Predrag 8 jul 2003 QUESTIONS, REFS INCORPORATED Date: Mon, 21 Aug 95 From: Steve Giddings Dear Predrag: When I said that I thought we could figure out the independent invariants, I was alluding to the case of E6. It looked like by the assumption that only the d's are primitive, and also by the assumption that any loop diagrams are expressible in terms of tree diagrams, that one could make a fair amount of progress in getting the independent invariants. Having looked at it further, it seems to be a little more complicated. If there is some chance that the loop diagrams can't be reduced without more primitive invariants that would certainly make life even more complicated ... if you can't prove it, is there at least good evidence for it? As for references, yours and the one by Behrends et al were really the most useful. For exceptional groups other references I have used is that old preprint by Ramond, Slansky's physics report, and some material in Green, Schwarz, and Witten's string theory book. I'm not aware of much else, so if you have any other pointers that would be helpful. Also a paper by Kephart and Vaughn, Tensor methods in E6, Ann. Phys. 145 (1983) 162. (PC: THIS ONE IS REFERENCED) I suppose that a spires search might turn up a little more. The paper that we wrote on these supersymmetric gauge theories and in particular on G2 is on the Los Alamos preprint archive, hep-th/9506196. (PC: THIS ONE IS REFERENCED) If you can't easily get I can send a tex file. With best regards, Steve Giddings Date: Fri, 18 Aug 1995 From: Steve Giddings Subject: Re: exceptional groups Dear Predrag: Ann Nelson, Pierre Ramond, and I are continuing to investigate some aspects of supersymmetric models based on exceptional groups. I did finally get volume I of your book, but it has become clear that it would be useful to find more on the other exceptional groups. Is there any way we could get a copy of the relevant material? In particular we are interested in the catalog of independent invariants that can be formed from the primitive invariants. (I believe I know how to figure this out in some cases, but if you've already done it that might be simpler.) I am beginning to appreciate the power of bird tracks -- they're pretty clever. But, I have a general question for you: how does one know that one has found all the primitive invariants? For example, suppose I claim to have a list of them. Then how do I know that some complicated loop diagram (or even the gluon projection operator) doesn't require additional primitive invariants in order to be decomposable in terms of tree diagrams? Finally, you state in your old Phys Rev paper (Group theory for Feynman diagrams ...) that the only relation among the primitive invariants of E6 is the Springer relation, and cite unpublished work. I would be most curious to know how you prove that. With best regards, Steve Giddings ---------------------------------------------------------------------- Steve Giddings | Associate Profesor Department of Physics | phone: (805) 893-4750 University of California | fax: (805) 893-2902 Santa Barbara, CA 93106 | internet: giddings@denali.physics.ucsb.edu ----------------------------------------------------------------------