Noncommutative linear sigma models |
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| Institution: | 1. Department of Electrical and Electronics & Communication Engineering, DIT University, Dehradun 248009, Uttarakhand, India;2. Shandong Key Laboratory of Optical Communication Science and Technology, School of Physics Science and Information Technology, Liaocheng University, Liaocheng 252059, Shandong, China;3. Department of Electronics and Communication Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India;1. Department of Physics, LEPP, Cornell University, Ithaca, NY 14853, USA;2. Department of Physics, Princeton University, Princeton, NJ 08544, USA;3. Ernest Orlando Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA;4. Department of Physics, University of California, Berkeley, CA 94720, USA;5. Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel |
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| Abstract: | We examine noncommutative linear sigma models with U(N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that Nambu–Goldstone symmetry realization is inconsistent with continuum renormalization. Specifically we find no violation of Goldstone's theorem at one-loop for the U(N) models with the quartic term ordering consistent with possible noncommutative gauging of the model. The difference is due to terms involving noncommutative commutator interactions, which vanish in the commutative limit. We also examine the U(2), and O(4) linear sigma models with matter in the adjoint representation, and find that the former is consistent with Goldstone's theorem at one-loop if we include only trace invariants consistent with possible noncommutative gauging of the model, while the latter exhibits violations of Goldstone's theorem of the kind seen in the fundamental of O(N) for N>2. |
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