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

¹ Physics Department, INFN Roma1, Piazzale A. Moro 2, Roma, I-00185, Italy
² Physics Department, “Sapienza” University of Rome and INFN Roma1, Piazzale Aldo Moro 2, I-00185 Roma, Italy

^* e-mail: marco.bochicchio@roma1.infn.it
^** e-mail: mauro.papinutto@roma1.infn.it
^*** e-mail: francesco.scardino@roma1.infn.it

Published online: 10 December 2024

Abstract

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.