Exact scheme independence at two loops
arXiv:hep-th/0309242 · doi:10.1103/PhysRevD.69.065009
Abstract
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively,by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularisation scheme.
16 pages, 20 figures, uses revtex4. One- and two-loop seed action contributions added, typos corrected, version to appear in PRD
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- Essential renormalisation group
- Manifestly diffeomorphism invariant classical Exact Renormalization Group
- Manifestly gauge invariant QED
- Scheme dependence and universality in the functional renormalization group
- Renormalization Group Flow as Optimal Transport
- Triviality from the Exact Renormalization Group
- BRST in the Exact RG
- A Manifestly Gauge Invariant and Universal Calculus for SU(N) Yang-Mills
- Functional Renormalization and
- Scheme Independence to all Loops
- Background independent exact renormalisation
- General Computations Without Fixing the Gauge
- Universality From Very General Nonperturbative Flow Equations in QCD
- A Primer for Manifestly Gauge Invariant Computations in SU(N) Yang-Mills
- BRST invariant RG flows
- A Resummable beta-Function for Massless QED
- Limit of vanishing regulator in the functional renormalization group
- Conformal anomaly from gauge fields without gauge fixing
- Factorization of integrals, defining the beta-function, into integrals of total derivatives in N=1 SQED, regularized by higher derivatives
- Properties of a proposed background independent exact renormalization group
- Perturbative versus Non-Perturbative Renormalization
- Higher derivative extension of the functional renormalization group
- Sensitivity of Nonrenormalizable Trajectories to the Bare Scale