Abstract
Starting from a recently proposed linear formulation in terms of auxiliary fields, we study n-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the symmetry properties (including the characteristic self-duality) of the corresponding non-linear theory are manifest as on-shell duality symmetries and depend on the choice of the (homogeneous) manifold spanned by the auxiliary scalar fields and the symplectic frame. By suitably choosing these defining properties of the quadratic Lagrangian, we are able to reproduce some known multi-field Born-Infeld theories and to derive new non-linear models, such as the n-field Born theory. We also discuss non-Abelian generalizations of these theories obtained by choosing the vector fields in the adjoint representation of an off-shell compact global symmetry group K and replacing them by non-Abelian, K-covariant field strengths, thus promoting K to a gauge group.
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References
M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A 144 (1934) 425 [INSPIRE].
M. Born, Quantum theory of the electromagnetic field, Proc. Roy. Soc. Lond. A 143 (1934) 410 [INSPIRE].
P.A.M. Dirac, A Reformulation of the Born-Infeld Electrodynamics, Proc. Roy. Soc. Lond. A 257 (1960) 32.
E.A. Ivanov and B.M. Zupnik, New approach to nonlinear electrodynamics: Dualities as symmetries of interaction, Phys. Atom. Nucl. 67 (2004) 2188 [hep-th/0303192] [INSPIRE].
P. Aschieri, S. Ferrara and B. Zumino, Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity, Riv. Nuovo Cim. 31 (2008) 625 [arXiv:0807.4039] [INSPIRE].
E. Schrödinger, Contributions to Born’s New Theory of the Electromagnetic Field, Proc. Roy. Soc. Lond. A 150 (1935) 465 [INSPIRE].
G.W. Gibbons and D.A. Rasheed, Electric-magnetic duality rotations in nonlinear electrodynamics, Nucl. Phys. B 454 (1995) 185 [hep-th/9506035] [INSPIRE].
J. Plebanski, Lectures on Non-Linear Electrodynamics, Nordita, Copenhagen (1968).
C. Minz, H.-H. von Borzeszkowski, T. Chrobok and G. Schellstede, Shock wave polarizations and optical metrics in the Born and the Born-Infeld electrodynamics, Annals Phys. 364 (2016) 248 [arXiv:1411.3163] [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Nonlinear Electrodynamics from Quantized Strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].
A.A. Tseytlin, Born-Infeld action, supersymmetry and string theory, in The Many Faces of the Superworld: Yuri Golfand Memorial Volume, M.A. Shifman ed., World Scientific, pg. 417-452, hep-th/9908105 [INSPIRE].
S. Deser and R. Puzalowski, Supersymmetric Nonpolynomial Vector Multiplets and Causal Propagation, J. Phys. A 13 (1980) 2501 [INSPIRE].
S. Cecotti and S. Ferrara, Supersymmetric Born-Infeld Lagrangians, Phys. Lett. B 187 (1987) 335 [INSPIRE].
J. Bagger and A. Galperin, A new Goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177] [INSPIRE].
J. Bagger and A. Galperin, The tensor Goldstone multiplet for partially broken supersymmetry, Phys. Lett. B 412 (1997) 296 [hep-th/9707061] [INSPIRE].
I. Antoniadis, H. Partouche and T.R. Taylor, Spontaneous breaking of \( \mathcal{N} \) = 2 global supersymmetry, Phys. Lett. B 372 (1996) 83 [hep-th/9512006] [INSPIRE].
S. Ferrara, M. Porrati and A. Sagnotti, \( \mathcal{N} \) = 2 Born-Infeld attractors, JHEP 12 (2014) 065 [arXiv:1411.4954] [INSPIRE].
L. Andrianopoli, P. Concha, R. D’Auria, E. Rodriguez and M. Trigiante, Observations on BI from \( \mathcal{N} \) = 2 Supergravity and the General Ward Identity, JHEP 11 (2015) 061 [arXiv:1508.01474] [INSPIRE].
S. Ferrara, A. Sagnotti and A. Yeranyan, Doubly Self-Dual Actions in Various Dimensions, JHEP 05 (2015) 051 [arXiv:1503.04731] [INSPIRE].
S. Ferrara, A. Sagnotti and A. Yeranyan, Two-Field Born-Infeld with Diverse Dualities, CERN-TH-2016-017 [arXiv:1602.04566].
L. Andrianopoli, R. D’Auria, S. Ferrara and M. Trigiante, c-Map for Born-Infeld theories, Phys. Lett. B 758 (2016) 423 [arXiv:1603.03338] [INSPIRE].
M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
D. Brace, B. Morariu and B. Zumino, Duality invariant Born-Infeld theory, in The Many Faces of the Superworld: Yuri Golfand Memorial Volume, M.A. Shifman ed., World Scientific, pg. 103-110, hep-th/9905218 [INSPIRE].
P. Aschieri, D. Brace, B. Morariu and B. Zumino, Nonlinear selfduality in even dimensions, Nucl. Phys. B 574 (2000) 551 [hep-th/9909021] [INSPIRE].
L. Andrianopoli, R. D’Auria and M. Trigiante, On the dualization of Born-Infeld theories, Phys. Lett. B 744 (2015) 225 [arXiv:1412.6786] [INSPIRE].
M.K. Gaillard and B. Zumino, Duality Rotations for Interacting Fields, Nucl. Phys. B 193 (1981) 221 [INSPIRE].
M.K. Gaillard and B. Zumino, Selfduality in nonlinear electromagnetism, hep-th/9705226 [INSPIRE].
E.B. Dynkin, Maximal subgroups of the classical groups, Trudy Moscov. Mat. Obsh. 1 (1952) 39 [Am. Math. Soc. Transl. 2 (1957) 245], reprinted in Selected Papers of E.B. Dynkin with commentary, A.A. Yushkevich, G.M. Seitz and A.L. Onishchik eds., AMS and International Press (2000).
A.A. Tseytlin, On nonAbelian generalization of Born-Infeld action in string theory, Nucl. Phys. B 501 (1997) 41 [hep-th/9701125] [INSPIRE].
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
S.L. Cacciatori and B.L. Cerchiai, Exceptional groups, symmetric spaces and applications, invited article in Group Theory: Classes, Representation and Connections, and Applications, Charles W. Danellis ed., Nova Science Publishers, New York (2010), pg. 177-215, arXiv:0906.0121 [INSPIRE].
S. Bertini, S.L. Cacciatori and B.L. Cerchiai, On the Euler angles for SU(N ), J. Math. Phys. 47 (2006) 043510 [math-ph/0510075] [INSPIRE].
G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
A.M. Polyakov, Particle Spectrum in the Quantum Field Theory, JETP Lett. 20 (1974) 194 [INSPIRE].
C.-H. Liu and S.-T. Yau, Dynamics of D-branes I. The non-Abelian Dirac-Born-Infeld action, its first variation and the equations of motion for D-branes — with remarks on the non-Abelian Chern-Simons/Wess-Zumino term, arXiv:1606.08529 [INSPIRE].
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Cerchiai, B.L., Trigiante, M. On multifield Born and Born-Infeld theories and their non-Abelian generalizations. J. High Energ. Phys. 2016, 160 (2016). https://doi.org/10.1007/JHEP10(2016)160
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DOI: https://doi.org/10.1007/JHEP10(2016)160