Little tolerance with mathematical-physics questions

Question

I progressively feel that a typical user interested in the mathematical-physics tag, like me, is not welcomed in the community; not to mention, that at least as I can tell, the community is not explicit enough on exactly what is acceptable, or not, under this tag.

Personal examples:

1. My question "Geometric intuition for $\mathcal{L}^{-m} \oplus \mathcal{L}^{m} \rightarrow T^{2}$ Calabi-Yau threefolds was posted and voted-to-close four times on this site (PSE); at the end, it was migrated to Math Stack Exchange despite of the fact that I've received (and accepted) a really wonderful answer from a PSE user. My question manifestly was about the "physics way" to understand a mathematical idea used in physics papers (actually submitted to arXiv under the high energy physics label and no reference to mathematics) by famous physicists (Vafa and Jafferis). Honestly my question was about math, but, my point is that I consider my question as legitimate under the mathematical physics tag in PSE and not off-topic as the treatment it received from the community suggested.

2. I offered an answer, "Connectedness on Special Kaehler manifolds". Again, this question is about a mathematical topic (special geometry) discovered by physicists, relevant for (black hole-) physics that is virtually not discussed by mathematicians at all. A moderator in the question comments immediately pointed that this question was off-topic in this site. To me, this is also a legitimate question in PSE.

3. I had to close some drafts before posting the question "References on mathematical stacks for a string theory student". In all of them I received comments saying that this was off-topic in this site, until a version of the question was considered "acceptable" but still received comments saying: "this seems off-topic" or "I don't understand what you are saying"; despite of the fact that I specify that I'm a physics oriented student and my question was manifestly about the math-background needed to understand physics papers, written by physicists and that I didn't wanted an answer from a mathematician.

4. Finally, I have the possibly subjective perception that the community was far more tolerant in this respect before I started to post in PSE (four years ago). For example, I find the following questions and answers nice and not evidently different from the examples I gave, except that they are apparently on-topic 1. To be honest, I find very discouraging and ambiguous the treatment a question in this tag receives.

Then my question is: How can I understand better what a permissible mathematical-physics question is? Is this a generalized attitude against the mathematical-physics community?

Answer 1

• Generally speaking, mathematical physics questions are on-topic and more than welcome.

  Note that advanced questions naturally tend to have fewer views, upvotes, and potential answerers. But don't get discouraged by that. You'll just have to be patient. If Phys.SE currently don't have the expertise to answer them, we might get it in the future!

  Also it is a good idea to provide context, hyperlinks, and references to advanced questions to make them more accessible to the reader.

• Specifically about OP's examples:

  1. Geometric intuition for $\mathcal{L}^{-m} \oplus \mathcal{L}^{m} \rightarrow T^{2}$ Calabi-Yau threefolds is a typical mathematical physics question in string theory, and should not have been migrated.

  2. Connectedness on Special Kaehler manifolds in its current version (v6) is pure math. Consider to add physics context, cf. e.g. this meta question.

  3. References on mathematical stacks for a string theory student is a resource recommendation question. Such questions are restricted on Phys.SE, cf. various meta posts, cf. e.g. this meta question. Also the current version (v5) seems to be opinion-based.

  4. How algebraic geometry and motives appears in physics? is well received by the Phys.SE community although it is a bit broad.

Answer 2

I get the impression you are confusing the mathematical-physics tag on Physics SE with the one on Mathematics SE. They are not the same.

Physics SE :

Mathematical physics is the application of mathematics to problems in physics and mathematical methods suitable for such applications, e.g., partial differential equations (PDEs), functional analysis, variational calculus, and potential theory. It also includes the study of problems inspired by physics within a mathematically rigorous framework, such as rigorous derivation of an atomic energy spectrum, rigorous construction of a quantum field theoretic model, and rigorous description of a phase transition.

Do not use mathematical-physics just because your question involves math!

and on Mathematics SE it's :

DO NOT USE THIS TAG for elementary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

I really think it's clear your questions fit the Mathematics SE definition better than the Physics SE one.

These are also very specialist questions and while I have no doubt there are people on Physics SE who can handle them the mathematical level required is more likely to receive a match on Mathematics SE. You say you want a physics related answer to them, but there seems little physics here (like a lot of String Theory IMO). In at least two cases you yourself say they're more suited to Mathematics SE and one question never (as far as I can tell) had a mathematical-physics tag.

It's unfortunate you find this a problem, but I think the nature of your questions may be more suited to Mathematics Overflow or Physics Overflow.

Answer 3

I think that if the question is about mathematics per se, it is out of scope, even if the mathematics is commonly used in physics. It would be in scope if the question was about how to apply or interpret the mathematics in relation to physics. For example, if someone were to ask how to solve a quadratic equation, that would stand on its own mathematically and be out of scope, notwithstanding the fact that the solution of quadratic equations is a useful method in physics.

Answer 4

Perhaps it should be noted that the decision of this question is intimately linked with the question:

What should Physics do with String theory heritage?

It is an open secret among theoretical physicists that much of the String theory community has migrated during the past fifteen years to other questions than quantum gravity (the reasons are the positivity of the cosmological constant, the string theory landscape, and the absence of supersymmetry observed at LHC). Now it is concerned mainly with various QFT models that mostly find their application, if any, as highly idealized condensed-matter systems. The game is, for instance, to find various dualities that may translate various theories and their computable results into one another.

Many-a-theorist in "String theory/HEP theory/..." will admit to you that they are just doing some interesting mathematics and that they have no illusion of the applicability of their work to real systems. They will also admit that putting a "String theory heritage" label on their work allows them to work on the topics in high-status settings with a large and active community (unlike the case of a number of areas in Pure Mathematics). This is a self-sustaining effect, since research institutions are often largely financed on a citation-metric basis, and String theorists still hold tenured policy-making positions at Physics departments. Very often, String theory itself is not even involved any more, instead field theories and dualities that were discovered in the course of investigating String theory are used. This is why I call this field String theory heritage.

However, the way the work is motivated is nowadays more similar to Pure Mathematics. It would be simply untrue to say that Pure Mathematics has no applications in the real world. For instance, number theory has immensely important applications in banking. But would we call Number theory a branch of Banking? Do Pure Mathematicians working on Number theory really choose goals with banking applications in mind? Of course not, they have their own criteria. I feel similar statements are in order about at least some of the sectors of "HEP theory" that come from String theory heritage and their relation to Physics.

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This being said, I certainly do not want to say that the work done in String theory heritage is not generally scientifically interesting or done badly. Also, there are many areas of Theoretical and Mathematical physics where the very same statements would be possible; Exact solutions of Einstein equations are particularly close to home for me personally in this regard. Or, e.g., the proof of the positive-mass theorem not in dimension 4, but in general dimension.

For example, there are "singular sets" causing problems in the proof of the theorem for dimension larger than 7. Would I consider a detailed question about these sets as on-topic on PSE? No, I would not, but I am not ironclad. The line is really quite thin, because if you restrict these types of questions too much, you restrict the possibility of diversity and exploration.

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So really no final judgment here, I just wanted to point out that this is not the issue of just PSE, but of the entire Physics community at the moment. This is a choice the PSE community has to deal with, but either choice makes some sense!

Answer 5

I disagree.

1. For one, I don’t think you’re a typical user. Check the mathematical-physics tag to see typical questions.
2. For another, you present your question in a way that maximizes hifalutin mathematical jargon.
3. You admitted yourself - in reply to a comment of mine - that at least one of your question was basically a math question.
4. In case of the specific question “ References on mathematical stacks for a string theory student”, you actually supply your own background, which suggest the answer is unlikely to be useful to the community at large.

I’m not quite sure why you think the community has little tolerance to math/phys questions. The activity in the mathematical physics and cognate tags shows otherwise. Your questions (or answers) require quite specialized knowledge to understand, which restricts the number of people with the expertise to view or answer. None of your questions or answers you give in examples have been downvoted. Sorry if this shatters any illusion that mathematical physics is somehow equivalent to string theory: it is just not.