Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 002, 8 pages      math-ph/0601002      https://doi.org/10.3842/SIGMA.2006.002

On the Effective Action of Dressed Mean Fields for N = 4 Super-Yang-Mills Theory

Gorazd Cvetic a, Igor Kondrashuk a, b and Ivan Schmidt a
a) Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Casilla 110-V, Valparaiso, Chile
b) Departamento de Ciencias Basicas, Universidad del Bio-Bio, Campus Fernando May, Casilla 447, Avenida Andreas Bello, Chillan, Chile

Received October 30, 2005, in final form January 01, 2006; Published online January 09, 2006

Abstract
On the basis of the general considerations such as R-operation and Slavnov-Taylor identity we show that the effective action, being understood as Legendre transform of the logarithm of the path integral, possesses particular structure in N = 4 supersymmetric Yang-Mills theory for kernels of the effective action expressed in terms of the dressed effective fields. These dressed effective fields have been introduced in our previous papers as actual variables of the effective action. The concept of dressed effective fields naturally appears in the framework of solution to Slavnov-Taylor identity. The particularity of the structure is independence of these kernels on the ultraviolet regularization scale Λ. These kernels are functions of mutual spacetime distances and of the gauge coupling. The fact that β function in this theory vanishes is used significantly.

Key words: R-operation; gauge symmetry; N = 4 supersymmetry; Slavnov-Taylor identity.

pdf (209 kb)   ps (155 kb)   tex (34 kb)

References

  1. Slavnov A.A., Ward identities in gauge theories, Teor. Mat. Fiz., 1972, V.10, 153-161 (English transl.: Theor. Math. Phys., 1972, V.10, 99-107).
    Taylor J.C., Ward identities and charge renormalization of the Yang-Mills field, Nucl. Phys. B, 1971, V.33, 436-444.
    Slavnov A.A., Renormalization of supersymmetric gauge theories. 2. Nonabelian case, Nucl. Phys. B, 1975, V.97, 155-164.
  2. Becchi C., Rouet A., Stora R., Renormalization of the Abelian Higgs-Kibble model, Comm. Math. Phys., 1975, V.42, 127-162.
    Tyutin I.V., Gauge invariance in field theory and statistical physics in operator formalism, preprint FIAN Lebedev-75-39, 1975 (in Russian).
  3. Slavnov A., Faddeev L., Introduction to quantum theory of gauge fields, Moscow, Nauka, 1988.
  4. Kondrashuk I., Cvetic G., Schmidt I., Approach to solve Slavnov-Taylor identities in nonsupersymmetric non-Abelian gauge theories, Phys. Rev. D, 2003, V.67, 065006, 16 pages, hep-ph/0203014.
  5. Cvetic G., Kondrashuk I., Schmidt I., QCD effective action with dressing functions: consistency checks in perturbative regime, Phys. Rev. D, 2003, V.67, 065007, 16 pages, hep-ph/0210185.
  6. Bogolyubov N.N., Shirkov D.V., Introduction to the theory of quantized fields, Moscow, Nauka, 1984 (English transl.: Intersci. Monogr. Phys. Astron., 1959, V.3).
  7. Maldacena J.M., The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 1998, V.2, 231-252.
    Maldacena J.M., The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 1999, V.38, 1113-1133, hep-th/9711200.
  8. Berenstein D., Maldacena J.M., Nastase H., Strings in flat space and pp waves from N = 4 super-Yang-Mills, JHEP, 2002, V.0204, paper 013, 30 pages, hep-th/0202021.
  9. Witten E., Perturbative gauge theory as a string theory in twistor space, Comm. Math. Phys., 2004, V.252, 189-258, hep-th/0312171.
  10. Bern Z., Dixon L.J., Dunbar D.C., Kosower D.A., One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B, 1994, V.425, 217-260, hep-ph/9403226.
  11. Ferrara S., Zumino B., Supergauge invariant Yang-Mills theories, Nucl. Phys. B, 1974, V.79, 413-421.
  12. Jones D.R.T., Charge renormalization in a supersymmetric Yang-Mills theory, Phys. Lett. B, 1977, V.72, 199-200.
  13. Avdeev L.V., Tarasov O.V., Vladimirov A.A., Vanishing of the three loop charge renormalization function in a supersymmetric gauge theory, Phys. Lett. B, 1980, V.96, 94-96.
  14. Sohnius M.F., West P.C., Conformal invariance in N=4 supersymmetric Yang-Mills theory, Phys. Lett. B, 1981, V.100, 245-250.
  15. Siegel W., Supersymmetric dimensional regularization via dimensional reduction, Phys. Lett. B, 1979, V.84, 193-196.
  16. Krivoshchekov V.K., Invariant regularizations for supersymmetric gauge theories, Teor. Mat. Fiz., 1978, V.36, 291-302 (in Russian).
  17. West P.C., Higher derivative regulation of supersymmetric theories, Nucl. Phys. B, 1986, V.268, 113-124.
  18. Slavnov A.A., Stepanyantz K.V., Universal invariant renormalization of supersymmetric Yang-Mills theory, Teor. Mat. Fiz., 2004, V.139, 179-191 (English transl.: Theor. Math. Phys., 2004, V.139, 599-608), hep-th/0305128.
  19. Slavnov A.A., Stepanyantz K.V., Universal invariant renormalization for supersymmetric theories, Teor. Mat. Fiz., 2003, V.135, 265-279 (English transl.: Theor. Math. Phys., 2003, V.135, 673-684), hep-th/0208006.
  20. Slavnov A.A., Universal gauge invariant renormalization, Phys. Lett. B, 2001, V.518, 195-200.
  21. Martin C.P., Ruiz Ruiz F., Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD, Nucl. Phys. B, 1995, V.436, 545-581, hep-th/9410223.
  22. Bakeyev T.D., Slavnov A.A., Higher covariant derivative regularization revisited, Mod. Phys. Lett. A, 1996, V.11, 1539-1554, hep-th/9601092.
  23. Asorey M., Falceto F., On the consistency of the regularization of gauge theories by high covariant derivatives, Phys. Rev. D, 1996, V.54, 5290-5301, hep-th/9502025.
  24. Lee B.W., Transformation properties of proper vertices in gauge theories, Phys. Lett. B, 1973, V.46, 214-216.
    Lee B.W., Renormalization of gauge theories: unbroken and broken, Phys. Rev. D, 1974, V.9, 933-946.
    Zinn-Justin J., Renormalization of gauge theories, Lecture Note in Physics, Vol. 37, Berlin, Springer Verlag, 1975.
  25. Peskin M.E., Schroeder D.V., An introduction to quantum field theory, Addison-Wesley, 1995.
  26. Siegel W., Inconsistency of supersymmetric dimensional regularization, Phys. Lett. B, 1980, V.94, 37-40.
  27. Collins J.C., Duncan A., Joglekar S.D., Trace and dilatation anomalies in gauge theories, Phys. Rev. D, 1977, V.16, 438-449.
  28. Bern Z., Dixon L.J., Smirnov V.A., Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D, 2005, V.72, 085001, 27 pages, hep-th/0505205.

Previous article   Next article   Contents of Volume 2 (2006)