Paper detail

Yang-Mills mass gap, Floer homology, glueball spectrum, and conformal window in large-N QCD

Morse-Smale-Floer homology associates the critical points of the action functional of a classical field theory over a manifold to its homology. We associate to the intersection homology of certain Lagrangian submanifolds of R^4 the critical points of a quantum effective action of large-N SU(N) YM. For this purpose we construct in YM a trivial Topological Field Theory defined by twistor Wilson loops whose v.e.v. is 1 in the large-N limit for any shape of the loops supported on certain punctured Lagrangian submanifolds. We derive a new holomorphic loop equation for the twistor Wilson loops, that involves the change of variables in the YM functional integral from the connection to the anti-selfdual part of the curvature and the choice of a holomorphic gauge. Employing the holomorphic loop equation, and viewing Floer homology the other way around, we associate to arcs asymptotic in both directions to the cusps of the Lagrangian submanifolds the critical points of an effective action, that turn out to be surface operators of Z(N) holonomy. At the next-to-leading 1/N order a certain correlator of surface operators is non-topological and non-trivial, controls the mass gap of YM theory, and is saturated by an infinite sum of pure poles of scalar and pseudoscalar glueballs with positive charge conjugation. It satisfies asymptotically for large momentum fundamental universal constraints arising from the asymptotic freedom and the renormalization group. We predict at large-N the ratio of the masses of the two lower-mass scalar glueballs r=\sqrt 2=1.414, to be compared with the measure in lattice SU(8) YM by Meyer-Teper r=1.42(11), and with the value implied by PDG(2014) r=1.397(008). The construction extends to massless Veneziano large-N limit of QCD, for which we determine the lower edge of the conformal window N_f/N=5/2 and the corresponding quark-mass anomalous dimension gamma=-4/5.