Supertranslations to All Orders*

Author(s)
Rainer Dick

ABSTRACT

We calculate the transformation laws of the general linear superfield and chiral superfields under supertranslations to all orders in the translation parameters . We use the superfield formalism with complete expansions of the component fields in the coordinate shifts . The results show in particular how a general supertranslation transforms each component field of a supermultiplet into a complete superfield. The results also provide complete parametri-zations of orbits of component fields under supertranslations.

We calculate the transformation laws of the general linear superfield and chiral superfields under supertranslations to all orders in the translation parameters . We use the superfield formalism with complete expansions of the component fields in the coordinate shifts . The results show in particular how a general supertranslation transforms each component field of a supermultiplet into a complete superfield. The results also provide complete parametri-zations of orbits of component fields under supertranslations.

Cite this paper

nullR. Dick, "Supertranslations to All Orders*,"*Journal of Modern Physics*, Vol. 1 No. 1, 2010, pp. 59-66. doi: 10.4236/jmp.2010.11007.

nullR. Dick, "Supertranslations to All Orders*,"

References

[1] R. Clarkson, A. M. Ghezelbash and R. B. Mann, “New Reducible Membrane Solutions in D=11 Supergravity,” Journal of High Energy Physics, 2004.

[2] A. M. Ghezelbash, “Supergravity Solutions without Tri-Holomorphic U (1) Isometries,” Physical Review D, Vol. 78, 2008, p. 126002.

[3] de B. Wit, H. Nicolai and H. Samtleben “Gauged Super-gravities, Tensor Hierarchies and M-Theory,” Journal of High Energy Physics, Vol. 2, 2008, p. 044.

[4] G. Compère, K. Copsey, de S. Buyl and R. B. Mann, “Solitons in Five-Dimensional Minimal Supergravity: Local Charge, Exotic Ergoregions and Violations of the BPS Bound,” Journal of High Energy Physics, Vol. 12, No. 47, 2009, p. 46.

[5] U. Gran, J. Gutowski and G. Papadopoulos, “M-Theory Backgrounds with 30 Killing Spinors are Maximally Su-persymmetric,” ARXIV, 2010.

[6] R. Britto, E. Buchbinder, F. Cachazo and B. Feng, “One-Loop Amplitudes of Gluons in SQCD,” Physical Review D, Vol. 72, 2005, p. 27.

[7] R. Dick, “Implications of a Dilaton in Gauge Theory and Cosmology,”Fortschr der Physik, Vol. 45, 1997, pp. 537-587.

[8] R. Dick, “Heterotic String Dark Matter from the Graviton Multiplet,” Physics Letters B, Vol. 510, 2001, pp. 10-16.

[9] J. McDonald and N. Sahu, “Kev Warm Dark Matter Via the Supersymmetric Higgs Portal,” Physical Review D, Vol. 79, 2009, p. 6.

[10] A. A. Bytsenko, S. D. Odintsov and S. Zerbini, “The Effective Action in Gauged Supergravity on Hyperbolic Background and Induced Cosmological Constant,” Phys-ics Letters B, Vol. 336, 1994, pp. 355-361.

[11] E. Elizalde, S. Jhingan, S. Nojiri, S. D.Odintsov, M. Sami and I. Thongkool, “Dark Energy Generated From a (Su-per) String Effective Action with Higher Order Curvature Corrections and a Dynamical Dilaton,” European Physi-cal Journal C, Vol. 53, 2008, pp. 447-457.

[12] A. E. Nelson and N. Seiberg, “R-symmetry Breaking Versus Supersymmetry Breaking,” Nuclear Physics B, Vol. 416, 1994, 46-62.

[13] K. A. Intriligator, N. Seiberg and D. Shih, Supersym-metry Breaking, R-symmetry Breaking and Metastable Vacua,” Journal of High Energy Physics, Vol. 7, 2007, p. 19.

[14] M. Dine, G. Festuccia and Z. Komargodski, “A Bound on the Superpotential,” ARXIV, 2009, p. 2527.

[15] J. Wess and J. Bagger, “Supersymmetry and Supergravity, 2nd Edition,” Princeton University Press, 1992.

[16] J. Wess and B. Zumino, “Supergauge Transformations in four Dimensions,” Nuclear Physics B, Vol. 70, pp. 39-50; “A Lagrangian Model Invariant under Supergauge Transforma-tions,” Physics Letters B, Vol. 49, 1974, pp. 52-54.

[17] A. Salam and J. Strathdee, “Supergauge Transforma-tions,” Nuclear Physics B, Vol. 76, 1974, pp. 477-482.

[18] S. Ferrara, J. Wess and B. Zumino, “Supergauge Multi-plets and Superfields,” Physics Letters B, Vol. 51, 1974, pp. 239-241.

[19] A. Salam and J. Strathdee, “On Superfields and Fermi-Bose Symmetry,” Physical Review D, Vol. 11, 1975, pp. 1521-1535.

[1] R. Clarkson, A. M. Ghezelbash and R. B. Mann, “New Reducible Membrane Solutions in D=11 Supergravity,” Journal of High Energy Physics, 2004.

[2] A. M. Ghezelbash, “Supergravity Solutions without Tri-Holomorphic U (1) Isometries,” Physical Review D, Vol. 78, 2008, p. 126002.

[3] de B. Wit, H. Nicolai and H. Samtleben “Gauged Super-gravities, Tensor Hierarchies and M-Theory,” Journal of High Energy Physics, Vol. 2, 2008, p. 044.

[4] G. Compère, K. Copsey, de S. Buyl and R. B. Mann, “Solitons in Five-Dimensional Minimal Supergravity: Local Charge, Exotic Ergoregions and Violations of the BPS Bound,” Journal of High Energy Physics, Vol. 12, No. 47, 2009, p. 46.

[5] U. Gran, J. Gutowski and G. Papadopoulos, “M-Theory Backgrounds with 30 Killing Spinors are Maximally Su-persymmetric,” ARXIV, 2010.

[6] R. Britto, E. Buchbinder, F. Cachazo and B. Feng, “One-Loop Amplitudes of Gluons in SQCD,” Physical Review D, Vol. 72, 2005, p. 27.

[7] R. Dick, “Implications of a Dilaton in Gauge Theory and Cosmology,”Fortschr der Physik, Vol. 45, 1997, pp. 537-587.

[8] R. Dick, “Heterotic String Dark Matter from the Graviton Multiplet,” Physics Letters B, Vol. 510, 2001, pp. 10-16.

[9] J. McDonald and N. Sahu, “Kev Warm Dark Matter Via the Supersymmetric Higgs Portal,” Physical Review D, Vol. 79, 2009, p. 6.

[10] A. A. Bytsenko, S. D. Odintsov and S. Zerbini, “The Effective Action in Gauged Supergravity on Hyperbolic Background and Induced Cosmological Constant,” Phys-ics Letters B, Vol. 336, 1994, pp. 355-361.

[11] E. Elizalde, S. Jhingan, S. Nojiri, S. D.Odintsov, M. Sami and I. Thongkool, “Dark Energy Generated From a (Su-per) String Effective Action with Higher Order Curvature Corrections and a Dynamical Dilaton,” European Physi-cal Journal C, Vol. 53, 2008, pp. 447-457.

[12] A. E. Nelson and N. Seiberg, “R-symmetry Breaking Versus Supersymmetry Breaking,” Nuclear Physics B, Vol. 416, 1994, 46-62.

[13] K. A. Intriligator, N. Seiberg and D. Shih, Supersym-metry Breaking, R-symmetry Breaking and Metastable Vacua,” Journal of High Energy Physics, Vol. 7, 2007, p. 19.

[14] M. Dine, G. Festuccia and Z. Komargodski, “A Bound on the Superpotential,” ARXIV, 2009, p. 2527.

[15] J. Wess and J. Bagger, “Supersymmetry and Supergravity, 2nd Edition,” Princeton University Press, 1992.

[16] J. Wess and B. Zumino, “Supergauge Transformations in four Dimensions,” Nuclear Physics B, Vol. 70, pp. 39-50; “A Lagrangian Model Invariant under Supergauge Transforma-tions,” Physics Letters B, Vol. 49, 1974, pp. 52-54.

[17] A. Salam and J. Strathdee, “Supergauge Transforma-tions,” Nuclear Physics B, Vol. 76, 1974, pp. 477-482.

[18] S. Ferrara, J. Wess and B. Zumino, “Supergauge Multi-plets and Superfields,” Physics Letters B, Vol. 51, 1974, pp. 239-241.

[19] A. Salam and J. Strathdee, “On Superfields and Fermi-Bose Symmetry,” Physical Review D, Vol. 11, 1975, pp. 1521-1535.