Abstract
Integral invariants in maximally supersymmetric Yang-Mills theories are discussed in spacetime dimensions 4 ≤ D ≤ 10 for SU(k) gauge groups. It is shown that, in addition to the action, there are three special invariants in all dimensions. Two of these, the single-and double-trace F 4 invariants, are of Chern-Simons type in D = 9, 10 and BPS type in D ≤ 8, while the third, the double-trace of two derivatives acting on F 4, can be expressed in terms of a gauge-invariant super-D -form in all dimensions. We show that the super-ten-forms for D = 10 F 4 invariants have interesting cohomological properties and we also discuss some features of other invariants, including the single-trace d 2 F 4, which has a special form in D = 10. The implications of these results for ultra-violet divergences are discussed in the framework of algebraic renormalisation.
Article PDF
Similar content being viewed by others
References
P.S. Howe, K.S. Stelle and P.K. Townsend, Superactions, Nucl. Phys. B 191 (1981) 445 [SPIRES].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N =2 matter, Yang-Mills and supergravity theories in harmonic superspace, Class. Quant. Grav. 1 (1984) 469 [SPIRES].
J.M. Drummond, P.J. Heslop, P.S. Howe and S.F. Kerstan, Integral invariants in N =4 SYM and the effective action for coincident D-branes, JHEP 08 (2003) 016 [hep-th/0305202] [SPIRES].
G. Bossard, P.S. Howe and K.S. Stelle, A note on the UV behaviour of maximally supersymmetric Yang-Mills theories, Phys. Lett. B 682 (2009) 137 [arXiv:0908.3883] [SPIRES].
P.S. Howe, H. Nicolai and A. Van Proeyen, Auxiliary fields and a superspace Lagrangian for linearized ten-dimensional supergravity, Phys. Lett. B 112 (1982) 446 [SPIRES].
T. Voronov, Geometric integration theory on supermanifolds, Sov. Sci. Rev. C. Math. Phys. 9 (1992) 1.
S.J. Gates Jr., Ectoplasm has no topology: the prelude, hep-th/9709104 [SPIRES].
S.J. Gates Jr., M.T. Grisaru, M.E. Knutt-Wehlau and W. Siegel, Component actions from curved superspace: normal coordinates and ectoplasm, Phys. Lett. B 421 (1998) 203 [hep-th/9711151] [SPIRES].
N. Berkovits and P.S. Howe, The cohomology of superspace, pure spinors and invariant integrals, JHEP 06 (2008) 046 [arXiv:0803.3024] [SPIRES].
L. Bonora, P. Pasti and M. Tonin, Superspace formulation of 10-D SUGRA+SYM theory a la Green-Schwarz, Phys. Lett. B 188 (1987) 335 [SPIRES].
M. Cederwall, B.E.W. Nilsson and D. Tsimpis, Spinorial cohomology and maximally supersymmetric theories, JHEP 02 (2002) 009 [hep-th/0110069] [SPIRES].
P.S. Howe and D. Tsimpis, On higher-order corrections in M-theory, JHEP 09 (2003) 038 [hep-th/0305129] [SPIRES].
N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059 [SPIRES].
P.S. Howe, Pure spinors lines in superspace and ten-dimensional supersymmetric theories, Phys. Lett. B 258 (1991) 141 [Addendum ibid. B 259 (1991) 511] [SPIRES].
P.S. Howe, Pure spinors, function superspaces and supergravity theories in ten-dimensions and eleven-dimensions, Phys. Lett. B 273 (1991) 90 [SPIRES].
L. Bonora, P. Pasti and M. Tonin, Chiral anomalies in higher dimensional supersymmetric theories, Nucl. Phys. B 286 (1987) 150 [SPIRES].
P.S. Howe, O. Raetzel and E. Sezgin, On brane actions and superembeddings, JHEP 08 (1998) 011 [hep-th/9804051] [SPIRES].
M. Movshev and A. Schwarz, Supersymmetric deformations of maximally supersymmetric gauge theories. I, arXiv:0910.0620 [SPIRES].
P. Koerber and A. Sevrin, The non-abelian D-brane effective action through order α′4, JHEP 10 (2002) 046 [hep-th/0208044] [SPIRES].
P.S. Howe, U. Lindström and L. Wulff, D = 10 supersymmetric Yang-Mills theory at α′4, JHEP 07 (2010) 028 [arXiv:1004.3466] [SPIRES].
S. Deser and U. Lindström, Extended supersymmetry invariants by dimensional reduction, Phys. Lett. B 90 (1980) 68 [SPIRES].
G. Bossard, P.S. Howe and K.S. Stelle, The ultra-violet question in maximally supersymmetric field theories, Gen. Rel. Grav. 41 (2009) 919 [arXiv:0901.4661] [SPIRES].
P. Breitenlohner, D. Maison and K.S. Stelle, Anomalous dimensions and the Adler-Bardeen theorem in supersymmetric Yang-Mills theories, Phys. Lett. B 134 (1984) 63 [SPIRES].
N. Marcus and A. Sagnotti, The ultraviolet behavior of N =4 Yang-Mills and the power counting of extended superspace, Nucl. Phys. B 256 (1985) 77 [SPIRES].
Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [hep-th/9802162] [SPIRES].
Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The complete four-loop four-point amplitude in N =4 super-Yang-Mills theory, Phys. Rev. D 82 (2010) 125040 [arXiv:1008.3327] [SPIRES].
N. Berkovits, M.B. Green, J.G. Russo and P. Vanhove, Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory, JHEP 11 (2009) 063 [arXiv:0908.1923] [SPIRES].
J. Bjornsson and M.B. Green, 5 loops in 24/5 dimensions, JHEP 08 (2010) 132 [arXiv:1004.2692] [SPIRES].
P.J. Heslop and P.S. Howe, A note on composite operators in N =4 SYM, Phys. Lett. B 516 (2001) 367 [hep-th/0106238] [SPIRES].
G. Arutyunov, S. Frolov and A.C. Petkou, Operator product expansion of the lowest weight CPOs in N =4 SYM(4) at strong coupling, Nucl. Phys. B 586 (2000) 547 [Erratum ibid. B 609 (2001) 539] [hep-th/0005182] [SPIRES].
B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial non-renormalisation of the stress-tensor four-point function in N =4 SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint:1012.3142
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bossard, G., Howe, P.S., Lindström, U. et al. Integral invariants in maximally supersymmetric Yang-Mills theories. J. High Energ. Phys. 2011, 21 (2011). https://doi.org/10.1007/JHEP05(2011)021
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2011)021