Abstract
We explore various geometrical aspects of an action for six-dimensional chiral 2-forms based on the formalism of 1903.12196. We elucidate the coupling to general backgrounds and construct the full supersymmetric completion to an abelian (2, 0) superconformal lagrangian including matter. We investigate the non-standard diffeomorphism properties of the fields and their relation to the hamiltonian formulation. We also test the action by considering compactifications on a circle, K3 and a Riemann surface. The results are consistent with expectations for an action describing the low-energy physics of an M5-brane in M-theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Lambert, (2, 0) Lagrangian structures, Phys. Lett.B7 98 (2019) 134948 [arXiv:1908.10752].
P.S. Howe, E. Sezgin and P.C. West, Covariant field equations of the M-theory five-brane, Phys. Lett.B 399 (1997) 49 [hep-th/9702008] [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].
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].
B. McClain, F. Yu and Y.S. Wu, Covariant quantization of chiral bosons and OSp(1, 1|2) symmetry, Nucl. Phys.B 343 (1990) 689 [INSPIRE].
C. Wotzasek, The Wess-Zumino term for chiral bosons, Phys. Rev. Lett.66 (1991) 129 [INSPIRE].
I. Martin and A. Restuccia, Duality symmetric actions and canonical quantization, Phys. Lett.B 323 (1994) 311 [INSPIRE].
F.P. Devecchi and M. Henneaux, Covariant path integral for chiral p forms, Phys. Rev.D 54 (1996) 1606 [hep-th/9603031] [INSPIRE].
L.D. Faddeev and S.L. Shatashvili, Realization of the Schwinger term in the Gauss law and the possibility of correct quantization of a theory with anomalies, Phys. Lett.B 167 (1986) 225.
I. Bengtsson and A. Kleppe, On chiral p forms, Int. J. Mod. Phys.A 12 (1997) 3397 [hep-th/9609102] [INSPIRE].
N. Berkovits, Manifest electromagnetic duality in closed superstring field theory, Phys. Lett.B 388 (1996) 743 [hep-th/9607070] [INSPIRE].
N. Berkovits, Local actions with electric and magnetic sources, Phys. Lett.B 395 (1997) 28 [hep-th/9610134] [INSPIRE].
D. Belov and G.W. Moore, Holographic action for the self-dual field, hep-th/0605038 [INSPIRE].
E. Witten, Five-brane effective action in M-theory, J. Geom. Phys.22 (1997) 103 [hep-th/9610234] [INSPIRE].
E. Witten, Duality relations among topological effects in string theory, JHEP05 (2000) 031 [hep-th/9912086] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, Space-time symmetries in duality symmetric models, in the proceedings of Gauge theories, applied supersymmetry, quantum gravity July 10–14, Leuven, Belgium (1995), hep-th/9509052 [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].
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, JHEP07 (1998) 017 [hep-th/9806140] [INSPIRE].
G. Dall’Agata, K. Lechner and M. Tonin, Action for IIB supergravity in 10-dimensions, Lect. Notes Phys.525 (1999) 416 [hep-th/9812170] [INSPIRE].
I. Bandos, On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology, JHEP08 (2014) 048 [arXiv:1406.5185] [INSPIRE].
C. Sämann and M. Wolf, On twistors and conformal field theories from six dimensions, J. Math. Phys.54 (2013) 013507 [arXiv:1111.2539] [INSPIRE].
L.J. Mason, R.A. Reid-Edwards and A. Taghavi-Chabert, Conformal field theories in six-dimensional twistor space, J. Geom. Phys.62 (2012) 2353 [arXiv:1111.2585] [INSPIRE].
K.-W. Huang, R. Roiban and A.A. Tseytlin, Self-dual 6d 2-form fields coupled to non-abelian gauge field: quantum corrections, JHEP06 (2018) 134 [arXiv:1804.05059] [INSPIRE].
K. Mkrtchyan, On covariant actions for chiral p-forms, JHEP12 (2019) 076 [arXiv:1908.01789] [INSPIRE].
G. Buratti, K. Lechner, and L. Melotti, Self-interacting chiral p-forms in higher dimensions, Phys. Lett.B 798 (2019) 135018 [arXiv:1909.10404].
B. Jurčo et al., L∞-algebras, the BV formalism and classical fields, Fortsch. Phys.67 (2019) 1910025 [arXiv:1903.02887] [INSPIRE].
C. Sämann and L. Schmidt, Towards an M 5-brane model II: metric string structures, arXiv:1908.08086 [INSPIRE].
P.K. Townsend, Manifestly Lorentz invariant chiral boson action, Phys. Rev. Lett.124 (2020) 101604 [arXiv:1912.04773] [INSPIRE].
A. Sen, Covariant action for type IIB supergravity, JHEP07 (2016) 017 [arXiv:1511.08220] [INSPIRE].
A. Sen, Self-dual forms: action, Hamiltonian and compactification, J. Phys.A 53 (2020) 084002 [arXiv:1903.12196] [INSPIRE].
E. Witten, Geometric Langlands from six dimensions, arXiv:0905.2720 [INSPIRE].
P.S. Howe, N.D. Lambert and P.C. West, Classical M-five-brane dynamics and quantum N = 2 Yang-Mills, Phys. Lett.B 418 (1998) 85 [hep-th/9710034] [INSPIRE].
N.D. Lambert and P.C. West, Gauge fields and M five-brane dynamics, Nucl. Phys.B 524 (1998) 141 [hep-th/9712040] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys.B 426 (1994) 19 [Erratum ibid.B 430 (1994) 485] [hep-th/9407087] [INSPIRE].
N. Lambert and C. Papageorgakis, Nonabelian (2, 0) tensor multiplets and 3-algebras, JHEP08 (2010) 083 [arXiv:1007.2982] [INSPIRE].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys.B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys.B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
S.A. Cherkis and J.H. Schwarz, Wrapping the M-theory five-brane on K 3, Phys. Lett.B 403 (1997) 225 [hep-th/9703062] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys.B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
E.P. Verlinde, Global aspects of electric-magnetic duality, Nucl. Phys.B 455 (1995) 211 [hep-th/9506011] [INSPIRE].
N.S. Manton, A remark on the scattering of BPS monopoles, Phys. Lett.110B (1982) 54 [INSPIRE].
A. Mikhailov, BPS states and minimal surfaces, Nucl. Phys.B 533 (1998) 243 [hep-th/9708068] [INSPIRE].
J.H. Schwarz and A. Sen, Duality symmetric actions, Nucl. Phys.B 411 (1994) 35 [hep-th/9304154] [INSPIRE].
R. Medina and N. Berkovits, Pasti-Sorokin-Tonin actions in the presence of sources, Phys. Rev.D 56 (1997) 6388 [hep-th/9704093] [INSPIRE].
N. Rosen, General relativity and flat space. I, Phys. Rev.57 (1940) 147 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 2003.10567
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Andriolo, E., Lambert, N. & Papageorgakis, C. Geometrical aspects of an Abelian (2,0) action. J. High Energ. Phys. 2020, 200 (2020). https://doi.org/10.1007/JHEP04(2020)200
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2020)200