I can’t say how strongly I disagree.

Consider the statement:

QCD is a confining gauge theory

You cannot take the non-observation of free quarks as evidence for the above proposition.

The evidence for that proposition comes from theoretical work (both analytical and numerical, using Lattice Gauge Theory). In the absence of that theoretical justification, the non-observation of free quarks would be viewed as evidence against QCD, rather than for it.

Consider another proposition:

The nonrelativistic quark model explains the Δ=1/2 Rule.

I would argue against this proposition, on the grounds that the nonrelativistic quark model is not a-priori theoretically justified. To “explain” the Δ=1/2 Rule, one needs to derive it from the underlying QCD.
(Having done so, you can, post-hoc, justify the applicability of the nonrelativistic quark model to certain processes.)

Phenomenological models are not “blessed by nature,” just because they agree with experiment.

It’s an (incorrect) caricature of the way science work to assert that agreement with experiment is a substitute for theoretical consistency and that theoretical consistency is only achieved when one has a mathematically rigourous formulation (ie, essentially never in Physics).

This methodology which has worked well for physics cannot be carried over with the same confidence to where there is contact with nature. Perhaps the best term for this field is not physics, but experimental mathematics. It may be deeper but in principle no different from observing that 3,5,7 are prime and conjecturing that all odd natural numbers are prime.

Per your example, I doubt there’s much effort devoted to developing mathematical structures that would be relevant or interesting, only if the Riemann Hypothesis turned out to be false.

Someone working on a topic, sufficiently far-removed from the behaviour of N=1 SQCD, can afford to be agnostic about whether Seiberg’s conjecture is correct, just as someone, working in a branch of mathematics far removed from any implications of the (truth or falsity of) the Riemann Hypothesis, can afford to be agnostic about it.

Someone working in a more closely-related subject has no such luxury. And such a person would be foolish, indeed, to predicate a significant amount of their own work on the “contrarian” premise that the conjecture is false.

if physicists can predict the outcome of thousands of experiments, the fact that they don’t have a rigorous proof is a minor nuisance.

There are other kinds of evidence, besides experimental measurements.

And this isn’t like the normal physics versus mathematics cultural difference — if physicists can predict the outcome of thousands of experiments, the fact that they don’t have a rigorous proof is a minor nuisance. A conjecture about a theory that at the moment only exists inside human heads really is a gray area in a way that Feynman diagrams are not.

I’m not saying that the mathematician’s attitude is the right one. If Seiberg duality is true, then any amount of skepticism is a waste of time. I’m just curious, as an outsider, how the culture of theoretical physics works.

Most of theoretical physics, indeed most of science, exists in such a gray area. There are very, very few results which can be said to have been rigourously proven.

At best, one can say that the preponderance of evidence (sometimes, an overwhelming preponderance of evidence) favours a certain conclusion.

In the case at hand, Seiberg and others have amassed a fair amount of evidence in favour of the conjecture. No single piece of evidence is particularly conclusive, but taken together, they have convinced most experts that the conjecture is correct.

So what if it’s just my opinion that Seiberg duality is wrong? I don’t have a counterargument; I just find the existing evidence not very compelling. What would be the reaction then?

I think a reasonable person would ask for an alternative conjecture for the infrared behaviour of N=1 SQCD. One that passes all of the consistency checks that Seiberg’s does.

So what if it’s just my opinion that Seiberg duality is wrong? I don’t have a counterargument; I just find the existing evidence not very compelling. What would be the reaction then?

(Just to be clear, I have no opinion on Seiberg duality.)

If you had evidence that Seiberg duality was wrong, people would be very interested in your results. I’m guessing it would quickly become the “hottest” topic on hep-th, until the implications of your results were worked out. For example it would be interesting to understand whether you invalidated all the isomorphisms or just some of them.

You would certainly not be ignored simply because what you say goes against current belief. High energy theorists are interested in the truth, just like other scientists.

What would be the reception if I announced that I thought that Seiberg duality is false?

False always? Or false for particular values of Nf and Nc?

Seiberg duality (and related developments) represent a huge advance in our understanding of the low-energy dynamics of strongly coupled gauge theories. But it’s certainly not the last word on the subject. In particular, if you discovered some feature of the low-energy dynamics that would distinguish between the two gauge theories, whose behaviour Seiberg says is identical, that would be interesting …

Jacques: That’s a very interesting result.

I’m not sure it’s that “interesting.” In some sense, it’s pretty obvious.

In any case, it’s the sort of result one would be expected to know, if one were writing essays on this subject…

Jacques: That’s a very interesting result.