All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory

Fröb, Markus B.; Holland, Jan; Hollands, Stefan

doi:10.1063/1.4967747

Cited by 16 publications

(61 citation statements)

References 82 publications

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“…Thus first we need a consistent combination of the Wilsonian RG and Batalin-Vilkovisky framework.This has been addressed in refs. [40][41][42][43][44][45][46][47][48], and adapted and applied especially to QED and Yang-Mills theory. 3 However as reviewed in sec.…”

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confidence: 99%

Quantum gravity, renormalizability and diffeomorphism invariance

Morris

2018

SciPost Phys.

156

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We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Around the Gaussian fixed point, RG properties of the conformal factor of the metric allow the construction of a Hilbert space L of renormalizable interactions, nonperturbative in , and involving arbitrarily high powers of the gravitational fluctuations. We show that diffeomorphism invariance is violated for interactions that lie inside L, in the sense that only a trivial quantum BRST cohomology exists for interactions at first order in the couplings.However by taking a limit to the boundary of L, the couplings can be constrained to recover Newton's constant, and standard realisations of diffeomorphism invariance, whilst retaining renormalizability. The limits are sufficiently flexible to allow this also at higher orders. This leaves open a number of questions that should find their answer at second order. We develop much of the framework that will allow these calculations to be performed.At the classical, and strictly local, level, this question is addressed by the well developed subject of BRST cohomology [18][19][20][21][22] (for reviews see [23][24][25]), exploiting properties of the Batalin-Vilkovisky antibracket formalism [26][27][28][29] to ask simultaneously for consistent deformations of linearised diffeomorphism invariance and local actions that would realise it, whilst automatically taking into account all local reparametrisations. Under rather broad assumptions the answer is unique:General Relativity is the only solution [22]. (For earlier alternative approaches, see refs. [30][31][32][33][34][35][36][37][38][39].)What we require however is the generalisation of this question to the quantum case, appropriately regularised in a way that respects the Wilsonian RG properties of the operators. Thus first we need a consistent combination of the Wilsonian RG and Batalin-Vilkovisky framework.This has been addressed in refs. [40][41][42][43][44][45][46][47][48], and adapted and applied especially to QED and Yang-Mills theory. 3 However as reviewed in sec. 2.5 these formulations have drawbacks, because they either leave the Batalin-Vilkovisky measure term ∆ [26,27] unregularised when acting on local functionals, or destroy the locality of the BRST (and Koszul-Tate) transformations. This in turn would imply that the quantum BRST algebra cannot close on local functionals. It would thus force us to work even at first order in the 'deformation parameter' κ, with expansions to infinite order in derivatives.In sec. 2.4, we show however that this is not inevitable. There exists a particularly natural formulation that solves these problems. As we explain in sec. 2.6, at first order in κ it results in a regularised ∆ (when acting on arbitrary local functionals), but leaves the rest of the BRST structure unmodified. It thus allows us to inves...

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confidence: 99%

Quantum gravity, renormalizability and diffeomorphism invariance

Morris

2018

SciPost Phys.

156

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“…In this paper we apply this approach to the regularization of a general renormalizable YM theory by the explicit UV momentum cutoff defined in section 3 (see [37][38][39][40][41][42][43] for partially related applications in the context of the Wilson-Polchinski renormalization group). Below we recall the general procedure based on the QAP and specify our way of fixing its arbitrariness (our renormalization conditions).…”

Section: Jhep11(2016)105mentioning

confidence: 99%

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

Chankowski

Lewandowski

Meissner

2016

J. High Energ. Phys.

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We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional MS scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the MS scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

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“…We proceed by integrating out the high energy degrees of freedom in YM theory down to some infrared cutoff Λ, obtaining the effective action Γ Λ . This calculation is performed with the aid of the renormalization group flow equations [7], for clarification see the comment below (46). Our calculation is performed in the Maximal Abelian Gauge (MAG) including, as usual, gauge fixing and ghost terms into the YM action.…”

Section: Introductionmentioning

confidence: 99%

The gluon condensate in an effective SU(2) Yang–Mills theory

Efremov

2019

Int. J. Mod. Phys. A

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We make progress towards a derivation of a low energy effective theory for SU (2) Yang-Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov-Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by L.D. Faddeev and A.J. Niemi. The resulting action describes a pair of non-linear O(3) and σ-models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the σ-model fields whose excitations correspond to glueball states.

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All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory

Cited by 16 publications

References 82 publications

Quantum gravity, renormalizability and diffeomorphism invariance

Quantum gravity, renormalizability and diffeomorphism invariance

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

The gluon condensate in an effective SU(2) Yang–Mills theory

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