Abstract
We consider the (2,0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. The naive invariance of the model under such transformations is however explicitly broken by anomalies: The electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet suffers from a classical anomaly, and there is also a one-loop quantum anomaly from the chiral fermions on the string world-sheet. Both of these contributions are proportional to the Euler class of the normal bundle of the string world-sheet, and consistency of the model requires that they cancel. This imposes strong constraints on possible models, which are found to obey an ADE-classification. We then consider the decoupled world-sheet theory that describes low-energy fluctuations (compared to the scale set by the string tension) around a configuration with a static, straight string. The anomaly structure determines this to be a supersymmetric version of the level one Wess-Zumino-Witten model based on the group
Similar content being viewed by others
References
Arvidsson, P., Flink, E., Henningson, M.: The (2, 0) supersymmetric theory of tensor multiplets and self-dual strings in six dimensions. JHEP 0405, 048 (2004)
Witten, E.: Quantum field theory and the jones polynomial. Commun. Math. Phys. 121, 351 (1989)
Freed, D., Harvey, J.A., Minasian, R., Moore, G.W.: Gravitational anomaly cancellation for M-theory fivebranes. Adv. Theor. Math. Phys. 2, 601 (1998)
Brax, P., Mourad, J.: Open supermembranes coupled to M-theory five-branes. Phys. Lett. B 416, 295 (1998)
Boyarsky, A., Harvey, J.A., Ruchayskiy, O.: A toy model of the M5-brane: Anomalies of monopole strings in five dimensions. Annals Phys. 301, 1 (2002)
Witten, E.: Some comments on string dynamics. http://arxiv.org/list/hep-th/9507121, 1995
Atiyah, M.F., Singer, I.M.: Dirac operators coupled to vector potentials. Proc. Nat. Acad. Sci. 81, 2597 (1984)
Zumino, B.: In: Relativity, Groups, and Topology II, B.S. deWitt, R. Stora (eds.), Amsterdam: North Holland, 1984
Bott, R., Tu, L.W.: Differential Forms in Algebraic Topology. Berlin-Heidelberg-New York: Springer Verlag, 1982
Madsen, I., Tornehave, J.: From Calculus to Cohomology: de Rham cohomology and characteristic classes. Cambridge: Cambridge University Press, 1997
Witten, E.: Five-brane effective action in M-theory. J. Geom. Phys. 22, 103 (1997)
Henningson, M.: The quantum Hilbert space of a chiral two-form in d = 5+1 dimensions. JHEP 0203, 021 (2002)
Deser, S., Gomberoff, A., Henneaux, M., Teitelboim, C.: p-brane dyons and electric-magnetic duality. Nucl. Phys. B 520, 179 (1998)
Witten, E.: Nonabelian bosonization in two dimensions. Commun. Math. Phys. 92, 455 (1984)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by N.A. Nekrasov
Rights and permissions
About this article
Cite this article
Henningson, M. Self-Dual Strings in Six Dimensions: Anomalies, the ADE-Classification, and the World-Sheet WZW-Model. Commun. Math. Phys. 257, 291–302 (2005). https://doi.org/10.1007/s00220-005-1324-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-005-1324-7