Skip to main content
Log in

Abstract.

Topological excitations are prominent candidates for explaining nonperturbative effects in QCD like confinement. In these lectures, I cover both formal treatments and applications of topological objects. The typical phenomena like BPS bounds, topology, the semiclassical approximation and chiral fermions are introduced by virtue of kinks. Then I proceed in higher dimensions with magnetic monopoles and instantons and special emphasis on calorons. Analytical aspects are discussed and an overview over models based on these objects as well as lattice results is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • F. Bruckmann, E.-M. Ilgenfritz, B.V. Martemyanov, P. van Baal, Phys. Rev. D 70, 105013 (2004) [hep-lat/0408004]

  • R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam, 1982)

  • R. Jackiw, C. Rebbi, Phys. Rev. D 13, 3398 (1976)

    Google Scholar 

  • R. Bott, R. Seeley, Commun. Math. Phys. 62, 235 (1978)

    Google Scholar 

  • G.H. Derrick, J. Math. Phys. 5, 1252 (1964)

    Google Scholar 

  • G. 't Hooft, Nucl. Phys. B 79, 276 (1974)

    Google Scholar 

  • A.M. Polyakov, Sov. Phys. JETP Lett. 20, 194 (1974)

  • E.B. Bogomol'nyi, Sov. J. Nucl. Phys. 24, 449 (1976)

  • M.K. Prasad, C.M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975)

    Google Scholar 

  • K. Uhlenbeck, Bull. Amer. Math. Soc. 1, 579 (1978)

    Google Scholar 

  • A.A. Belavin, A.M. Polyakov, A.S. Schwartz, Yu.S. Tyupkin, Phys. Lett. B 59, 85 (1975)

    Google Scholar 

  • G. 't Hooft (1976) (unpublished)

  • E. Corrigan, D.B. Fairlie, Phys. Lett. B 67, 69 (1977)

    Google Scholar 

  • F. Wilczek, in Quark Confinement and Field Theory, edited by D. Stamp, D. Weingarten (Wiley, New York, 1977)

  • M.F. Atiyah, I.M. Singer, Ann. Math. 93, 119 (1971)

    Google Scholar 

  • M.F. Atiyah, A.V. Patodi, I. Singer, Math. Proc. Cambridge Phil. Soc. 79, 71 (1980)

    Google Scholar 

  • W. Nahm, Phys. Lett. B 90, 413 (1980)

    Google Scholar 

  • P.J. Braam, P. van Baal, Commun. Math. Phys. 122, 267 (1989)

    Google Scholar 

  • M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, Y.A. Manin, Phys. Lett. A 65, 185 (1978)

    Google Scholar 

  • N.H. Christ, E.J. Weinberg, N.K. Stanton, Phys. Rev. D 18, 2013 (1978)

  • M. Jardim, Commun. Math. Phys. 216, 1 (2001) [math.dg/9909069]

  • C. Ford, J.M. Pawlowski, Phys. Lett. B 540, 153 (2002) [hep-th/0205116]

  • P. van Baal, Nucl. Phys. Proc. Suppl. 49, 238 (1996) [hep-th/9512223]

  • B.J. Harrington, H.K. Shepard, Phys. Rev. D 17, 2122 (1978)

    Google Scholar 

  • P. Rossi, Nucl. Phys. B 149, 170 (1979)

    Google Scholar 

  • T.C. Kraan, P. van Baal, Nucl. Phys. B 533, 627 (1998) [hep-th/9805168]

  • K. Lee, C. Lu, Phys. Rev. D 58, 025011 (1998) [hep-th/9802108]

  • F. Bruckmann, P. van Baal, Nucl. Phys. B 645, 105 (2002) [hep-th/0209010]

  • F. Bruckmann, D. Nogradi, P. van Baal, Nucl. Phys. B 698, 233 (2004) [hep-th/0404210]

  • F. Bruckmann, D. Nogradi, P. van Baal, Acta Phys. Polon. B 34, 5717 (2003) [hep-th/0309008]

  • A.A. Belavin, V.A. Fateev, A.S. Schwarz, Yu.S. Tyupkin, Phys. Lett. B 83, 317 (1979)

    Google Scholar 

  • C. Ford et al., Ann. Phys. 269, 26 (1998) [hep-th/9802191]

  • H. Reinhardt, Nucl. Phys. B 503, 505 (1997) [hep-th/9702049]

  • O. Jahn, F. Lenz, Phys. Rev. D 58, 085006 (1998) [hep-th/9803177]

  • P. Forgacs, Z. Horvath, L. Palla, Nucl. Phys. B 192, 141 (1981)

    Google Scholar 

  • T.M. Nye, M.A. Singer, J. Funct. Anal. 177, 203 (2000) [math.dg/0009144]

  • M. Garcia Perez, A. Gonzalez-Arroyo, C. Pena, P. van Baal, Phys. Rev. D 60, 031901 (1999) [hep-th/9905016]

  • F. Bruckmann, D. Nogradi, P. van Baal, Nucl. Phys. B 666, 197 (2003) [hep-th/0305063]

  • C. Callias, Commun. Math. Phys. 62, 213 (1978)

    Google Scholar 

  • F. Bruckmann, Phys. Rev. D 71, 101701 (2005) [hep-th/0411252]

  • J. Greensite, Eur. Phys. J. Special Topics 140, 1 (2007)

    Google Scholar 

  • T. Banks, A. Casher, Nucl. Phys. B 169, 103 (1980)

    Google Scholar 

  • T. Schäfer, E.V. Shuryak, Rev. Mod. Phys. 70, 323 (1998) [hep-ph/9610451]

  • G. 't Hooft [hep-th/0010225]

  • D. Diakonov, Prog. Part. Nucl. Phys. 51 (2002) [hep-ph/0212026]

  • G. 't Hooft, Phys. Rev. D 14, 3432 (1976)

    Google Scholar 

  • E.-M. Ilgenfritz, M. Müller-Preußker, Nucl. Phys. B 184, 443 (1981)

    Google Scholar 

  • G. Münster, Zeit. Phys. C 12, 43 (1982)

    Google Scholar 

  • D. Diakonov, V.Y. Petrov, Nucl. Phys. B 245, 259 (1984)

    Google Scholar 

  • E.V. Shuryak, Nucl. Phys. B 203, 93 (1982)

    Google Scholar 

  • D. Diakonov, V. Petrov, in Nonperturbative Approaches to Quantum Chromodynamics (Trento, 1995), p. 239

  • A. Gonzalez-Arroyo, A. Montero, Phys. Lett. B 387, 823 (1996) [hep-th/9604017]

  • J. Negele, F. Lenz, M. Thies, Nucl. Phys. Proc. Suppl. 140, 629 (2005) [hep-lat/0409083]

  • E. Witten, Nucl. Phys. B 156, 269 (1979)

    Google Scholar 

  • G. Veneziano, Nucl. Phys. B 159, 213 (1979)

    Google Scholar 

  • N.M. Davies, T.J. Hollowood, V.V. Khoze, M.P. Mattis, Nucl. Phys. B 559, 123 (1999) [hep-th/9905015]

  • D. Diakonov, V. Petrov, Phys. Rev. D 67, 105007 (2003)

    Google Scholar 

  • D. Diakonov, N. Gromov, V. Petrov, S. Slizovskiy, Phys. Rev. D 70, 036003 (2004) [hep-th/0404042]

  • P. Gerhold, E.M. Ilgenfritz, M. Müller-Preußker, Nucl. Phys. B 760, 1 (2007) [hep-ph/0607315]

  • Y. Nambu, Phys. Rev. D 10, 4262 (1974)

    Google Scholar 

  • G. Parisi, Phys. Rev. D 11, 970 (1975)

    Google Scholar 

  • S. Mandelstam, Phys. Rep. C 23, 245 (1976)

    Google Scholar 

  • G. 't Hooft, in High Energy Physics, Proceedings of the EPS International Conference, Palermo 1975, edited by A. Zichichi (Editrice Compositori, Bologna, 1976)

  • G. 't Hooft, Nucl. Phys. B 190, 455 (1981)

    Google Scholar 

  • A.J. van der Sijs, Nucl. Phys. B: Proc. Suppl. 53, 535 (1997) [hep-lat/9608041]

  • O. Jahn, J. Phys. A 33, 2997 (2000) [hep-th/9909004]

  • F. Bruckmann, Monopoles from Instantons, in Confinement, Topology, and Other Non-Perturbative Aspects of QCD (2002) [hep-th/0204241]

  • A. Hart, M. Teper, Phys. Lett. B 371, 261 (1996) [hep-lat/9511016]

  • R. Brower, K. Orginos, C.I. Tan, Phys. Rev. D 55, 6313 (1997) [hep-th/9610101]

  • T.A. DeGrand, D. Toussaint, Phys. Rev. D 22, 2478 (1980)

    Google Scholar 

  • A.S. Kronfeld, M.L. Laursen, G. Schierholz, U.J. Wiese, Phys. Lett. B 198, 516 (1987)

    Google Scholar 

  • T. Suzuki, I. Yotsuyanagi, Phys. Rev. D 42, 4257 (1990)

    Google Scholar 

  • J.D. Stack, S.D. Neiman, R.J. Wensley, Phys. Rev. D 50, 3399 (1994) [hep-lat/9404014]

  • B. Berg, Phys. Lett. B 104, 475 (1981)

    Google Scholar 

  • J. Hoek, M. Teper, J. Waterhouse, Nucl. Phys. B 288, 589 (1987)

    Google Scholar 

  • E.-M. Ilgenfritz et al., Nucl. Phys. B 268, 693 (1986)

  • T. DeGrand, A. Hasenfratz, T.G. Kovacs, Nucl. Phys. B 520, 301 (1998) [hep-lat/9711032]

  • Y. Iwasaki, T.T. Yoshie, Phys. Lett. B 131, 159 (1983)

    Google Scholar 

  • M. Garcia Perez, A. Gonzalez-Arroyo, J. Snippe, P. van Baal, Nucl. Phys. B 413, 535 (1994) [hep-lat/9309009]

  • C. Gattringer, S. Schaefer, Nucl. Phys. B 654, 30 (2003) [hep-lat/0212029]

  • C. Aubin et al. (MILC), Nucl. Phys. Proc. Suppl. 140, 626 (2005) [hep-lat/0410024]

  • F.V. Gubarev, S.M. Morozov, M.I. Polikarpov, V.I. Zakharov, JETP Lett. 82, 343 (2005) [hep-lat/0505016]

  • P. de Forcrand, AIP Conf. Proc. 892, 29 (2007) [hep-lat/0611034]

  • F. Niedermayer, Nucl. Phys. Proc. Suppl. 73, 105 (1999) [hep-lat/9810026]

  • I. Horvath et al., Phys. Rev. D 68, 114505 (2003) [hep-lat/0302009]

  • E.-M. Ilgenfritz et al., Phys. Rev. D [arXiv:hep-lat/0705.0018] (to be published)

  • F. Bruckmann, E.-M. Ilgenfritz, Phys. Rev. D 72, 114502 (2005) [hep-lat/0509020]

  • C. Gattringer, Phys. Rev. Lett. 97, 032003 (2006) [hep-lat/0605018]

  • F. Bruckmann, C. Gattringer, C. Hagen, Phys. Lett. B 647, 56 (2007) [hep-lat/0612020]

  • F. Synatschke, A. Wipf, C. Wozar, Phys. Rev. D 75, 114003 (2007) [hep-lat/0703018]

  • F. Bruckmann et al., Eur. Phys. J. A [hep-lat/0612024] (to be published)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F. Bruckmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruckmann, F. Topological objects in QCD. Eur. Phys. J. Spec. Top. 152, 61–88 (2007). https://doi.org/10.1140/epjst/e2007-00377-2

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2007-00377-2

Keywords

Navigation