Abstract
We study the Lagrangian description of chiral bosons, p-form gauge fields with (anti–)self-dual gauge field strengths, in D = 2p + 2 dimensional spacetime of non-trivial topology. We show that the manifestly Lorentz and diffeomorphism invariant Pasti-Sorokin-Tonin (PST) approach is consistent and produces the (anti-)self-duality equation also in topologically nontrivial spacetime. We discuss in what circumstances the nontrivial topology makes difference between two disconnected, da-timelike and da-spacelike branches of the PST system, the gauge fixed version of which are described by not manifestly invariant Henneaux-Teitelboim (HT) and Perry-Schwarz (PS) actions, respectively.
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References
P. Pasti, D.P. Sorokin and M. Tonin, Duality symmetric actions with manifest space-time symmetries, Phys. Rev. D 52 (1995) 4277 [hep-th/9506109] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, On Lorentz invariant actions for chiral p forms, Phys. Rev. D 55 (1997) 6292 [hep-th/9611100] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, Covariant action for a D = 11 five-brane with the chiral field, Phys. Lett. B 398 (1997) 41 [hep-th/9701037] [INSPIRE].
I.A. Bandos et al., Covariant action for the superfive-brane of M-theory, Phys. Rev. Lett. 78 (1997) 4332 [hep-th/9701149] [INSPIRE].
M. Aganagic, J. Park, C. Popescu and J.H. Schwarz, World volume action of the M-theory five-brane, Nucl. Phys. B 496 (1997) 191 [hep-th/9701166] [INSPIRE].
M. Henneaux and C. Teitelboim, Dynamics of Chiral (Selfdual) P Forms, Phys. Lett. B 206 (1988) 650 [INSPIRE].
M. Perry and J.H. Schwarz, Interacting chiral gauge fields in six-dimensions and Born-Infeld theory, Nucl. Phys. B 489 (1997) 47 [hep-th/9611065] [INSPIRE].
P. Pasti, I. Samsonov, D. Sorokin and M. Tonin, BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D = 6 and M5-branes, Phys. Rev. D 80 (2009) 086008 [arXiv:0907.4596] [INSPIRE].
S.-L. Ko, D. Sorokin and P. Vanichchapongjaroen, The M5-brane action revisited, JHEP 11 (2013) 072 [arXiv:1308.2231] [INSPIRE].
D. Belov and G.W. Moore, Holographic Action for the Self-Dual Field, hep-th/0605038 [INSPIRE].
P.-M. Ho and Y. Matsuo, M5 from M2, JHEP 06 (2008) 105 [arXiv:0804.3629] [INSPIRE].
W.-M. Chen and P.-M. Ho, Lagrangian Formulations of Self-dual Gauge Theories in Diverse Dimensions, Nucl. Phys. B 837 (2010) 1 [arXiv:1001.3608] [INSPIRE].
G. Dall’Agata, K. Lechner and M. Tonin, Covariant actions for N = 1, D = 6 supergravity theories with chiral bosons, Nucl. Phys. B 512 (1998) 179 [hep-th/9710127] [INSPIRE].
I.A. Bandos, N. Berkovits and D.P. Sorokin, Duality symmetric eleven-dimensional supergravity and its coupling to M-branes, Nucl. Phys. B 522 (1998) 214 [hep-th/9711055] [INSPIRE].
G. Dall’Agata, K. Lechner and D.P. Sorokin, Covariant actions for the bosonic sector of D = 10 IIB supergravity, Class. Quant. Grav. 14 (1997) L195 [hep-th/9707044] [INSPIRE].
G. Dall’Agata, K. Lechner and M. Tonin, D = 10, N = IIB supergravity: Lorentz invariant actions and duality, JHEP 07 (1998) 017 [hep-th/9806140] [INSPIRE].
I. Bandos, H. Samtleben and D. Sorokin, Duality-symmetric actions for non-Abelian tensor fields, Phys. Rev. D 88 (2013) 025024 [arXiv:1305.1304] [INSPIRE].
X. Bekaert and M. Henneaux, Comments on chiral p forms, Int. J. Theor. Phys. 38 (1999) 1161 [hep-th/9806062] [INSPIRE].
A. Maznytsia, C.R. Preitschopf and D.P. Sorokin, Duality of selfdual actions, Nucl. Phys. B 539 (1999) 438 [hep-th/9805110] [INSPIRE].
R. Floreanini and R. Jackiw, Selfdual Fields as Charge Density Solitons, Phys. Rev. Lett. 59 (1987) 1873 [INSPIRE].
C. Nash and S. Sen, Topology And Geometry For Physicists, Academic Press INC LTD, London U.K. (1983).
N.J. Hitchin, The geometry of three-forms in six and seven dimensions, math/0010054 [INSPIRE].
N.J. Hitchin, The Geometry of three forms in six-dimensions, J. Diff. Geom. 55 (2000) 547 [INSPIRE].
N. Berkovits, Manifest electromagnetic duality in closed superstring field theory, Phys. Lett. B 388 (1996) 743 [hep-th/9607070] [INSPIRE].
I. Bengtsson and A. Kleppe, On chiral p forms, Int. J. Mod. Phys. A 12 (1997) 3397 [hep-th/9609102] [INSPIRE].
I. Giannakis and V.P. Nair, Symplectic structures and selfdual fields in (4k+2)-dimensions, Phys. Lett. B 409 (1997) 145 [hep-th/9702024] [INSPIRE].
E. Bergshoeff, R. Kallosh, T. Ortín, D. Roest and A. Van Proeyen, New formulations of D = 10 supersymmetry and D8 - O8 domain walls, Class. Quant. Grav. 18 (2001) 3359 [hep-th/0103233] [INSPIRE].
M. Cederwall, B.E.W. Nilsson and P. Sundell, An Action for the superfive-brane in D = 11 supergravity, JHEP 04 (1998) 007 [hep-th/9712059] [INSPIRE].
D. Zwanziger, Local Lagrangian quantum field theory of electric and magnetic charges, Phys. Rev. D 3 (1971) 880 [INSPIRE].
A. Sevrin and D.C. Thompson, A Note on Supersymmetric Chiral Bosons, JHEP 07 (2013) 086 [arXiv:1305.4848] [INSPIRE].
M. Henneaux and C. Teitelboim, Consistent quantum mechanics of chiral p-forms, In Santiago 1987, Proceedings, Quantum mechanics of fundamental systems V2, 113-152 (1987).
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton University Press, Princeton U.S.A. (1994).
C.M. Hull and N. Lambert, Emergent Time and the M5-Brane, JHEP 06 (2014) 016 [arXiv:1403.4532] [INSPIRE].
N. Berkovits, Super Poincaré covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [INSPIRE].
N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, JHEP 09 (2004) 047 [hep-th/0406055] [INSPIRE].
E. Witten, Five-brane effective action in M-theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234] [INSPIRE].
W.-M. Chen, P.-M. Ho, H.-c. Kao, F.S. Khoo and Y. Matsuo, Partition function of a chiral boson on a 2-torus from the Floreanini-Jackiw Lagrangian, PTEP 2014 (2014) 033B02 [arXiv:1307.2172] [INSPIRE].
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Bandos, I. On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology. J. High Energ. Phys. 2014, 48 (2014). https://doi.org/10.1007/JHEP08(2014)048
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DOI: https://doi.org/10.1007/JHEP08(2014)048