers explorer
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Rethinking Dimensional Regularization in Critical Phenomena
A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
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Hard cutoff and gauge theories
A hard-cutoff scheme for scalar and fermionic QED is constructed that preserves gauge invariance and reproduces the standard Euler-Heisenberg effective action up to cutoff-suppressed periodic corrections.
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Quantum gravity contributions to the gauge and Yukawa couplings in proper time flow
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
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Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.