Magnetic Bion Condensation: A New Mechanism ofConfinement and Mass Gap in Four Dimensions Page: 2 of 32
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1. Introduction 1
2. Dynamics of SU(2) QCD(adj) on small S1 x R3 5
2.1 Perturbation theory 5
2.2 Nonperturbative effects and abelian duality 7
2.3 Pairings and attractive multi-fermion exchanges 10
2.4 Noncompact Higgs with adjoint fermions on R3, and the lack of confinement 12
2.5 Magnetic bions in A = 1 SYM on small S' x 1R3 13
2.6 The A = 2 SYM on 1R3 and lack of confinement, again 15
3. SU(N) QCD(adj), bions, and secret integrability? 15
3.1 Attractive channels, bions, and a prepotential 18
3.2 The vacuum structure of QCD(adj) 20
3.2.1 Mass gap in the gauge sector 21
3.2.2 Area law of confinement and monodromy 22
3.2.3 Chiral symmetry realizations 25
3.3 Noncompact versus compact adjoint Higgs, final pass 27
4. Outlook: Confinement, and more on its persona and anima 28
Probably, the most robust and important experimental and phenomenological observation
about SU(3) QCD is confinement, i.e., the absence of the free colored particles in isolation.
Numerical lattice simulations unambiguously establish confinement in pure Yang-Mills theory
and QCD. However, to date the analytical success had been limited. For reviews, see [1-3]
The QCD of Nature belongs to a subclass of asymptotically free and confining vector-
like(QCD-like) gauge theories with no elementary scalars. This is a sufficiently good reason
to warrant the study of the dynamics of such four dimensional QCD-like theories. In the last
two decades, most theoretical efforts is concentrated into the dynamics of supersymmetric
theories. It would be fair to say that despite many remarkable results obtained in such
theories, its benefit to the QCD-like theories is still in its infancy. There is a very good
reason for this. On R4, there only exist one QCD-like supersymmetric theory, the pure
= 1 SYM. All other supersymmetric theories have scalars, and hence non QCD-like by
definition. In regimes where such theories are solved or understood quantitatively, such as
mass deformation of A = 2 SYM down to A = 1 , the scalars never decouples from the
dynamics. If they are forced to decouple by tuning certain parameters, one usually looses the
theoretical control over the theory .
Our goal in this paper is more direct and motivated by the following question:
Here’s what’s next.
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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/m1/2/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.