Abstract
We construct infinite-dimensional symmetries of the two dimensional equation which results from the dimensional reduction of the self-duality condition in (2, 2) signature space-time. These are symmetries of the dimensionally reduced Chalmers-Siegel action and so hold off-shell.
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References
N.J. Hitchin, The Self-Duality equations on a Riemann surface, Proc. Lond. Math. Soc. 55 (1987) 59 [SPIRES].
M.A.C. Kneipp, Hitchin’s equations and integrability of BPS Z(N) strings in Yang-Mills theories, JHEP 11 (2008) 049 [arXiv:0801.0720] [SPIRES].
M. Bochicchio, Solving loop equations by Hitchin systems via holography in large-N QCD 4, JHEP 06 (2003) 026 [hep-th/0305088] [SPIRES].
T.A. Ivanova and A.D. Popov, Self-Dual Yang-Mills fields and Nahm’s equations, Lett. Math. Phys. 23 (1991) 29 [SPIRES].
R.A. Mosna and M. Jardim, Nonsingular solutions of Hitchin’s equations for noncompact gauge groups, Nonlinearity 20 (2007) 1893 [math-ph/0609001] [SPIRES].
P. Mansfield and A. Wardlow, Infinite Dimensional Symmetries of Self-Dual Yang-Mills, JHEP 08 (2009) 072 [arXiv:0903.2042] [SPIRES].
G. Chalmers and W. Siegel, The self-dual sector of QCD amplitudes, Phys. Rev. D 54 (1996) 7628 [hep-th/9606061] [SPIRES].
L.A. Dolan, A new symmetry group of real self-dual Yang-Mills, Phys. Lett. B 113 (1982) 387 [SPIRES].
L.-L. Chau, M.-l. Ge and Y.-s. Wu, The Kac-Moody algebra in the self-dual Yang-Mills equation, Phys. Rev. D 25 (1982) 1086 [SPIRES].
A.D. Popov and C.R. Preitschopf, Conformal Symmetries of the Self-Dual Yang-Mills Equations, Phys. Lett. B 374 (1996) 71 [hep-th/9512130] [SPIRES].
A.D. Popov, Self-dual Yang-Mills: Symmetries and moduli space, Rev. Math. Phys. 11 (1999) 1091 [hep-th/9803183] [SPIRES].
T.A. Ivanova and O. Lechtenfeld, Hidden symmetries of the open N = 2 string, Int. J. Mod. Phys. A 16 (2001) 303 [hep-th/0007049] [SPIRES].
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [SPIRES].
R. Boels, L.J. Mason and D. Skinner, From Twistor Actions to MHV Diagrams, Phys. Lett. B 648 (2007) 90 [hep-th/0702035] [SPIRES].
F. A. Cachazo, Mhv diagrams and tree amplitudes of gluons, in PoS jhw2004 (2004) 015 [SPIRES].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [SPIRES].
J.H. Ettle and T.R. Morris, Structure of the MHV-rules Lagrangian, JHEP 08 (2006) 003 [hep-th/0605121] [SPIRES].
P. Mansfield, The Lagrangian origin of MHV rules, JHEP 03 (2006) 037 [hep-th/0511264] [SPIRES].
H. Feng and Y.-t. Huang, MHV lagrangian for N = 4 super Yang-Mills, JHEP 04 (2009) 047 [hep-th/0611164] [SPIRES].
A. Wardlow, Symmetries of the Self-Dual Sector of N = 4 Super Yang-Mills on the Light Cone, JHEP 11 (2009) 106 [arXiv:0909.4447] [SPIRES].
E. Brézin, C. Itzykson, J. Zinn-Justin and J.B. Zuber, Remarks About the Existence of Nonlocal Charges in Two-Dimensional Models, Phys. Lett. B 82 (1979) 442 [SPIRES].
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ArXiv ePrint: 1011.0301
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Mansfield, P., Wardlow, A. Symmetries of self-dual Yang-Mills equations dimensionally reduced from (2, 2) space-time. J. High Energ. Phys. 2011, 97 (2011). https://doi.org/10.1007/JHEP01(2011)097
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DOI: https://doi.org/10.1007/JHEP01(2011)097