Download PDF - Vacuum Structure of 2+1-Dimensional Gauge TheoriesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Vacuum Structure of 2+1-Dimensional Gauge Theories

Authors 1, 1, 1, 1

Affiliations

  1. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Abstract

We analyse some non-perturbative properties of the Yang-Mills vacuum in two-dimensional spaces in the presence of Chern-Simons interactions. We show that the vacuum functional vanishes for some gauge field configurations. We have identified some of those nodal configurations which are characterized by the property of carrying a non-trivial magnetic charge. In abelian gauge theories this fact explains why magnetic monopoles are suppressed by Chern-Simons interactions. In non-abelian theories it suggests a relevant role for nodal gauge field configurations in the confinement mechanism of Yang-Mills theories. In topological Chern-Simons theories nodal configurations belong to Atiyah-Bott strata with non-null codimension in the space of gauge field configurations. In the presence of external static quarks some nodes of the vacuum functional with non-trivial magnetic charge are removed and they are responsible for the increase of vacuum energy.

Bibliography

  1. I. Affleck, J. Harvey, L. Palla, G. W. Semenoff, The Chern-Simons Term Versus the Monopole, Nuclear Phys. B 328 (1989), 575-584.
  2. M. Asorey, Spin and Statistics in Topologically Massive Theories, Phys. Lett. B 174 (1986), 199-202.
  3. M. Asorey, Topological Effects in Yang-Mills Theory in 2+1 Dimensions, in: Fields and Geometry, Ed. A. Jadczyk, World Scientific, Singapore, 1986, 31-47.
  4. M. Asorey, Topological Phases of Quantum Theories. Chern-Simons Theory, J. Geom. Phys. 11 (1993), 63-94.
  5. M. Asorey, S. Carlip, F. Falceto, Chern-Simons States and Topologically Massive Gauge Theories, Phys. Lett. B 312 (1993) 477-485.
  6. M. Asorey, F. Falceto, J. L. Lopez, G. Luzon, Nodes, Monopoles and Confinement in 2+1-Dimensional Gauge Theories, Phys. Lett. B 349 (1995), 125-130.
  7. M. Asorey, P. K. Mitter, Cohomology of the Yang-Mills Gauge Orbit Space and Dimensional Reduction, Ann. Inst. H. Poincaré Phys. Théor. 45 (1986), 61-78.
  8. M. Asorey, P. K. Mitter, Cohomology of the Gauge Orbit Space and 2+1-Dimensional Yang-Mills Theory with Chern-Simons Term, Phys. Lett. B 153 (1985), 147-152.
  9. M. Atiyah, R. Bott, The Yang-Mills Equations over Riemann Surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1982), 523-615.
  10. V. L. Berezinskii, Destruction of Long-Range Order in One-Dimensional and Two-Dimensional Systems Having a Continuous Symmetry Group. I: Classical Systems, Zh. Eksper. Teoret. Fiz. 59 (1970), 907-920 (in Russian); translated as Soviet Physics JETP 32 (1971), 493-500.
  11. M. Bos, V. P. Nair, U(1) Chern-Simons and c=1 Conformal Blocks, Phys. Lett. B 223 (1989), 61-66.
  12. M. Bos, V. P. Nair, Coherent State Quantization of Chern-Simons Theory, Internat. J. Modern Phys. A 5 (1990), 959-988.
  13. M. Crescimanno, S. A. Hotes, Monopoles, Modular Invariance and Chern-Simons Theory, Nuclear Phys. B 372 (1992), 683-700.
  14. S. Deser, R. Jackiw, S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48 (1982), 975-978.
  15. S. Deser, R. Jackiw, S. Templeton, Topologically Massive Gauge Theories, Ann. Physics 140 (1982), 372-411.
  16. M. C. Diamantini, P. Sodano, C. A. Trugenberger, Topological Excitations In Compact Maxwell-Chern-Simons Theory, Phys. Rev. Lett. 71 (1993), 1969-1972.
  17. F. Falceto, K. Gawędzki, Chern-Simons States at Genus One, Comm. Math. Phys. 159 (1994), 549-579.
  18. R. Feynman, The Qualitative Behavior of Yang-Mills Theory in (2+1)-Dimensions, Nuclear Phys. B 188 (1981), 479-512.
  19. K. Gawędzki, A. Kupiainen, SU(2) Chern-Simons Theory at Genus Zero, Comm. Math. Phys. 135 (1991), 531-546.
  20. G.'t Hooft, Gauge Theories with Unified Weak, Electromagnetic and Strong Interactions, High Energy Physics, Ed. A. Zichichi, Ed. Compositori, Bologna, 1976.
  21. G.'t Hooft, Topology of the Gauge Condition and new Confinement Phases in non-Abelian Gauge Theories, Nuclear Phys. B 190 [FS3] (1981), 455-478.
  22. R. Jackiw, Gauge Theories in Three Dimensions (= at High Temperature), in: Gauge Theories of the Eighties, Eds. E. Ratio, J. Lindfords, Lecture Notes in Physics 181, Springer, 1983, 157-219.
  23. A. Kupiainen, J. Mickelsson, What is the Effective Action in Two Dimensions?, Phys. Lett. B 185 (1987), 107-110.
  24. S. Mandelstam, Vortices and Quark Confinement in on-Abelian Gauge Theories, Phys. Rep. 23 (1976), 245-249.
  25. S. Mandelstam, General Introduction to Confinement, Phys. Rep. 67 (1980), 109-121.
  26. A. Polyakov, Compact Gauge Fields and the Infrared Catastrophe, Phys. Lett. B 59 (1975), 82-84.
  27. A. Polyakov, Quark Confinement and Topology of Gauge Groups, Nuclear Phys. 120 (1977), 429-458.
  28. A. P. Polychronakos, On the Quantization of the Coefficient of the Abelian Chern-Simons Term, Phys. Lett. B 241 (1990), 37-40.
  29. A. P. Polychronakos, Abelian Chern-Simons Theories and Conformal Blocks, preprint UFIFT-89-9 (1989).
  30. N. Seiberg, E. Witten, Electro-Magnetic Duality, Monopole Condensation, and Confinement in N=2 Supersymmetric Yang-Mills Theory, Nuclear Phys. B 426 (1994), 19-52; Erratum: ibid. 430 (1994), 485-486.
Banach Center Publications
1997/39/1
Export to PBN, Opens in new tab
Pages:
183-199
Main language of publication
English
Published
1997
Exact and natural sciences