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Journals / Turkish Journal of Physics / 2017 / Cilt: 41 - Sayı: 3

Perturbative construction of the two-dimensional O(N) nonlinear sigma modelwith ERG

BEKİR CAN LÜTFÜOĞLU
Hidenori SONODA
Pages
244–255
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally we show how the beta functions and theanomalous dimensions arise in the model up to 1-loop.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We use the exact renormalization group (ERG) perturbatively to construct the Wilson action for the two-dimensional O(N) nonlinear sigma model (NLSM).
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Key Findings & Data:We construct two composite operators that generate in nitesimal changeof the coupling constant and the renormalization of the scalar elds.
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Conclusion & Impact:Finally we show how the beta functions and theanomalous dimensions arise in the model up to 1-loop.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We use the exact renormalization group (ERG) perturbatively to construct the Wilson action for the two-dimensional O(N) nonlinear sigma model (NLSM). The construction amounts to regularization of a nonlinear symmetrywith a momentum cutoff. We nd out that the model is parameterized by three functions. We show how to tune them byimposing the Ward{Takahashi (WT) identity. We construct two composite operators that generate in nitesimal changeof the coupling constant and the renormalization of the scalar elds. Finally we show how the beta functions and theanomalous dimensions arise in the model up to 1-loop.

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Cite This Article

LÜTFÜOĞLU, B. C., SONODA, H. (2017). Perturbative construction of the two-dimensional O(N) nonlinear sigma modelwith ERG. Turkish Journal of Physics, Cilt: 41 - Sayı: 3, 244–255. https://ajindex.com/articles/378329

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References (2)

  1. Novikov, V. A.; Shifman, M. A.; Vainshtein, A. I.; Zakharov, V. I.Phys. Rep.1984,116, 103-171. [2]D\'Adda, A.; Luscher, M.; Vecchia, P. Di.Nucl. Phys. B1978,146, 63-76. [3]Witten, E.Nucl. Phys. B1979,160, 57-115. [4]Gross, D.; Neveu, A.Phys. Rev. D1974,10, 3235-3253. [5]Bardeen, W.; Lee, B. W.; Shrock, R. E.Phys. Rev. D1976,14, 985-1005. [6]Coleman, S.Aspects of Symmetry; Cambridge University Press:
  2. New York, NY, USA, 1985. [7]Callan, C. G.; Friedan, D.; Martinec, E. J.; Perry, M. J.Nucl. Phys. B1985,262, 593-609. [8]Osborn, H.Nucl. Phys. B1988,308, 629-661. [9]Curci, G.; Paffuti, G.Nucl. Phys. B1989,312, 227-252. [10]Polyakov, A. M.Phys. Lett. B1975,59, 79-81. [11]Bollini, C. G.; Giambiagi, J. J.Nuovo Cim. B1972,12, 20-26. [12]Hooft, G.; Veltman, M. J. G.Nucl. Phys. B1972,44, 189-213. [13]Brezin, E.; Zinn-Justin, J.; Le Guillou, J. C.Phys. Rev. D1976,14, 2615-2661. [14]Rosten, O. J.Phys. Rep.2012,511, 177-272. [15]Wilson, K. G.; Kogut, J. B.Phys. Rep.1974,12, 75-199. [16]Polchinski, J.Nucl. Phys. B1984,231, 269-295. [17]Igarashi, I.; Itoh, K.; Sonoda, H.Prog. Theor. Phys. Suppl.2010,181, 1-166. [18]Mitter, P. K.; Ramadas, T. D.Commun. Math. Phys.1989,122, 575-596. [19]C. Becchi, \\On the construction of renormalized gauge theories using renormalization group techniques,\" arXiv:hep-th/9607188. [20]Pernici, M.; Raciti, M.Nucl. Phys. B1998,531, 560-592.[21]Sonoda, H.Phys. Rev. D2003,67, 065011.[22]Sonoda, H.J. Phys. A2007,40, 5733-5749.[23]Hooft, G.Nucl. Phys. B1973,61, 455-468.255