Charges in the UV completion of neutral electrodynamics. (English) Zbl 07716801
Summary: A theory with a non-compact form-symmetry is described by two closed form fields of degrees \(k\) and \(d - k\). Effective theory examples are non-linear electrodynamics, a photon field coupled to a neutron field, and a low energy Goldstone boson. We show these models cannot be completed in the UV without breaking the non-compact form-symmetry down to a compact one. This amounts to the existence of electric or magnetic charges. A theory with an unbroken non-compact \(k\)-form symmetry is massless and free.
MSC:
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 81T12 | Effective quantum field theories |
Keywords:
gauge symmetry; global symmetries; Wilson; ’t Hooft and Polyakov loops; renormalization and regularizationReferences:
| [1] | Russo, JG; Townsend, PK, Nonlinear electrodynamics without birefringence, JHEP, 01, 039 (2023) · Zbl 1540.81175 · doi:10.1007/JHEP01(2023)039 |
| [2] | A. Guerrieri, H. Murali, J. Penedones and P. Vieira, Where is M-theory in the space of scattering amplitudes?, arXiv:2212.00151 [INSPIRE]. · Zbl 07716770 |
| [3] | M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A144 (1934) 425 [INSPIRE]. · Zbl 0008.42203 |
| [4] | Gaiotto, D.; Kapustin, A.; Seiberg, N.; Willett, B., Generalized Global Symmetries, JHEP, 02, 172 (2015) · Zbl 1388.83656 · doi:10.1007/JHEP02(2015)172 |
| [5] | Casini, H.; Huerta, M.; Magán, JM; Pontello, D., Entropic order parameters for the phases of QFT, JHEP, 04, 277 (2021) · Zbl 1462.81127 · doi:10.1007/JHEP04(2021)277 |
| [6] | Casini, H.; Magán, JM, On completeness and generalized symmetries in quantum field theory, Mod. Phys. Lett. A, 36, 2130025 (2021) · doi:10.1142/S0217732321300251 |
| [7] | Benedetti, V.; Casini, H.; Magán, JM, Generalized symmetries and Noether’s theorem in QFT, JHEP, 08, 304 (2022) · Zbl 1522.81454 · doi:10.1007/JHEP08(2022)304 |
| [8] | Casini, H.; Magán, JM; Martínez, PJ, Entropic order parameters in weakly coupled gauge theories, JHEP, 01, 079 (2022) · Zbl 1521.81436 · doi:10.1007/JHEP01(2022)079 |
| [9] | Benedetti, V.; Casini, H.; Magán, JM, Generalized symmetries of the graviton, JHEP, 05, 045 (2022) · Zbl 1522.83056 · doi:10.1007/JHEP05(2022)045 |
| [10] | G. de Rham, Differentiable manifolds, volume 266 of Grundlehren der mathematischen wissenschaften [fundamental principles of mathematical sciences], (1984). · Zbl 0534.58003 |
| [11] | P.G. Federbush and K.A. Johnson, Uniqueness Property of the Twofold Vacuum Expectation Value, Phys. Rev.120 (1960) 1926 [INSPIRE]. · Zbl 0090.19902 |
| [12] | D. Buchholz and K. Fredenhagen, Dilations and Interaction, J. Math. Phys.18 (1977) 1107 [INSPIRE]. |
| [13] | Argyres, PC; Plesser, MR; Seiberg, N.; Witten, E., New N=2 superconformal field theories in four-dimensions, Nucl. Phys. B, 461, 71 (1996) · Zbl 1004.81557 · doi:10.1016/0550-3213(95)00671-0 |
| [14] | Hofman, DM; Iqbal, N., Goldstone modes and photonization for higher form symmetries, SciPost Phys., 6, 006 (2019) · doi:10.21468/SciPostPhys.6.1.006 |
| [15] | G. Mack, All unitary ray representations of the conformal group SU(2,2) with positive energy, Commun. Math. Phys.55 (1977) 1 [INSPIRE]. · Zbl 0352.22012 |
| [16] | W. Siegel, All Free Conformal Representations in All Dimensions, Int. J. Mod. Phys. A4 (1989) 2015 [INSPIRE]. |
| [17] | Minwalla, S., Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys., 2, 783 (1998) · Zbl 1041.81534 · doi:10.4310/ATMP.1998.v2.n4.a4 |
| [18] | Costa, MS; Hansen, T., Conformal correlators of mixed-symmetry tensors, JHEP, 02, 151 (2015) · Zbl 1388.53102 · doi:10.1007/JHEP02(2015)151 |
| [19] | Bostelmann, H.; D’Antoni, C.; Morsella, G., On dilation symmetries arising from scaling limits, Commun. Math. Phys., 294, 21 (2010) · Zbl 1207.81050 · doi:10.1007/s00220-009-0899-9 |
| [20] | S. Weinberg and E. Witten, Limits on Massless Particles, Phys. Lett. B96 (1980) 59 [INSPIRE]. |
| [21] | J. Polchinski, Monopoles, duality, and string theory, Int. J. Mod. Phys. A19S1 (2004) 145 [hep-th/0304042] [INSPIRE]. · Zbl 1080.81582 |
| [22] | Banks, T.; Seiberg, N., Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D, 83 (2011) · doi:10.1103/PhysRevD.83.084019 |
| [23] | Heidenreich, B., Non-invertible global symmetries and completeness of the spectrum, JHEP, 09, 203 (2021) · Zbl 1472.81232 · doi:10.1007/JHEP09(2021)203 |
| [24] | R.E. Peierls, The commutation laws of relativistic field theory, Proc. Roy. Soc. Lond. A214 (1952) 143 [INSPIRE]. · Zbl 0048.44606 |
| [25] | B.S. DeWitt, Quantum Theory of Gravity. 2. The Manifestly Covariant Theory, Phys. Rev.162 (1967) 1195 [INSPIRE]. · Zbl 0161.46501 |
| [26] | B. de Witt, Dynamical theory of groups and fields, Relativity, groups and topology, Publ. Gordon and Breach (1963). |
| [27] | Achucarro, A.; de Carlos, B.; Casas, JA; Doplicher, L., De Sitter vacua from uplifting D-terms in effective supergravities from realistic strings, JHEP, 06, 014 (2006) · doi:10.1088/1126-6708/2006/06/014 |
| [28] | H.J. Groenewold, On the Principles of elementary quantum mechanics, Physica12 (1946) 405 [INSPIRE]. · Zbl 0060.45002 |
| [29] | K. Baumann, When Is a Field Theory a Generalized Free Field?, Commun. Math. Phys.43 (1975) 221 [INSPIRE]. · Zbl 1358.81135 |
| [30] | R. Jost, Properties of wightman functions, Lectures on Field Theory: The many Body Problem, Academic Press, New York, U.S.A. (1961). · Zbl 0111.45404 |
| [31] | K. Pohlmeyer, The jost-schroer theorem for zero-mass fields, Commun. Math. Phys.12 (1969) 204 [INSPIRE]. · Zbl 0177.56902 |
| [32] | D. Robinson, Support of field in momentum space, Helv. Phys. Acta35 (1962). · Zbl 0108.22302 |
| [33] | Buchholz, D.; Longo, R.; Rehren, K-H, Causal Lie Products of Free Fields and the Emergence of Quantum Field Theory, Found. Phys., 52, 108 (2022) · Zbl 1512.81057 · doi:10.1007/s10701-022-00629-y |
| [34] | A. Truman, Spectrality, cluster decomposition and small distance properties in wightman field theory, J. Math. Phys.15 (1974) 1680 [INSPIRE]. |
| [35] | S. Axler, P. Bourdon and R. Wade, Harmonic function theory, vol. 137, Springer Science & Business Media (2013). · Zbl 0959.31001 |
| [36] | Gaberdiel, MR, An introduction to conformal field theory, Rept. Prog. Phys., 63, 607 (2000) · doi:10.1088/0034-4885/63/4/203 |
| [37] | R. Haag and D. Kastler, An algebraic approach to quantum field theory, J. Math. Phys.5 (1964) 848 [INSPIRE]. · Zbl 0139.46003 |
| [38] | R.F. Streater and A.S. Wightman, PCT, spin and statistics, and all that, Princeton University Press (2000) [INSPIRE]. · Zbl 1026.81027 |
| [39] | Guido, D., Modular theory for the von Neumann algebras of Local Quantum Physics, Contemp. Math., 534, 97 (2011) · Zbl 1219.46062 · doi:10.1090/conm/534/10523 |
| [40] | K. Fredenhagen and J. Hertel, Local Algebras of Observables and Point-Like Localized Fields, Commun. Math. Phys.80 (1981) 555 [INSPIRE]. · Zbl 0472.46051 |
| [41] | J. Rehberg and M. Wollenberg, Quantum fields as pointlike localized objects, Math. Nachr.125 (1986) 259. · Zbl 0617.46080 |
| [42] | H. Bostelmann, Phase space properties and the short distance structure in quantum field theory, J. Math. Phys.46 (2005) 052301 [math-ph/0409070] [INSPIRE]. · Zbl 1110.81132 |
| [43] | Buchholz, D.; Verch, R., Scaling algebras and renormalization group in algebraic quantum field theory, Rev. Math. Phys., 7, 1195 (1995) · Zbl 0842.46052 · doi:10.1142/S0129055X9500044X |
| [44] | Bostelmann, H.; D’Antoni, C.; Morsella, G., Scaling algebras and pointlike fields: A nonperturbative approach to renormalization, Commun. Math. Phys., 285, 763 (2009) · Zbl 1155.81029 · doi:10.1007/s00220-008-0613-3 |
| [45] | H. Bostelmann, Operator product expansions as a consequence of phase space properties, J. Math. Phys.46 (2005) 082304 [math-ph/0502004] [INSPIRE]. · Zbl 1110.81133 |
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