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

By M. Unsal. 2007

167 citations recorded by the source corpus.

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. Because of 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 non-self-dual topological excitations, the magnetically charged, topologically null molecules of a BPS monopole and KK antimonopole, which we refer to as magnetic bions. An immediate puzzle with this proposal is the apparent Coulomb repulsion between the 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 mass gap in the gauge sector. We currently do not know the extension to R4.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3dafca6fc18846f7d007e8b1e7f3ed9ff9fdbfad

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In Nuclear and High Energy Physics

1. G. Dunne
2. Daniele Dorigoni
3. M. Unsal
4. A. Cherman
5. P. Argyres
6. E. Poppitz
7. T. Schäfer
8. Yuji Tachikawa

In Statistical and Nonlinear Physics

1. Daniele Dorigoni
2. A. Cherman
3. P. Argyres
4. G. Dunne
5. M. Unsal
6. E. Poppitz

Citations in the corpus

• Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “The mechanism of pairing in CPN−1 with Nf ≥ 1 is the same as in QCD(adj) with Nf ≥ 1 [9], as well as quantum mechanics with fermions [25]; and for Nf = 0, the deformed bosonic CPN−1 , the pairing takes place in the same way as in deformed YM [85], as well as bosonic quantum mechanics [19].”
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, background): “3.1 Perturbation theory on R2 and IR-renormalons 22”
• Continuity, deconfinement, and (super) Yang-Mills theory (2012, background): “[13, 14], in general gauge theories with massless adjoint fermions (i.”
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, methodology): “For example, in QCD(adj) it is not the neutral [BijBji] molecule (which is the realization of the IR renormalon in the semi-classical domain), but the proliferation of their constituent magnetic bions, Bij, which leads to quark confinement [3].”