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I. Jack

Publications and source records attributed to I. Jack.

At least 19 recordsLinked to original sources
arXiv2026

Asymptotic Pad\'e Predictions up to Six Loops in QCD and Eight Loops in $\lambda\phi^4$

We assess the accuracy of our previous Asymptotic Pad\'e predictions of the five-loop QCD $\beta$-function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in powers of $N_F$ (the number of flavours) were correct to within $1\%$. Furthermore an examination of recent results in $\lambda\phi^4$ theory indicates that the Asymptotic Pad\'e methods deliver predictions which increase in accuracy with loop order. Encouraged by this, we present six-loop Asymptotic Pad\'e predictions for the QCD $\beta$-function and quark mass anomalous dimension, and also for the eight-loop $\beta$-function in $O(N)$ $\lambda\phi^4$ theory.

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arXiv2025

An alternative formulation of infra-red counterterms

We present an alternative procedure for defining infra-red counterterms within dimensional regularisation for use in the $R^*$ procedure. The counterterms are given by simple closed expressions, and lead to the standard MSbar UV counterterms.

hep-th↗
arXiv2023

No-$\pi$ schemes for multi-coupling theories

We show that even $\zeta$-functions may be removed from the $\beta$-functions of general multi-coupling theories up to high loop order by means of coupling redefinitions. For theories whose $\beta$-function is determined by the anomalous dimensions of the fields, such as supersymmetric theories, this corresponds to a renormalisation scheme change to a momentum subtraction scheme.

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arXiv2021

Scaling dimensions at large charge for cubic $\phi^3$ theory in six dimensions

The $O(N)$ model with scalar quartic interactions at its ultraviolet fixed point, and the $O(N)$ model with scalar cubic interactions at its infra-red fixed point are conjectured to be equivalent. This has been checked by comparing various features of the two models at their respective fixed points. Recently, the scaling dimensions of a family of operators of fixed charge $Q$ have been shown to match at the FPs up to $\cal{O}\left(\frac{1}{N^2}\right)$at leading order (LO) and next-to-leading order (NLO) in $Q$ using a semiclassical computation which is valid to all orders in the coupling. Here we perform a complementary but overlapping comparison using a perturbative calculation in six dimensions, up to three-loop order in the coupling, to compare these critical scaling dimensions beyond NLO in $Q$, in fact to all relevant orders in $Q$. We also obtain the corresponding results at $\cal{O}\left(\frac{1}{N^3}\right)$ for the cubic theory.

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arXiv2021

Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions

Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\bar\phi\phi)^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$, and this was verified to two loop order in perturbation theory at leading and subleading $n$. This result was subsequently generalised to operators of fixed charge $Q$ in $O(N)$ theory and verified up to four loops in perturbation theory at leading and subleading $Q$. More recently, similar semiclassical calculations have been performed for the classically scale-invariant $U(N)\times U(N)$ theory in four dimensions, and verified up to two loops, once again at leading and subleading $Q$. Here we extend this verification to four loops. We also consider the corresponding classically scale-invariant theory in three dimensions, similarly verifying the leading and subleading semiclassical results up to four loops in perturbation theory.

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arXiv2021

Anomalous dimensions at large charge in d=4 O(N) theory

Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\phi^*\phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$ and this was verified to two loop order in perturbation theory at leading and sub-leading $n$. In subsequent work, this result was generalised to operators of fixed charge $Q$ in $O(N)$ theory and verified up to three loops in perturbation theory at leading and sub-leading order. Here we extend this verification to four loops in $O(N)$ theory, once again at leading and sub-leading order. We also investigate the strong-coupling regime.

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arXiv2020

Anomalous dimensions for $\phi^n$ in scale invariant $d=3$ theory

Recently it was shown that the scaling dimension of the operator $\phi^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading $n$. Here we extend this verification to six loops, once again at leading and subleading $n$. We then perform a similar exercise for a theory with a multiplet of real scalars and an $O(N)$ invariant hexic interaction. We also investigate the strong-coupling regime for this example.

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arXiv2020

One-loop beta-functions for renormalisable gravity

We compute the one-loop beta-functions for renormalisable quantum gravity coupled to scalars using the co-ordinate space approach and generalised Schwinger De Witt technique. We resolve apparent contradictions with the corresponding momentum space calculations, and indicate how our results also resolve similar inconsistencies in the fermion case.

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arXiv2018

Scheme invariants in phi^4 theory in four dimensions

We provide an analysis of the structure of renormalisation scheme invariants for the case of $ϕ^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at five loops, showing that there are considerably more invariants than one might naively have expected. We also show that one-vertex reducible contributions may consistently be omitted in a well-defined class of schemes which of course includes MSbar.

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arXiv2017

The a-function for gauge theories

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We construct the a-function at four loop order for a general gauge theory with fermions and scalars, using only one and two loop beta-functions; we are then able to provide a stringent consistency check on the general three-loop gauge beta-function. In the case of an N=1 supersymmetric gauge theory, we present a general condition on the chiral field anomalous dimension which guarantees an exact all-orders expression for the a-function; and we verify this up to fifth order (corresponding to the three-loop anomalous dimension).

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arXiv2017

The a-function for N=2 supersymmetric gauge theories in three dimensions

Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.

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arXiv2017

The a-function in three dimensions: beyond leading order

Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and shown to be related to the beta-functions by a gradient flow equation with positive-definite metric as in four dimensions. Here, we extend this lowest-order calculation to a general abelian Chern-Simons gauge theory coupled to fermions and scalars, and derive a prediction for part of the four-loop Yukawa beta-function. We also compute the complete four-loop Yukawa beta-function for the scalar-fermion theory and show that it is entirely consistent with the gradient flow equations at next-to-leading order.

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arXiv2016

Consistency of non-minimal renormalisation schemes

Non-minimal renormalisation schemes such as the momentum subtraction scheme (MOM) have frequently been used for physical computations. The consistency of such a scheme relies on the existence of a coupling redefinition linking it to MSbar. We discuss the implementation of this procedure in detail for a general theory and show how to construct the relevant redefinition up to three-loop order, for the case of a general theory of fermions and scalars in four dimensions and a general scalar theory in six dimensions.

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arXiv2016

The a-function in six dimensions

The a-function is a proposed quantity defined in even dimensions which has a monotonic behaviour along RG flows, related to the beta-functions via a gradient flow equation. We study the a-function for a general scalar theory in six dimensions, using the beta-functions up to three-loop order for both the MSbar and MOM schemes (the latter presented here for the first time at three loops).

hep-th↗
arXiv2015

Gradient flows in three dimensions

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite metric. We demonstrate the existence of a candidate a-function for renormalisable Chern-Simons theories in three dimensions, involving scalar and fermion fields, in both non-supersymmetric and supersymmetric cases.

hep-th↗
arXiv2015

Constraints on RG Flow for Four Dimensional Quantum Field Theories

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 $e^{2σ}$ to a form which involves running couplings $g_σ$ 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 $β$-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 $β\to B$, a modified $β$-function, and that the equations provide strong constraints on the detailed form of the three loop Yukawa $β$-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.

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arXiv2013

Superconformal Chern-Simons theories beyond leading order

We discuss higher-order corrections to superconformal invariance for a class of N=2 supersymmetric Chern-Simons theories including the ABJM model. We argue that corrections are inevitable for general theories in this class; but that it is probable that any corrections are of a particular "maximally transcendental" form.

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