Aviso: para depositar documentos, por favor, inicia sesión e identifícate con tu cuenta de correo institucional de la UCM con el botón MI CUENTA UCM. No emplees la opción AUTENTICACIÓN CON CONTRASEÑA
 

UV/IR mixing and the Goldstone theorem in noncommutative field theory

dc.contributor.authorRuiz Ruiz, Fernando
dc.date.accessioned2023-06-20T18:57:23Z
dc.date.available2023-06-20T18:57:23Z
dc.date.issued2002-08-19
dc.description© 2002 Elsevier Science B.V. All rights reserved. The author is grateful to C.P. Martín formany illuminating conversations and for reading the manuscript. He also acknowledges financial support from CICyT, Spain through grant No. PB98-0842.
dc.description.abstractNoncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, lambda(1) and lambda(2), associated to the two noncommutative extensions phi* star phi star phi* star phi and phi* star phi* star phi star phi of the interaction term \phi\(4) on commutative spacetime. It is shown that the symmetric phase is one loop renormalizable for all lambda(1) and lambda(2) compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if lambda(2) = 0, a condition required by the Ward identities for global U(I) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter theta.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipCICyT
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/25067
dc.identifier.doi10.1016/S0550-3213(02)00447-9
dc.identifier.issn0550-3213
dc.identifier.officialurlhttp://dx.doi.org/10.1016/S0550-3213(02)00447-9
dc.identifier.relatedurlhttp://arxiv.org/abs/hep-th/0202011
dc.identifier.relatedurlhttp://www.sciencedirect.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/58993
dc.journal.titlePhysics Letters B
dc.language.isoeng
dc.page.final167
dc.page.initial143
dc.publisherElsevier Science Bv
dc.relation.projectIDPB98-0842
dc.rights.accessRightsopen access
dc.subject.cdu53
dc.subject.keywordYang-Mills Theory
dc.subject.keywordOne-Loop
dc.subject.keywordTachyonic Instabilities
dc.subject.keywordString Theory
dc.subject.keywordUnitarity
dc.subject.keywordDiagrams
dc.subject.keywordModel
dc.subject.keywordU(1)
dc.subject.ucmFísica (Física)
dc.subject.unesco22 Física
dc.titleUV/IR mixing and the Goldstone theorem in noncommutative field theory
dc.typejournal article
dc.volume.number637
dcterms.references[1] For recent reviews on noncommutative field theory, see M.R. Douglas, N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2002) 977; R.J. Szabo, Quantum field theory on noncommutative spaces, IEEE Trans. Nucl. Sci. 48 (2001); I.Ya. Aref’eva, D.M. Belov, A.A. Giryavets, A.S. Koshelev, P.B.Medvedev, Noncommutative field theories and super)string field theories, hep-th/0111208. [2] S.Minwalla, M.V. Raamsdonk, N. Seiberg, Noncommutative perturbative dynamics, JHEP 0002 (2000) 020. [3] M. Hayakawa, Perturbative analysis of IR aspects of noncommutative QED on R4, Phys. Lett. B 478 (2000) 394. [4] A. Matusis, L. Susskind, N. Toumbas, The IR/UV connection in the noncommutative gauge theories, JHEP 0012 (2000) 002. [5] C.P. Martín, F. Ruiz Ruiz, Paramagnetic dominance, the sign of the beta function and UV/IR mixing in noncommutative U(1), Nucl. Phys. B 597 (2001) 197. [6] F. Ruiz Ruiz, Gauge-fixing independence of IR divergences in noncommutative U(1), perturbative tachyonic instabilities and supersymmetry, Phys. Lett. B 502 (2001) 274. [7] O. Andreev, H. Dorn, Diagrams of noncommutative φ3 theory from string theory, Nucl. Phys. B 583 (2000) 145; A. Bilal, C.-S. Chu, R. Russo, String theory and noncommutative field theories at one loop, Nucl. Phys. B 582 (2000) 65; Y. Kiem, S. Lee, UV/IR mixing in noncommutative field theory via open string loops, Nucl. Phys. B 586 (2000) 303; H. Liu, J. Michelson, Stretched strings in noncommutative field theory, Phys. Rev. D 62 (2000) 066003; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, S. Shenker, Non-commutative gauge dynamics from the string worldsheet, JHEP 0008 (2000) 011; A. Armoni, E. López, UV/IR mixing via closed strings and tachyonic instabilities, Nucl. Phys. B 632 (2002) 240. [8] An explicit proof of two-loop renormalizability for λφ4 is given in I.Ya. Aref’eva, D.M. Belov, A.S. Koshelev, Two loop diagrams in noncommutative ϕ4 4 theory, Phys. Lett. B 476 (2000) 431; Particular types of n-loop diagrams in λφ4 have been studied in I. Chepelev, R. Roiban, Convergence theorem for noncommutative Feynman graphs and renormalization, JHEP 0103 (2001) 001; A Wilsonian approach can be found in L. Griguolo, M. Pietroni, Hard noncommutative loops resumation, hep-th/0102070. [9] H.O. Girotti, M. Gomes, V.O. Rivelles, A.J. da Silva, A consistent noncommutative field theory: the Wess– Zumino model, Nucl. Phys. B 587 (2000) 299; H.O. Girotti, M. Gomes, Yu. Petrov, The three-dimensional noncommutative nonlinear sigma model in superspace, Phys. Lett. B 521 (2001) 119. [10] J. Gomis, T. Mehen, M.B. Wise, Quantum Field theories with compact noncommutative extra dimensions, JHEP 0008 (2000) 029; J. Gomis, K. Landsteiner, E. López, Non-relativistic noncommutative field theory and UV/IR mixing, Phys. Rev. D 62 (2000) 105006; K. Landsteiner, E. López, M.H.G. Tytgat, Instability of noncommutative SYM theories at finite temperature, JHEP 0009 (2000) 027. [11] C.P. Martín, D. Sánchez-Ruiz, The on-loop UV structure of U(1) Yang–Mills theory in noncommutative R4, Phys. Rev. Lett. 83 (1999) 476; M. Sheikh-Jabbari, Renormalizability of the supersymmetric Yang–Mills theories on the noncommutative torus, JHEP 9906 (1999) 015; T. Krajewski, R.Wulkenhaar, Perturbative quantum gauge fields on the noncommutative torus, J. Mod. Phys. A 15 (2000) 1011; A. Armoni, Comments on perturbative dynamics of noncommutative Yang–Mills theory, Nucl. Phys. 593 (2001) 229; C.P. Martín, D. Sánchez-Ruiz, The BRS invariance of noncommutative U(N) Yang–Mills theory at the one loop level, Nucl. Phys. B 598 (2001) 348. F. Ruiz Ruiz / Nuclear Physics B 637 (2002) 143 167 167 [12] J. Gomis, T. Mehen, Space–time noncommutative field theories and unitarity, Nucl. Phys. B 591 (2000) 265; L. Alvarez-Gaumé, J.L.F. Barbón, Remarks on time-space noncommutative field theories, JHEP 0105 (2001) 057; A. Bassetto, L. Griguolo, G. Nardelli, F. Vian, On the unitarity of quantum gauge theories on noncommutative spaces, JHEP 0107 (2001) 008; C.-S. Chu, J. Lukierski, W.J. Zakrzewski, Hermitian analyticity, IR/UV mixing and unitarity of noncommutative field theories, Nucl. Phys. B 632 (2002) 219. [13] B.A. Campbell, K. Kaminsky, Non-commutative field theory and spontaneous symmetry breaking, Nucl. Phys. B 581 (2000) 240; B.A. Campbell, K. Kaminsky, Non-commutative linear sigma models, Nucl. Phys. B 606 (2001) 613. [14] S. Sarkar, B. Sathiapalan, Comments on the renormalizability of the broken symmetry phase in noncommutative scalar field theory, JHEP 0105 (2001) 049. [15] F. Petriello, The Higgs mechanism in noncommutative gauge theories, Nucl. Phys. B 601 (2001) 169. [16] Y. Liao, One-loop renormalization of spontaneously broken U(2) gauge theory on noncommutative spacetime, JHEP 0111 (2001) 067; Y. Liao, One-loop renormalizability of spontaneously broken gauge theory with a product of gauge groups noncommutative spacetime: the U(1) ×U(1) case, hep th/0201135
dspace.entity.typePublication
relation.isAuthorOfPublication00879a8b-f834-4645-adb9-01e259407707
relation.isAuthorOfPublication.latestForDiscovery00879a8b-f834-4645-adb9-01e259407707

Download

Original bundle

Now showing 1 - 2 of 2
Loading...
Thumbnail Image
Name:
Ruiz FR11.pdf
Size:
213.77 KB
Format:
Adobe Portable Document Format
Loading...
Thumbnail Image
Name:
Ruiz FR11preprint.pdf
Size:
311.15 KB
Format:
Adobe Portable Document Format

Collections