Abstract
We generalize a recently developed ADHMN-like construction of self-dual string solitons using loop space. In particular, we present two extensions: The first one starts from solutions to the Basu-Harvey equation for the ABJM model, the second one starts from solutions to a corresponding BPS equation in an \( \mathcal{N} = 2 \) supersymmetric deformation of the BLG model. Both constructions yield solutions to the abelian and the nonabelian self-dual string equation transgressed to loop space. These equations might provide an effective description of M2-branes suspended between M5-branes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].
A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [SPIRES].
S. Mukhi and C. Papageorgakis, M2 to D2, JHEP 05 (2008) 085 [arXiv:0803.3218] [SPIRES].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].
N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [SPIRES].
E. Corrigan and P. Goddard, Construction of instanton and monopole solutions and reciprocity, Ann. Phys. 154 (1984) 253 [SPIRES].
P.J. Braam and P. van Baal, Nahm’s transformation for instantons, Commun. Math. Phys. 122 (1989) 267 [SPIRES].
W. Nahm, A simple formalism for the BPS monopole, Phys. Lett. B 90 (1980) 413 [SPIRES].
W. Nahm, All selfdual multi-monopoles for arbitrary gauge groups, presented at Internation summer institute on theoretical physics, August 31–September 11, Freiburg, Germany (1981).
W. Nahm, The construction of all selfdual multi-monopoles by the ADHM method, talk at the Meeting on monopoles in quantum field theory, December 11–15, ICTP, Trieste (1981).
N.J. Hitchin, On the construction of monopoles, Commun. Math. Phys. 89 (1983) 145 [SPIRES].
A. Basu and J.A. Harvey, The M2–M5 brane system and a generalized Nahm’s equation, Nucl. Phys. B 713 (2005) 136 [hep-th/0412310] [SPIRES].
P.S. Howe, N.D. Lambert and P.C. West, The self-dual string soliton, Nucl. Phys. B 515 (1998) 203 [hep-th/9709014] [SPIRES].
A. Gustavsson, Selfdual strings and loop space Nahm equations, JHEP 04 (2008) 083 [arXiv:0802.3456] [SPIRES].
C. Sämann, Constructing self-dual strings, Commun. Math. Phys. 305 (2011) 513 [arXiv:1007.3301] [SPIRES].
S. Kawamoto and N. Sasakura, Open membranes in a constant C-field background and noncommutative boundary strings, JHEP 07 (2000) 014 [hep-th/0005123] [SPIRES].
E. Bergshoeff, D.S. Berman, J.P. van der Schaar and P. Sundell, A noncommutative M-theory five-brane, Nucl. Phys. B 590 (2000) 173 [hep-th/0005026] [SPIRES].
A. Gustavsson, The non-Abelian tensor multiplet in loop space, JHEP 01 (2006) 165 [hep-th/0512341] [SPIRES].
C. Papageorgakis and C. Sämann, The 3-Lie algebra (2, 0) tensor multiplet and equations of motion on loop space, JHEP 05 (2011) 099 [arXiv:1103.6192] [SPIRES].
N. Lambert and C. Papageorgakis, Nonabelian (2, 0) tensor multiplets and 3-algebras, JHEP 08 (2010) 083 [arXiv:1007.2982] [SPIRES].
J. Bagger and N. Lambert, Three-algebras and N = 6 Chern-Simons gauge theories, Phys. Rev. D 79 (2009) 025002 [arXiv:0807.0163] [SPIRES].
S.A. Cherkis and C. Sämann, Multiple M2-branes and generalized 3-Lie algebras, Phys. Rev. D 78 (2008) 066019 [arXiv:0807.0808] [SPIRES].
C.Sämann and R.J. Szabo, Branes, quantization and fuzzy spheres, PoS(CNCFG2010)005 [arXiv:1101.5987] [SPIRES].
D.-E. Diaconescu, D-branes, monopoles and Nahm equations, Nucl. Phys. B 503 (1997) 220 [hep-th/9608163] [SPIRES].
D. Tsimpis, Nahm equations and boundary conditions, Phys. Lett. B 433 (1998) 287 [hep-th/9804081] [SPIRES].
N.R. Constable, R.C. Myers and O. Tafjord, The noncommutative bion core, Phys. Rev. D 61 (2000) 106009 [hep-th/9911136] [SPIRES].
P. Rossi, Exact results in the theory of nonabelian magnetic monopoles, Phys. Rept. 86 (1982) 317 [SPIRES].
M. Adler and P. van Moerbeke, Linearization of hamiltonian systems, Jacobi varieties and representation theory, Adv. Math. 38 (1980) 318.
L. Takhtajan, On foundation of the generalized Nambu mechanics (second version), Commun. Math. Phys. 160 (1994) 295 [hep-th/9301111] [SPIRES].
D. Nogradi, M2-branes stretching between M5-branes, JHEP 01 (2006) 010 [hep-th/0511091] [SPIRES].
M. Pawellek, On a generalization of Jacobi’s elliptic functions and the double sine-Gordon kink chain, arXiv:0909.2026 [SPIRES].
J.-L. Brylinski, Loop spaces, characteristic classes and geometric quantization, Birkhäuser, Boston U.S.A. (2007).
S. Cherkis, V. Dotsenko and C. Sämann, On superspace actions for multiple M2-branes, metric 3-algebras and their classification, Phys. Rev. D 79 (2009) 086002 [arXiv:0812.3127] [SPIRES].
J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, A massive study of M2-brane proposals, JHEP 09 (2008) 113 [arXiv:0807.1074] [SPIRES].
S. Terashima, On M5-branes in N = 6 membrane action, JHEP 08 (2008) 080 [arXiv:0807.0197] [SPIRES].
K. Hanaki and H. Lin, M2–M5 systems in N = 6 Chern-Simons theory, JHEP 09 (2008) 067 [arXiv:0807.2074] [SPIRES].
V.T. Filippov, n-Lie algebras, Sib. Mat. Zh. 26 (1985) 126.
P. de Medeiros, J. Figueroa-O’Farrill, E. Mendez-Escobar and P. Ritter, On the Lie-algebraic origin of metric 3-algebras, Commun. Math. Phys. 290 (2009) 871 [arXiv:0809.1086] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Palmer, S., Sämann, C. Constructing generalized self-dual strings. J. High Energ. Phys. 2011, 8 (2011). https://doi.org/10.1007/JHEP10(2011)008
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2011)008