Suggested questions

From new ones to old. Lightly edited to make questions anonymous. In my opinion the questions submitted so far were all quite advanced. I would prefer more basic and/or naive questions! So please keep them coming.

No.Question
10. Here are some questions that I am interested in string theory:
  1. Non-perturbative approach: Nowadays, we can study QFTs by axioms such as Wightman axioms and Haag-Kastler axioms. Are there any axioms we could postulate for string theories? Then can we construct examples satisfying those axioms ?
  2. Noncommutative Geometry: Does noncommutative geometry naturally appear in string theory and why? Will noncommutative geometry serve a crucial role for solving some problems in string theory?
  3. Relations between string theories and 2+1d and 3+1d CFTs? Loop groups are natural objects to study for string people, I understand. But how about group of smooth mappings from M $\to$ G, where M is a Riemannian surface and G is SU(n)?
  4. It seems to me that 1+1d CFTs shows up in both string theory and critical points of statistical models. But string theory and statistical models are very different languages and philosophies to me. Do these two different viewpoints reconcile (in some larger framework)?
  5. String theory makes HUGE impact on mathematics. I personally do not believe this could be a "coincidence". I always wonder why string theory is so magical. I would really appreciate it if some examples will be explained, for example, Gepner models and mirror symmetry. Please inform us if there are ideas in string theory not translated to the math side, or ideas whose importance not appreciated by the math community, if there are any.
  6. Last but not the least, what are the problems lying at the very core of string theory? So that some people say string theory is dead because these problems are not solved.
9. もし先生が今弦理論の教科書を書くとしたらどういう目次, 構成, 内容にしますか?また, 過去の有名な教科書(GSW, ポルチンスキー)を現在の視点から批評してみてください.
8. Given recent advances in AI, do you think we could see major progress toward—or even the completion of—a theory of quantum gravity? What is your best estimate of how many years it might take for a major breakthrough to occur? In addition, how likely do you think it is that such a theory could be experimentally verified?
7. I am a graduate student in condensed matter physics. I notice this when I try to find the update of your algebraic topology note. Personally, I don't have a strong interest in quantum gravity (because I don't even understand what people really mean when they talk about quantum gravity); rather, my interest in string theory is driven by the following fascinating facts I have come across:
  1. The relationship between string scattering and 2D Conformal Field Theory (CFT): I understand that one of the primary motivations for the early development of CFT was 2D string scattering. Since different amplitudes correspond to different Riemann surfaces, string theory is intimately connected to 2D complex geometry. Furthermore, I am curious about how we sum over Riemann surfaces for different spacetime backgrounds, which seems to imply a broader type of gauging.
  2. String theory's profound impact on pure mathematics, particularly low-dimensional geometry and topology: I would love to know how physicists back then were able to use string theory to provide non-rigorous "proofs" or predictions for so many theorems in topology and arithmetic geometry before mathematicians could formalize them.
  3. Anomalies and Generalized Symmetries: These concepts are currently highly popular even outside high-energy formal theory (such as in condensed matter physics). Were the motivations of the pioneers who first initiated this line of research, like Nathan Seiberg, related to string theory? How do symmetries and anomalies manifest themselves within string theory, and what unique or much clearer structural insights does string theory provide that cannot be easily seen in standard quantum field theories?
6. わからないなあと思ったのは、non-critical dimensionでのstringの運動というのはどう記述すべきかということです。例えば、D=3+1でcosmic stringを考えると、その運動のモードはNG作用で書けると思っているわけですが、Polyakov actionにして量子化するとWeyl anomalyがあるので、量子力学的にはスカラー$\phi$を導入してリウビル理論として考えないといけませんね。このstringが場の理論から出てきていると思ったとき、$X^\mu$は並進のmoduliから来ていた場ですが、$\phi$は何に対応するのでしょう？stringの内部構造かなとかとも思いましたが、相互作用は割とユニバーサルに書けているし、そもそもWeyl anomalyがあるから積分できない自由度なので、それでいいのかなあ？と思っています。
5. brane engineering を用いて QFT の duality を導出する話など、弦理論を用いて場の量子論の性質を理解する系統の話が聞きたいです。
4. 物性物理との関連が気になります。
3. Is string theory really not falsifiable? Sometimes I hear this statement. But I am not sure if it is because of the limitation of technology to achieve higher energy, or it is because of some essential limitation of this theory itself.
2.
  • It may not be mathematically rigorous, but there is a concept in quantum gravity theory that suggests the physics of our everyday world can be reproduced by an approximation that sets 1/c, G, and \hbar to zero. Since string theory is supposed to have no tunable parameters, I’m curious about the procedure by which it approximates known theories.
  • I imagine mathematicians are also researching string theory, but how far along is the attempt to mathematically define it? What are the standard references for mathematicians? I’d also like to know about its relationship to algebraic geometry.
  • I like to understand physics using graphical notations such as tensor networks. Since tensor networks don’t seem to be very effective for CFT, I don’t expect them to work well, but what about string theory? For example, do matrix models offer any hints in this regard, similar to ’t Hooft’s genus expansion?
1. クラスS理論、AGT対応等

email: yuji.tachikawa_at_ipmu.jp