Thom Curtright

University of Miami

Talk presented at BASIC 2019, Saturday, 12 January.

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Albert De Roeck briefly described the vacuum stability issue in his talk last Tuesday. This brought to mind my 1977 Caltech PhD thesis ...

wherein

"Renormalization group analysis is used to show the supersymmetric point in the effective coupling constant space is an unstable fixed point for several model gauge theories. The physical significance of this result is discussed in terms of the stability of the semiclassical ground state." This work extended ideas in an earlier paper ...

In fact, if you search InSPIRE for title words "vacuum", "stability", and "supersymmetry" before the year 2000, this is the only paper that comes up. My thesis dealt with "toy" models, but I believe the essential idea applies to the standard model as well.

Under RG flow in terms of the scalar field expectation value, the effective potential evinces a stable vacuum iff the effective quartic scalar field couplings remain non-negative.

For a supersymmetric model this is guaranteed because the quartic scalar couplings are the squares of Yukawa and/or gauge couplings. More Reminiscences about the 20th century

Afshordi’stalk on Thursday provided an argument against having very high mass elementary particles, such as would appear along linearly rising Regge trajectories in string theory. Perhaps higher dimensions circumvent his argument. In any case, string theories in higher dimensions yield not only high mass excitations of the string, but in addition, they provide such states in the form of rather exotic rotation group representations – neither totally symmetric nor totally antisymmetric tensors. This brought to mind another problem that I worked on during the last century.

During my last several months as a Robert R. McCormick post-doctoral fellow from 1978-1980, at the Enrico Fermi Institute of the University of Chicago, I suppose out of early winter boredom, I was thinking about string theory.

In particular, I was thinking about the local ﬁelds that can couple to the string world- sheet, namely, the Kalb-Ramond ﬁeld and its higher-dimensional extensions.

1 I worked out an array of ghost ﬁelds for such antisymmetric tensors, including “ghosts for ghosts.” Cosmas Zachos then reminded me that Paul Townsend had given a talk about such things at the Stonybrook Supergravity Workshop, 27-29 September 1979. I looked up the paper corresponding to Paul’stalk and noticed some disparities between my results and his, so I wrote a letter to him. Paul wrote back to me, although nothing resulted directly from this correspondence, but I continued to think about the subject as a background mental thread.

Winter continued. I slugged through, traveling back and forth between Hyde Park and Homewood Illinois on the “Highliners” of the IC, now known as the Metra Electric main line.

2 Then in early 1980, for various other reasons that are no longer completely clear, it occurred to me to consider other gauge fields based not just on totally symmetric tensors (such as Einstein gravity) or totally antisymmetric tensors (such as the Kalb-Ramond field) but instead on tensors of any rank with arbitrary permutation symmetry on their indices. For the simplest example, there is the T[ab]c field. The free field formalism for such gauge fields was not very diffi cult to carry through, in principle, although it involved the usual débauche of indices.

I wrote this down in February 1980, sent it out as an EFI preprint, solely authored, and I submitted it to Physics Letters B.

3 4 I continued working on the subject in collaboration with Peter Freund, in an eﬀort to construct interacting theories for such ﬁelds, while waiting to hear from Physics Letters.

Eventually the journal responded.

The Referee rejected my solo paper.

The Editor sided with the referee.

5 On the other hand, the follow-up paper with Peter Freund was accepted by Nuclear Physics B without a fuss.

This was the second of two papers that I wrote with Peter. There was an opportunity to write a third paper, but that’sa story for another occasion.

6 I was greatly saddened when Peter died last year, on 6 March. I shall always remember him and our work together.

7 There is an evocative statement in this paper which I cannot resist bringing to your attention.

Now, Peter and I were certainly not thinking about axions when we wrote this paper. Nor was anyone else in April 1980, at least not in a cosmological setting. On the other 3 hand, if you set g = 1/m in the above, the resulting value for the mass is m 10− eV, which is on a par with the current best estimates for the axion mass. ∼

8 I mulled over the Referee’sremarks about my solo paper and, in the meantime, I moved to the University of Florida in Gainesville. (Enough of Chicago winters already!) I soon settled into a routine there. Time seemed to pass quickly.

But I did not forget about mixed-symmetry tensor ﬁelds. I wrote another paper that used such gauge ﬁelds in the context of supersymmetry, in twelve-dimensional spacetime, just for fun, mostly.

9 10 Alas, this paper was also panned by the referee and again it went unpublished. I was beginning to think that no one cared about such esoteric stuﬀ.

Nevertheless, this second rejected paper did aﬀord me an opportunity to express my earlier thoughts about ghost arrays. Those thoughts became more succinct after Brian Wybourne pointed out that what I was doing to determine the ghosts was, in fact, the group theoretic technique known as S-function division. I seem to recall that Brian did this while visiting the University of Florida following participation in a Coral Gables conference.

More time passed. I worked on sigma models, among other things. Then strings came back into vogue.

11 In 1985 I noticed a paper by Barton Zwiebach, who pointed out the curvature squared terms that arose in the eﬀective local ﬁeld theory produced by strings were topological (“Lovelock Lagrangian”in 4D spacetime) and gave no propagating modes.

That rang a bell. I seemed to me this was just a consequence of gauge invariance for the T[ab]c ﬁeld. This motivated me to look back at the referee’sreport and editorial comments on my solo paper. Remarkably, the editor had actually left the ball in my court by oﬀering to me an opportunity to refute the referee’srejection.

So I did. Adding a comment about and a citation of Zwiebach’spaper.

12 The (new) Editor then accepted the paper immediately!

Perhaps the ﬁnal outcome was also due, in part, to a change of editors (Kabir Georgi) during 1980-1985. →

13 So, it took almost six years from the date it was received at Physics Letters B (coinci- dentally, Einstein’s 101st birthday, as well as my youngest daughter’s day of birth) to the date it ﬁnally appeared in that journal. That length of time must be a record for a letters journal.

The paper was cited by no one but me during that submission = publication time period. ⇒

14 After it appeared in the journal, the paper was cited by others a few more times, but then faded away “exponentially”in a way typical of most papers.

15 Only to re-surface later, when it ﬁnally became of interest.

The current interest in the paper is as a model of “dual gravity” especially in higher dimensions.

For some recent discussions of all this, see here.

16 As I mentioned already, my other 1982 solo paper on exotic gauge ﬁelds was rejected and did not get published. Until last month ... some 36 years later!

OK, there are other things to do, so I’ll stop. Thank you for your time and attention.

But considering the various time-delays in publishing a couple of these papers, perhaps there is a take-away

Moral: Have respect for the comments of the referee, and the opinion of the editor, but of course, ultimately they may change their minds.

Usually their comments are professional and well-meaning. But occasionally they may seem a bit personal. In those situations, it is all the more important to put things in perspective.

Or as expressed in the cinema in a similar situation ...