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References
The suggestion that confinement of quarks can be understood as dual superconductivity was made by Y. Nambu, in Phys. Rep. 23, 250 (1976). This was developed by G.’ t Hooft, Nucl. Phys. B138, 1 (1978); ibid. B153, 141 (1979); S. Mandelstam, Phys. Lett. B53, 476 (1975); Phys. Rev. D19, 2391 (1979).
The Wilson loop and the area law are due to K.G. Wilson, Phys. Rev. D14, 2455 (1974).
For topological vortices, see A.A. Abrikosov, Sov. Phys. JETP 5, 1174 (1957); H.B. Nielsen and P. Olesen, Nucl. Phys. B61, 45 (1973).
The T (C’) operators and their algebra are in’ t Hooft’s papers, reference 1.
Magnetic monopoles in nonabelian gauge theory were obtained by G. ’t Hooft, Nucl. Phys. B79, 276 (1974); A.M. Polyakov, JETP Lett. 20, 194 (1974). This subject has developed enormously; some general results are in Monopoles in Quantum Field Theory, Proceedings of the Monopole Meeting, Trieste, P. Goddard. W. Nahm and N.S. Craigie (eds.), World Scientific Pub. Co. (1982); A. Jaffe and C. Taubes, Vortices and Monopoles, Birkhauser (1980).
For the \(\mathcal{N}\) = 2 supersymmetric gauge theory, it is possible to give an exact analysis of the vacuum structure; see N. Seiberg and E. Witten, Nucl. Phys. B426, 19 (1994). This has led to a number of new developments; for a recent review, see M. Strassler, in Trieste 2001: Superstrings and Related Matters, Abdus Salam ICTP, Trieste (2001).
The 1/N expansion for gauge theories was introduced by G. ’t Hooft, Nucl. Phys. B72, 461 (1974); ibid. B75, 461 (1974).
The large N argument for chiral symmetry breaking is from S. Coleman and E. Witten, Phys. Rev. Lett. 45, 100 (1980).
Anomaly matching conditions are given in G. ’t Hooft, Cargèse Lectures, 1979, reprinted in G.’ t Hooft, Under the Spell of the Gauge Principle, World Scientific Pub. Co. (1994). In this context, see also S. Coleman and B. Grossman, Nucl. Phys. B203, 205 (1982).
The Vafa-Witten theorem is in C. Vafa and E. Witten, Phys. Rev. Lett. 53, 535 (1984); Nucl. Phys. B234, 173 (1984); Commun. Math. Phys. 95, 257 (1984).
The suppression of glueball and meson decays, and baryons as solitons at large N, are shown in E. Witten, Nucl. Phys. B160, 57 (1979).
General references on older work on skyrmions are: T.H.R. Skyrme, Proc. Roy. Soc. A260, 127 (1961); Nucl. Phys. 31, 556 (1962); J. Math. Phys. 12, 1735 (1970); J.G. Williams, J. Math. Phys. 11, 2611 (1970); N.K. Pak and H.Ch. Tze, Ann. Phys. 117, 164 (1979).
The computation of the baryon number is from A.P. Balachandran, V.P. Nair, S.G. Rajeev and A. Stern, Phys. Rev. Lett. 49, 1124 (1982); Phys. Rev. D27, 1153 (1983).
The analysis of the spin and flavor of skyrmions, as well as the proof of their fermionic nature, are due to E. Witten, Nucl. Phys. B223, 422, 433 (1983). See also G. Adkins, C. Nappi and E. Witten, Nucl. Phys. B228, 552 (1983). Our analysis follows A.P. Balachandran, F. Lizzi, V.G.J. Rodgers and A. Stern, Nucl. Phys. B256, 525 (1985).
For reviews on the soliton approach to baryons, see I. Zahed and G.E. Brown, Phys. Rep. 142, 1 (1986); A.P. Balachandran, Classical Topology and Quantum States, World Scientific Pub. Co. (1991).
For further study of lattice gauge theory, the following books are useful: M. Creutz, Quarks, Gluons and Lattices, Cambridge University Press (1985); C. Itzykson and J-M. Drouffe, Statistical Field Theory, volumes 1 and 2, Cambridge University Press (1991); H.J. Rothe, Lattice Gauge Theories: An Introduction, World Scientific Pub. Co. (1998).
The theorem on fermion doubling is due to H.B. Nielsen and M. Ninomiya, Nucl. Phys. B185, 20 (1981); Erratum ibid. B195, 541 (1982); ibid. B193, 173 (1981); Phys. Lett. B105, 219 (1981). For a recent review which discusses new directions, such as the domain wall approach of D. Kaplan and the overlap formalism of H. Neuberger and R. Narayanan for chiral fermions on the lattice, see M. Creutz, Rev. Mod. Phys. 73, 119 (2001).
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(2005). Gauge theory: Nonperturbative questions. In: Quantum Field Theory. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/0-387-25098-0_19
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