Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions

In recent work, we derived the long distance confining dynamics of certain QCDlike gauge theories formulated on small S1 × R3 based on symmetries, an index theorem and abelian duality. Here, we give the microscopic derivation. The solution reveals a new mechanism of confinement in QCD(adj) in the regime where we have control over both perturbative and nonperturbative aspects. In particular, consider SU(2) QCD(adj) theory with 1 ≤ nf ≤ 4 Majorana fermions, a theory which undergoes gauge symmetry breaking at small S1. If the magnetic charge of the BPS monopole is normalized to unity, we show that confinement occurs due to condensation of objects with magnetic charge 2, not 1. Due to index theorems, we know that such an object cannot be a two identical monopole configuration. Its net topological charge must vanish, and hence it must be topologically indistinguishable from the perturbative vacuum. We construct such objects, the magnetically charged, topologically null molecules of a BPS monopole and KK antimonopole, which we refer as magnetic bions. An immediate puzzle with this proposal is the apparent Coulomb repulsion between BPS-KK pair. An attraction which overcomes the Coulomb repulsion between the two is induced by 2nf -fermion exchange. Bion condensation is also the mechanism of confinement in N = 1 SYM on the same four-manifold. The SU(N) generalization hints a possible hidden integrability behind nonsupersymmetric QCD of affine Toda type, and allows us to analytically compute the string tensions and thicknesses. We currently do not know the extension to R4.