REVIEW 8 cited by
Constraints on RG Flow for Four Dimensional Quantum Field Theories
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve $a$, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered. Previous consistency conditions for the anomalous terms, which implicitly define a metric $G$ on the space of couplings and give rise to gradient flow like equations for $a$, are derived taking into account the role of lower dimension operators. The results for infinitesimal Weyl rescaling are integrated to finite rescalings $e^{2\sigma}$ to a form which involves running couplings $g_\sigma$ and which interpolates between IR and UV fixed points. The results are also restricted to flat space where they give rise to broken conformal Ward identities. Expressions for the three loop Yukawa $\beta$-functions for a general scalar/fermion theory are obtained and the three loop contribution to the metric $G$ for this theory are also calculated. These results are used to check the gradient flow equations to higher order than previously. It is shown that these are only valid when $\beta \to B$, a modified $\beta$-function, and that the equations provide strong constraints on the detailed form of the three loop Yukawa $\beta$-function. ${\cal N}=1$ supersymmetric Wess-Zumino theories are also considered as a special case. It is shown that the metric for the complex couplings in such theories may be restricted to a hermitian form.
Forward citations
Cited by 8 Pith papers
-
On the Renormalization Group in EFTs: On-Shell Bases, Ambiguities, and Divergences
Two-loop RG divergences in on-shell EFT bases are spurious: they vanish when non-minimal source terms are included, leaving only unphysical flavor-rotation flow.
-
Gradient RG Flow in Scalar-Fermion QFTs
RG flow in scalar-fermion theories is gradient through four loops only when the 'beta shift' is included, via over a thousand scheme-independent constraints that hold wherever current data allow a check.
-
On the scalar sector of 2HDM: ring of basis invariants, syzygies, and six-loop renormalization-group equations
Six-loop renormalization-group equations for the 22 basis invariants of the 2HDM scalar potential are derived with invariant theory and Groebner bases, including the 63 minimal syzygies.
-
Gauge coupling beta functions and gauge field anomalous dimensions at four loops in the Standard Model
Four-loop Standard Model gauge beta functions are confirmed by a direct Feynman-diagram calculation, and four-loop gauge-field anomalous dimensions are computed for the first time.
-
Matching $A$ with $F$ in long-range QFTs
RG flow in long-range φ⁴ theories obeys gradient structure ∂_I A = G_IJ β^J up to three loops, with A matching F-tilde and G matching C_IJ at leading nontrivial order.
-
Fixed points of the renormalisation group running of quark and fermion mixing matrices in the Standard Model and beyond
Six fixed points exist for the massless one-loop RG running of three-generation fermion mixing matrices, remaining fixed points to all orders via geometric properties of vector fields on the space of mixing matrices.
-
Gradient properties of $\varphi^3$ in $d=6-\varepsilon$
The d = 6 gradient (A-function) structure of the phi^3 RG flow extends to d = 6 − epsilon, requiring one new three-loop constraint, Eq. (22), that the MS coefficients satisfy.
-
Gradient Flows and the Curvature of Theory Space
The space of multiscalar field theories carries a curved metric determined by gradient flow, and the gradient-flow potential and metric can be matched to F-tilde and the Zamolodchikov metric at fixed points.
Discussion (0). Continue with ORCID to comment.