There have been many proposal of a mathematical definition of Quantum Field Theory, for instance through Wightman or Osterwalder-Schrader axioms. Were there any efforts toward doing the same for String theory?
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3$\begingroup$ No, string theory is not a "theory" based on a set of rules that may then be defined axiomatically. In that sense it is altogether different from quantum field theory. $\endgroup$Carlo Beenakker– Carlo Beenakker2022-03-09 12:39:28 +00:00Commented Mar 9, 2022 at 12:39
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$\begingroup$ QFT is a part of mathematics produced mostly by mathematicians while String Theory is not. Various people produce results which are thought to belong to ST, but these are just individual results. $\endgroup$markvs– markvs2022-03-09 16:54:23 +00:00Commented Mar 9, 2022 at 16:54
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$\begingroup$ @CarloBeenakker Could you elaborate a little why this is so? $\endgroup$Jules Lamers– Jules Lamers2022-03-09 17:06:56 +00:00Commented Mar 9, 2022 at 17:06
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5$\begingroup$ @markvs Surely the standard model and what all those people do at CERN is physics‽ There are some very special examples of QFTs (non-interacting, topological, conformal, ...) that have become part of mathematics, but QFT is certainly physics. In fact, one could argue the opposite of what you say: QFT has produced experimentally testable predictions; afaik, if anything, string theory has so far produced more mathematics than any real physics (I do not know if applications of AdS/CFT to the quark-gluon plasma or condensed matter theory produced new results that can be tested by experiments) $\endgroup$Jules Lamers– Jules Lamers2022-03-09 17:18:10 +00:00Commented Mar 9, 2022 at 17:18
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$\begingroup$ In CERN, they discovered Higgs boson, which is indeed, a confirmation of some mathematical result. But math part of ST is just a union of disjoint facts unlike QFT, IMHO. $\endgroup$markvs– markvs2022-03-09 17:24:55 +00:00Commented Mar 9, 2022 at 17:24
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