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• W4386829049 abstract "The generating functional ${mathcal{W}}^{E}[{J}_{mathcal{O}}]$ of Euclidean correlators of twist-2 operators in $mathrm{SU}(N)$ Yang-Mills theory admits the 't Hooft large-$N$ expansion: ${mathcal{W}}^{E}[{J}_{mathcal{O}}]={mathcal{W}}_{text{sphere}}^{E}[{J}_{mathcal{O}}]+{mathcal{W}}_{text{torus}}^{E}[{J}_{mathcal{O}}]+ensuremath{cdots}$. Nonperturbatively, ${mathcal{W}}_{text{sphere}}^{E}[{J}_{mathcal{O}}]$ is a sum of tree diagrams involving glueball propagators and vertices, while ${mathcal{W}}_{text{torus}}^{E}[{J}_{mathcal{O}}]$ is a sum of glueball one-loop diagrams. Moreover, it has been predicted that ${mathcal{W}}_{text{torus}}^{E}[{J}_{mathcal{O}}]$ should admit the structure of the logarithm of a functional determinant summing glueball one-loop diagrams. We work out in a closed form the ultraviolet (UV) asymptotics of ${mathcal{W}}_{text{sphere}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]ensuremath{sim}{mathcal{W}}_{text{asym sphere}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]$ and ${mathcal{W}}_{text{torus}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]ensuremath{sim}{mathcal{W}}_{text{asym torus}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]$ in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor $ensuremath{lambda}ensuremath{rightarrow}0$. The calculation is performed in two steps. First, extending our previous work, we compute---directly from its functional-integral definition as a Gaussian integral---the generating functional of the conformal correlators ${mathcal{W}}_{mathrm{conf}}[{J}_{mathcal{O}}]={mathcal{W}}_{text{conf sphere}}[{J}_{mathcal{O}}]+{mathcal{W}}_{text{conf torus}}[{J}_{mathcal{O}}]$ to the lowest perturbative order of all the twist-2 operators with maximal spin along the ${p}_{+}$ direction, in both Minkowskian and---by analytical continuation---Euclidean spacetimes. Thus, we provide a purely perturbative explanation as to why ${mathcal{W}}_{mathrm{conf}}[{J}_{mathcal{O}}]$ has the structure of the logarithm of a functional determinant. Second, by means of a careful choice of the renormalization scheme that reduces the mixing of the above operators to the multiplicatively renormalizable case to all orders of perturbation theory, we lift the generating functional of the Euclidean conformal correlators ${mathcal{W}}_{mathrm{conf}}^{E}[{J}_{mathcal{O}}]$ to the generating functional of the renormalization-group improved correlators ${mathcal{W}}_{mathrm{asym}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]={mathcal{W}}_{text{asym sphere}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]+{mathcal{W}}_{text{asym torus}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]$ that inherits the very same structure of the logarithm of a functional determinant. Remarkably, we verify the above prediction that ${mathcal{W}}_{text{asym torus}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]$---being asymptotic in the UV to ${mathcal{W}}_{text{torus}}^{E}[{J}_{mathcal{O}},ensuremath{lambda}]$---admits the structure of the logarithm of a functional determinant as well. Hence, the computation above sets strong UV asymptotic constraints on the nonperturbative solution of large-$N$ Yang-Mills theory, and it may be a pivotal guide for the search of such a solution." @default.
• W4386829049 created "2023-09-19" @default.
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• W4386829049 date "2023-09-18" @default.
• W4386829049 modified "2023-09-26" @default.
• W4386829049 title "UV asymptotics of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>n</mml:mi></mml:math> -point correlators of twist-2 operators in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>SU</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:math> Yang-Mills theory" @default.
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• W4386829049 doi "https://doi.org/10.1103/physrevd.108.054023" @default.
• W4386829049 hasPublicationYear "2023" @default.
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