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.

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.

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.

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 t1×1, t2×2, …
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

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.

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.