On the structure of the large-N expansion in SU(N) Yang-Mills theory

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 $1\le p\le n$ 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.