Abstract
We derive the Feynman rules for the 1/N-expansion of the simplest σ-model in the class of models that we previously proposed. We consider the case where the target space is the flag manifold U(N)/(U(1) × U(1) × U(N − 2)).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Bykov, “Complex structures and zero-curvature equations for σ-models,” Phys. Lett. B, 760, 341–344 (2016); arXiv:1605.01093v1 [hep-th] (2016).
K. Pohlmeyer, “Integrable Hamiltonian systems and interactions through quadratic constraints,” Commun. Math. Phys., 46, 207–221 (1976).
V. E. Zakharov and A. V. Mikhailov, “Relativistically invariant two-dimensional models in field theory integrable by the inverse problem technique,” Sov. Phys. JETP, 47, 1017–1027 (1978).
H. Eichenherr and M. Forger, “On the dual symmetry of the non-linear sigma models,” Nucl. Phys. B, 155, 381–393 (1979).
D. V. Bykov, “A gauged linear formulation for flag-manifold σ-models,” Theor. Math. Phys., 193, 1737–1753 (2017).
E. Cremmer and J. Scherk, “The supersymmetric non-linear σ-model in four dimensions and its coupling to supergravity,” Phys. Lett. B, 74, 341–434 (1978).
A. D’Adda, M. Lüscher, and P. Di Vecchia, “A 1/n expandable series of non-linear σ-models with instantons,” Nucl. Phys. B, 146, 63–76 (1978).
R. Donagi and E. Sharpe, “GLSM’s for partial flag manifolds,” J. Geom. Phys., 58, 1662–1692 (2008).
D. Bykov, “Integrable properties of σ-models with non-symmetric target spaces,” Nucl. Phys. B, 894, 254–267 (2015); arXiv:1412.3746v1 [hep-th] (2014).
D. Bykov, “Classical solutions of a flag manifold σ-model,” Nucl. Phys. B, 902, 292–301 (2016); arXiv: 1506.08156v1 [hep-th] (2015).
A. M. Polyakov, Gauge Fields and Strings [in Russian], RKdD, Izhevsk (1999); English transl. prev. ed. (Contemp. Concepts Phys., Vol. 3), Harwood Academic, Chur (1987).
A. D’Adda, P. Di Vecchia, and M. Lüscher, “Confinement and chiral symmetry breaking in CPn−1 models with quarks,” Nucl. Phys. B, 152, 125–144 (1979).
M. Lüscher, “Quantum nonlocal charges and absence of particle production in the two-dimensional nonlinear sigma model,” Nucl. Phys. B, 135, 1–19 (1978).
Y. Y. Goldschmidt and E. Witten, “Conservation laws in some two-dimensional models,” Phys. Lett. B, 91, 392–396 (1980).
E. Abdalla, M. C. B. Abdalla, and M. Gomes, “Anomaly in the nonlocal quantum charge of the CP(n−1) model,” Phys. Rev. D, 23, 1800–1805 (1981).
E. Abdalla, M. Gomes, and M. Forger, “On the origin of anomalies in the quantum non-local charge for the generalized non-linear sigma models,” Nucl. Phys. B, 210, 181–192 (1982).
E. Abdalla, M. C. B. Abdalla, and M. Gomes, “Anomaly cancellations in the supersymmetric CPn−1 model,” Phys. Rev. D, 25, 452–460 (1982).
E. Abdalla, M. C. B. Abdalla, and M. Gomes, “On the nonlocal charge of the CPn−1 model and its supersymmetric extension to all orders,” Phys. Rev. D, 27, 825–836 (1983).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 197, No. 2, pp. 345–355, December, 2018.
This research was supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).
Rights and permissions
About this article
Cite this article
Bykov, D.V. The 1/N-Expansion for Flag-Manifold σ-Models. Theor Math Phys 197, 1691–1700 (2018). https://doi.org/10.1134/S0040577918120012
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577918120012