Revisiting the Okubo–Marshak Argument

Modular localization and the theory of string-localized fields have revolutionized several key aspects of quantum field theory. They reinforce the contention that local symmetry emerges directly from quantum theory, but global gauge invariance remains in general an unwarranted assumption to be examined case by case. Armed with those modern tools, we reconsider here the classical Okubo–Marshak argument on the non-existence of a “strong CP problem” in quantum chromodynamics.

Some comments on 6d global gauge anomalies

Global gauge anomalies in 6d associated with non-trivial homotopy groups π6(G) for G = SU(2), SU(3), and G2 were computed and utilized in the past. In the modern bordism point of view of anomalies, however, they come from the bordism groups Ω7spin (BG), which are in fact trivial and therefore preclude their existence. Instead, it was noticed that a proper treatment of the 6d Green-Schwarz mechanism reproduces the same anomaly cancellation conditions derived from π6(G). In this paper, we revisit and clarify the relation between these two different approaches.

A matrix model for QCD

Gribov's observation that global gauge fixing is impossible has led to suggestions that there may be a deep connection between gauge fixing and confinement. We find an unexpected relation between the topological nontriviality of the gauge bundle and colored states in SU (N) Yang–Mills theory, and show that such states are necessarily impure. We approximate QCD by a rectangular matrix model that captures the essential topological features of the gauge bundle, and demonstrate the impure nature of colored states explicitly. Our matrix model also allows the inclusion of the QCD θ-term, as well as to perform explicit computations of low-lying glueball masses. This mass spectrum is gapped. Since an impure state cannot evolve to a pure one by a unitary transformation, our result shows that the solution to the confinement problem in pure QCD is fundamentally quantum information-theoretic.