I came across this Phys.SE post, to which there is a particular answer that states the following, quoted:
``... but can tell you this. High Energy Physics goes nowhere now as String Theory fails to produce any measurable prediction in two decades. There is no progress in standard model too. Problems left in GR/math ph. are either very difficult or exotic. If I were you I'd choose a field as close to experiment as possible because standard theoretical physics is practically dead. "
My first reaction is best described by three letters: lol. However, I thought I would expand a little more on this, while listening to Style by Taylor Swift.
The statement that hep-th goes nowhere as far as string theory is concerned because it ``fails to produce any measurable prediction in two decades" is an absurd one. While I am not a string theorist, there have been plenty of developments as far as theoretical hep is concerned. If you want a debatable and non-trivial problem to work on, go for string theory and de Sitter space. Putting aside the part that there ``is no progress in standard model" (since I am not aware of it), there is the next statement that ``problems left in GR/math-ph are either very difficult of exotic". Putting aside that most of the problems in pure GR right now are either things appealing to math.DG or math.AP, or things requiring numerical brute-force computations (see the state of the gr-qc arXiv), I doubt there are many problems in the overlap of gr-qc and hep-th that are ``exotic", defined by the poster as meaning ``... of little importance to physics".
The second aspect of this is that in the face of modern hep-th, math-ph is a very hot topic. At any given time, the math-ph arXiv has at least two papers whose primary listing is hep-th. And for that matter, string theory in the mathematical physics arXiv is very infamous, owing to the fact that most of string theory appeals to a wide range to things like math.RT, math.QA, math.NT and math.DG to name a few. Hep-th does not simply mean the surface level works with AdS/CFT or so, and is a field that has very beautiful things to work with. And finally, as of ``... choose a field as close to experiment ... theoretical physics is practically dead", one may see the hep-th arXiv instead to get a better understanding of how very much alive theoretical physics is. From my side, there are some topics that I would provide as examples:
- JT gravity. For instance, today a paper appeared which works with the semiclassical Bousso bound in JT gravity. It has also worked alongside random matrix theory.
- Operator algebras. In all sorts of places, most strikingly in AdS/CFT.
- Information theoretic aspects with things like pseudo Renyi entropy and non-trivialization of Araki's definition of relative entropy for density matrices into complex valued entanglement entropy.
- de Sitter space. For instance, Chandrasekharan, Longo, Pennington and Witten recently worked on static patch algebra of observables and type II$_{1}$ algebras.
- Information problem and islands.
- Topological QFTs.
- Involvements of math.AG (see for instance Kapustin and Witten's paper on the electromagnetic duality and geometric Langlands).
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