UV asymptotics of 
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-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

Bochicchio, Marco; Papinutto, Mauro; Scardino, Francesco

doi:10.1103/physrevd.108.054023

Phys. Rev. D

2023

DOI: 10.1103/physrevd.108.054023

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UV asymptotics of n -point correlators of twist-2 operators in SU(N) Yang-Mills theory

Marco Bochicchio,

Mauro Papinutto,

Francesco Scardino

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2024

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Cited by 2 publications

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Topology of the large-N expansion in SU(N) Yang-Mills theory and spin-statistics theorem

Bochicchio,

Papinutto,

Scardino

2024

EPJ Web Conf.

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Recently, we computed the generating functional of Euclidean asymptotic correlators at short-distance of single-trace twist-2 operators in large-N SU(N) Yang-Mills (YM) theory to the leading-nonplanar order. Remarkably, it has the structure of the logarithm of a functional determinant, but with the sign opposite to the one arising from the spin-statistics theorem for the glueballs. To solve the sign puzzle, we reconsider the proof that in ’t Hooft large-N expansion of YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of n-punctured tori. We discover that for twist-2 operators it contains – in addition to the n-punctured tori – the normalization of tori with 1 ≤ p ≤ n pinches and n − p punctures. Once the existence of the new sector is taken into account, the violation of the spin-statistics theorem disappears. Besides, the new sector contributes trivially to the nonperturbative S matrix because – for example – the n-pinched torus represents nonperturbatively a loop of n glueball propagators with no external leg. This opens the way for an exact solution limited to the new sector that may be solvable thanks to the vanishing S matrix.

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Topology of the large-N expansion in SU(N) Yang-Mills theory and spin-statistics theorem

Bochicchio,

Papinutto,

Scardino

2024

EPJ Web Conf.

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Nonresonant renormalization scheme for twist-2 operators in SU(N) Yang–Mills theory

Scardino

2024

Eur. Phys. J. C

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Recently, the short-distance asymptotics of the generating functional of n-point correlators of twist-2 operators in SU(N) Yang–Mills (YM) theory has been worked out in Bochicchio et al. (Phys Rev D 108:054023, 2023). The above computation relies on a basis change of renormalized twist-2 operators, where $$-\gamma (g)/ \beta (g)$$ - γ ( g ) / β ( g ) reduces to $$\gamma _0/ (\beta _0\,g)$$ γ 0 / ( β 0 g ) to all orders of perturbation theory, with $$\gamma _0$$ γ 0 diagonal, $$\gamma (g) = \gamma _0 g^2+\cdots $$ γ ( g ) = γ 0 g 2 + ⋯ the anomalous-dimension matrix and $$\beta (g) = -\beta _0 g^3+\cdots $$ β ( g ) = - β 0 g 3 + ⋯ the beta function. The construction is based on a novel geometric interpretation of operator mixing (Bochicchio in Eur Phys J C 81:749, 2021), under the assumption that the eigenvalues of the matrix $$\gamma _0/ \beta _0$$ γ 0 / β 0 satisfy the nonresonant condition $$\lambda _i-\lambda _j\ne 2k$$ λ i - λ j ≠ 2 k , with $$\lambda _i$$ λ i in nonincreasing order and $$k\in {\mathbb {N}}^+$$ k ∈ N + . The nonresonant condition has been numerically verified up to $$i,j=10^4$$ i , j = 10 4 in Bochicchio et al. (Phys Rev D 108:054023, 2023). In the present paper we provide a number theoretic proof of the nonresonant condition for twist-2 operators essentially based on the classic result that Harmonic numbers are not integers. Our proof in YM theory can be extended with minor modifications to twist-2 operators in $$\mathcal {N}=1$$ N = 1 SUSY YM theory, large-N QCD with massless quarks and massless QCD-like theories.

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UV asymptotics of n -point correlators of twist-2 operators in SU(N) Yang-Mills theory

Cited by 2 publications

References 16 publications

Topology of the large-N expansion in SU(N) Yang-Mills theory and spin-statistics theorem

Topology of the large-N expansion in SU(N) Yang-Mills theory and spin-statistics theorem

Nonresonant renormalization scheme for twist-2 operators in SU(N) Yang–Mills theory

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