On the structure of the large-N expansion in SU(N) Yang-Mills theory
Year: 2025
Type: article
Abstract: Recently, we have computed the short-distance asymptotics of the generating functional of Euclidean correlators of single-trace twist-2 operators in the large- N expansion of 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 that would follow from the spin-statistics theorem for the glueballs. In order to solve this sign puzzle, we have reconsidered the proof in the literature that in the 't Hooft topological expansion of large- N YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of n -punctured tori. We have discovered 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. Moreover, 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.
Source: Nuclear Physics B
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408979425