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
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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
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