Graphical classification of global SO(n) invariants and independent general invariants

Journal of Mathematical Physics

Volumn 38, Issue 12, 1997, Pages 6475-6521

  Ichinose, Shoichi ^a,b   Ikeda, Noriaki ^c  

^a UNIVERSITY OF SHIZUOKA   (Japan)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031505368     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532183     Document Type: Article

References (22)

1. S. A. Fulling, R. C. King, B. G. Wybourne, and C. J. Cummins, Class. Quantum Grav. 9, 1151 (1992).
2. S. Ichinose, Class. Quantum Grav. 12, 1021 (1995).
3. 2 dimension in any space-dimension. We call it the mass-dimension when necessary.
4. The relations come from "Type 2" symmetry in Sec. II of Ref. 2. Note that the statement does not apply to those relations which come from "Type 3" symmetry. It is the symmetry depending on each dimension.
5. S. Ichinose and N. Ikeda, University of Shizuoka. US-96-03, 1996, hep-th/9609013, "Weak field expansion of gravity and graphical representation" (preprint).
6. bcn[ ] imply a general element of an array:bcn [0],...,bcn[l]. The same thing is for vcn[ ]. All quantities of indices are underlined in the following.
7. i.
8. As a general tendency, we see, from the result of Appendix B, the weight of a graph decreases as its suffix-loop no (l) increases.
9. αβ of Fig. 1.
10. H. Donnelly, Indiana Univ. Math. J. 24, 603 (1974).
11. P. B. Gilkey, J. Diff. Geom. 10, 601 (1975).
12. L. Bonora, P. Pasti, and M. Bregola, Class. Quantum Grav. 3, 635 (1986).
13. Note that in Ref. 2, total derivative terms are neglected, whereas they are not neglected in the present case.
14. 5. The one given in (24) of the present text is the right one.]
15. M. H. Goroff and A. Sagnotti, Nucl. Phys. B 266, 709 (1986).
16. S. Deser and A. Schwimmer, Phys. Lett. B 309, 279 (1993).
17. R. Kallosh, Nucl. Phys. B 78, 293 (1974).
18. P. van Nieuwenhuizen and C. C. Wu, J. Math. Phys. 18, 182 (1977).
19. The space-dimension is taken to be 2 in order to obtain the mass-dimensions of the couplings, (48), without introducing any additional mass parameters. Note that the present purpose is the graph classification. There the important thing is the topological structure of graphs. The space-dimension of the field theory is irrelevant.
20. S. Ichinose, University of Shizuoka, US-96-05, 1996, hep-th/9609014, Int. J. Mod. Phys. C (to be published) "New algorithm for tensor calculation in field thories" (preprint).
21. S. Ichinose and N. Ikeda, hep-th/9509073; Phys. Rev. D 53, 5932 (1996).
22. Among 90 terms listed in Appendix A, G3 and G13 only have the crossing number 3. As for the definition of the crossing number, see Sec. V B.