Jeff Harvey’s comment that it was Larry Yaffe who brought news of the Green-Schwarz anomaly cancellation result to Witten gave me the idea of contacting Larry to get a first-hand recollection of what the reaction was at Aspen back in 1984. He was a junior faculty member at Princeton at the time and I knew him since I had been a grad student there and we both were working on lattice gauge theory. I’ve always respected his work and had noticed that he was someone who had never joined the string bandwagon, so I took the opportunity to ask him for his views on string theory. I think they’re pretty reasonable and reflect the views of a lot of the sensible people in the particle theory community these days. He agreed to let me post them here:

“What Jeff Harvey related is correct: I was at Aspen when Green and Schwarz presented their anomaly cancellation result, and I told Ed and others about it a few days later when I got back to Princeton. (Of course, John and Michael may have sent Ed a copy of their paper completely independently. I don’t know about that. But he hadn’t seen it yet when I was asked “what’s the news from Aspen?”.)

As for whether it was Michael Green or John Schwarz who gave the seminar in Aspen, I think it was John — but I’m not 100% sure. (The different talks I’ve heard from John and Michael get mixed up in my memory.)

Concerning reaction to the Green-Schwarz result, my recollection is that there was relatively little immediate buzz about it at Aspen. John had a fairly diffident style of presentation, and I don’t recall anyone jumping up and saying ‘this will change the course of physics!’. As best as I can reconstruct my own reaction, it seemed like a technically slick calculation and a nice result but it wasn’t, of course, addressing any of the conceptually hard questions about quantum gravity, and it seemed very far removed from the practical concerns of particle physics. But the reaction back in Princeton was different: Ed certainly saw the significance immediately and I think others did as well (certainly quicker than I did). I think the speed with which others in the particle theory community jumped into string theory had a lot to do with Ed’s involvement and proselytizing, but I expect that even without his involvement, interest in string theory would have steadily grown, albeit slower.

Since you asked about my views on string theory, I’ll try to give a summary. I think it is clear that:

String theory has been wildly over-hyped by some people. Even calling it a ‘theory’ is really a misnomer, given the lack of any adequate non-perturbative definition of string theory.

String theory has not yet made any convincing connection with the world we live in.

The predictive power (or the falsifiability) of string theory leaves much to be desired, especially in light of the emerging picture of the landscape of string theory vacua.

But at the same time:

The oft-repeated argument that string theory is the most promising framework we have for combining quantum mechanics and gravity remains true. Even though there is no real non-perturbative definition of string theory, I don’t think one can dispute this assertion. (As an aside, so-called “loop quantum gravity” is an interesting one-parameter family of statistical mechanics models, but has not been shown to have anything to do with gravity. Does it have a large-volume limit? Does it have long distance dynamics described by some effective field theory plus classical GR? Who knows…)

The perturbative consistency of string theory, combined with all the consistency checks of the (largely unproven) web of duality relations, are compelling hints that there is something deep and meaningful to string theory, even though it remains poorly understood.

String theory has made remarkable contributions to mathematics, allowing previously unforeseen connections to be found between very different areas. This has shown up in new (provable!) results in enumerative geometry, Gromov-Witten invariants, mirror symmetry, etc.

String theory has given partial insight into a few conceptual questions involving quantum gravity, such as (the absence of) black hole information loss, via the connection between BPS states and extremal black holes.

Improved understanding of gauge theories, especially strongly interacting theories, is emerging from string theory via “gauge-string” (or AdS/CFT) duality. Understanding is, as usual, frustratingly incomplete, but I think the message that non-gravitational ordinary field theories, and higher dimensional theories containing gravity, can be different representations of the *same* physics is revolutionary, and hints at some synthesis we are far from understanding. I think this point is already somewhat lessening the split in the theory community between ‘string theorists’ and ‘non-string theorists’.

Personally, I find this last point the most compelling reason to be interested in string theory, despite its lack of experimentally testable predictions. It is, of course, a matter of personal taste whether the ‘pro’ reasons to work on string theory outweigh the ‘cons’. Some people are comfortable working on an intellectual enterprise whose connection with the real world may never emerge during their lifetime. Some people aren’t — and that’s fine.”

I’m just correcting your misapprehension about the mentioned work. I’ve done the pro- anti- string stuff way too often to have any desire to get into it now.

Aaron,

I didn’t claim to have a very good understanding about algebraic geometry. This was how I understood one of Witten’s original papers, and he didn’t say which xxx-Witten invariant he described there.

But my main point was really that no mathematical discovery, however cool, is by itself evidence that this math has anything to do with physics. This is true for various invariants and dualities in algebraic geometry, as well as the higher-dimensional generalizations of Virasoro and affine algebras and their global group generalizations.

For me to accept something as physics, something more is needed: experimental support. It seems to me undeniable that the groups of diffeomorphisms and gauge transformations play a significant role in experimentally confirmed theories. I don’t see such a role for various dualities, Gromov-Witten invariants or mirror symmetries. But maybe its just me being too skeptical about hidden worlds.

You’re understanding isn’t correct. I think you might be getting at issues in topological field theory where the correlation functions are independent of the metric. Donaldson-Witten theory is a twisted N=2 SYM, for example.

Gromov-Witten theory, mirror symmetry and the like come from topolgical versions of string theory where the worldsheet CFT is twisted into a topological theory.

String theory has made remarkable contributions to mathematics, allowing previously unforeseen connections to be found between very different areas. This has shown up in new (provable!) results in enumerative geometry, Gromov-Witten invariants, mirror symmetry, etc.My impression is that this has very little to do with physics, and not really that much with string theory neither (unless you define string theory to be whatever Witten does). My very limited understanding of these matters is that some correlation functions in N=4 SYM turn out to be independent of separation. This has two consequences:

1. These correlators are smooth (Gromov-Witten?) invariants of the underlying four-manifold.

2. We may freely move the points to convenient positions, probably very close to each other, where the correlators can actually be calculated.

This is wonderful in enumerative geometry, because it gives us calculable smooth invariants which you can use to prove a lot of theorems. But exactly the same properties seem to be rather useless in physics, where we usually want correlation functions to decay with distance.

D. R. Lunsford asked whether my string = worldline model does such things as

“eliminate time”, etc.

It does not, in my opinion. To see how it works in sufficient detail to answer

such questions, please read the entire CERN CDS preprint EXT-2004-031 at

http://cdsweb.cern.ch/search.py?recid=730325&ln=en

The spirit of the model is similar to that proposed by Elitzur and Dolev

in their paper at http://xxx.lanl.gov/abs/quant-ph/0207029

where they say:

“… we propose quantum mechanical experiments that yield inconsistent histories,

suggesting that not only events but also entire histories might be governed

by a more fundamental dynamics. …”.

The basic idea is that each “entire history” would be represented by a “string”.

and that the fundamental interactions of quantum theory are

not between mere point particles

but

are between strings/entire histories.

Elitzur and Dolev, in that article, describe

“… quantum mechanical experiments yielding apparently inconsistent histories …[which]… would give rise to an account like

“first a retarded interaction brings about history t1x1, t2x2, …

and then

an advanced interaction transforms this history into t1x’1, t2x’2 …”

and they say

“… Perhaps … changes affect not only events but also entire histories.

… Such a model will be better capable of explaining quantum peculiarities

of the kind described above, as well as a few other surprising results

discovered lately by similar techniques …”.

Please note that the Elitzur-Dolev paper also discusses some aspects of

Hawking’s recently recanted position regarding information loss in black holes,

but that aspect of the paper seems to me to be substantially independent

of their proposal that it is

interaction between entire histories (world-lines/strings)

and not

event-interactions between mere point particles

that is fundamental in quantum physics.

Tony Smith

Tony –

Doesn’t the usual argument against rigid bodies in relativity eliminate your interpretation of the world-line of a particle as a “string”? If not, then you are saying that a “stringicle” acts as a unit over its entire history – and that any creation-annihilation events in its history have to be included, extending the stringicle to another, to another etc. etc. So, in effect you’re eliminating time, and returning to a Eucldidean-Pythagorean static world picture without dynamics. Odd how this matches the “back to Democritus” approach implicit in the “nothing but fibers and the void” approach.

Larry Yaffe says “… String theory has not yet made any convincing connection with the world we live in. …”.

While that may be true of conventional formulations of string theory,

what about formulations based on unconventional physical interpretations

of strings (such as strings = world lines of point particles) from

which string theory structures such as 26-dim spacetime, D8 branes,

and discretizing by orbifolding can be used to make models such as

that described in CERN CDS preprint EXT-2004-031 at

http://cdsweb.cern.ch/search.py?recid=730325&ln=en

?

There has been a small bit of discussion about that model on sci.physics.strings,

where the model itself is labelled “Speculation” and comments range

from

“.. pure numerology … coincidence …”

to

“… a nice formulation of (bosonic) M-theory (as Susskind refers to the 27-dimensional theory), from where we work down dimensionally … to recover fermions …”.

The above quotes are given without stating full detailed context in order

to illustrate the range of opinions that seem to exist about the model.

Anyone who is really interested in details should read that sps thread

and the paper itself, as well as related material cited therein.

Anyhow, the basic point of this comment is that even though Larry Yaffe

may be correct that current conventional formulations of string theory

have “… not yet made any convincing connection with the world we live in …”,

his statement may not be correct with respect to some unconventional string-based models.