Abstract
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
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References
P.-M. Ho and Y. Matsuo, Note on non-Abelian two-form gauge fields, JHEP 09 (2012) 075 [arXiv:1206.5643] [INSPIRE].
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
E. Witten, Some comments on string dynamics, in the proceedings of the Future perspectives in string theory (STRINGS 95), March 13-18, Los Angeles, U.S.A. (1995), hep-th/9507121 [INSPIRE].
E. Witten, Geometric Langlands from six dimensions, arXiv:0905.2720 [INSPIRE].
N. Lambert and C. Papageorgakis, Nonabelian (2, 0) tensor multiplets and 3-algebras, JHEP 08 (2010) 083 [arXiv:1007.2982] [INSPIRE].
F. Bonetti, T.W. Grimm and S. Hohenegger, Non-abelian tensor towers and (2, 0) superconformal theories, JHEP 05 (2013) 129 [arXiv:1209.3017] [INSPIRE].
C.-S. Chu and S.-L. Ko, Non-abelian action for multiple five-branes with self-dual tensors, JHEP 05 (2012) 028 [arXiv:1203.4224] [INSPIRE].
P.-M. Ho and Y. Matsuo, Aspects of effective theory for multiple M 5-branes compactified on circle, JHEP 12 (2014) 154 [arXiv:1409.4060] [INSPIRE].
P. Ritter, C. Sämann and L. Schmidt, Generalized higher gauge theory, JHEP 04 (2016) 032 [arXiv:1512.07554] [INSPIRE].
P.-M. Ho, K.-W. Huang and Y. Matsuo, A non-abelian self-dual gauge theory in 5 + 1 dimensions, JHEP 07 (2011) 021 [arXiv:1104.4040] [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, D.P. Sorokin and M. Tonin, On Lorentz invariant actions for chiral p-forms, Phys. Rev. D 55 (1997) 6292 [hep-th/9611100] [INSPIRE].
M. Henneaux and B. Knaepen, All consistent interactions for exterior form gauge fields, Phys. Rev. D 56 (1997) 6076 [hep-th/9706119] [INSPIRE].
X. Bekaert, M. Henneaux and A. Sevrin, Chiral forms and their deformations, Commun. Math. Phys. 224 (2001) 683 [hep-th/0004049] [INSPIRE].
J.C. Baez and J. Huerta, An invitation to higher gauge theory, Gen. Rel. Grav. 43 (2011) 2335 [arXiv:1003.4485] [INSPIRE].
J.C. Baez and A.S. Crans, Higher-dimensional algebra VI: Lie 2-algebras, Theor. Appl. Categor. 12 (2004) 492 [math/0307263] [INSPIRE].
S. Palmer, Higher gauge theory and M-theory, arXiv:1407.0298 [INSPIRE].
P. van Nieuwenhuizen, Free graded differential superalgebras, in 11th International Colloquium on Group-theoretical Methods in Physics, August 31-September 4, Istanbul, Turkey (1982).
R. D’Auria, P. Fré, P.K. Townsend and P. van Nieuwenhuizen, Invariance of actions, rheonomy and the new minimal N = 1 supergravity in the group manifold approach, Annals Phys. 155 (1984) 423 [INSPIRE].
M. Bojowald, A. Kotov and T. Strobl, Lie algebroid morphisms, Poisson σ-models and off-shell closed gauge symmetries, J. Geom. Phys. 54 (2005) 400 [math/0406445] [INSPIRE].
S. Lavau, H. Samtleben and T. Strobl, Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions, J. Geom. Phys. 86 (2014) 497 [arXiv:1403.7114] [INSPIRE].
M. Grützmann and T. Strobl, General Yang-Mills type gauge theories for p-form gauge fields: from physics-based ideas to a mathematical framework or From Bianchi identities to twisted Courant algebroids, Int. J. Geom. Meth. Mod. Phys. 12 (2014) 1550009 [arXiv:1407.6759] [INSPIRE].
A.S. Schwarz, Geometry of Batalin-Vilkovisky quantization, Commun. Math. Phys. 155 (1993) 249 [hep-th/9205088] [INSPIRE].
A.S. Schwarz, Semiclassical approximation in Batalin-Vilkovisky formalism, Commun. Math. Phys. 158 (1993) 373 [hep-th/9210115] [INSPIRE].
L. Castellani, R. D’Auria and P. Fré, Supergravity and superstrings, volumes 1-3, World Scientific, Sincapore (1991).
D. Fiorenza, U. Schreiber and J. Stasheff, Čech cocycles for differential characteristic classes: an ∞-Lie theoretic construction, Adv. Theor. Math. Phys. 16 (2012) 149 [arXiv:1011.4735] [INSPIRE].
T. Bessho, M.A. Heller, N. Ikeda and S. Watamura, Topological membranes, current algebras and H-flux-R-flux duality based on Courant algebroids, JHEP 04 (2016) 170 [arXiv:1511.03425] [INSPIRE].
M. Alexandrov, M. Kontsevich, A. Schwartz and O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Mod. Phys. A 12 (1997) 1405 [hep-th/9502010] [INSPIRE].
N. Ikeda, Lectures on AKSZ sigma models for physicists, arXiv:1204.3714 [INSPIRE].
Z.-J. Liu, A. Weinstein and P. Xu, Manin triples for Lie bialgebroids, J. Diff. Geom. 45 (1997) 547 [dg-ga/9508013] [INSPIRE].
D. Roytenberg, Courant algebroids, derived brackets and even symplectic supermanifolds, Ph.D. Thesis, University of California, Berkeley, U.S.A. (1999), math/9910078.
J.C. Baez, Higher Yang-Mills theory, hep-th/0206130 [INSPIRE].
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Carow-Watamura, U., Heller, M.A., Ikeda, N. et al. Higher gauge theories from Lie n-algebras and off-shell covariantization. J. High Energ. Phys. 2016, 125 (2016). https://doi.org/10.1007/JHEP07(2016)125
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DOI: https://doi.org/10.1007/JHEP07(2016)125