Magnetic Bion Condensation: A New Mechanism ofConfinement and Mass Gap in Four Dimensions Page: 1 of 32
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Preprint typeset in JHEP style - HYPER VERSION SLAC-PUB-12825
Magnetic bion condensation: A new mechanism of
confinement and mass gap in four dimensions
1 SLAC, Stanford University, Menlo Park, CA 94025
Physics Department, Stanford University, Stanford, CA, 94305
ABSTRACT: In recent work, we derived the long distance confining dynamics of certain QCD-
like gauge theories formulated on small S1 x 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 per-
turbative and nonperturbative aspects. In particular, consider SU(2) QCD(adj) theory with
1 < f < 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 con-
finement 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 inte-
grability 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.
KEYWORDS: Nonperturbative QCD, Duality.
Submitted to Physical Review D
Work supported in part by US Department of Energy contract DE-AC02-76SF00515
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Unsal, Mithat & /SLAC /Stanford U., Phys. Dept. Magnetic Bion Condensation: A New Mechanism ofConfinement and Mass Gap in Four Dimensions, article, September 25, 2007; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc884887/m1/1/: accessed April 26, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.