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Axiomatic string theory?

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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?

This post imported from StackExchange MathOverflow at 2023-11-25 20:57 (UTC), posted by SE-user Giafazio

asked Mar 9, 2022 in Theoretical Physics by Giafazio (25 points) [ no revision ]
retagged Nov 25, 2023

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.

This post imported from StackExchange MathOverflow at 2023-11-25 20:57 (UTC), posted by SE-user Carlo Beenakker

commented Mar 9, 2022 by Carlo Beenakker (180 points) [ no revision ]

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.

This post imported from StackExchange MathOverflow at 2023-11-25 20:57 (UTC), posted by SE-user markvs

commented Mar 9, 2022 by markvs (0 points) [ no revision ]

@CarloBeenakker Could you elaborate a little why this is so?

This post imported from StackExchange MathOverflow at 2023-11-25 20:57 (UTC), posted by SE-user Jules Lamers

commented Mar 9, 2022 by Jules Lamers (0 points) [ no revision ]

@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)

This post imported from StackExchange MathOverflow at 2023-11-25 20:57 (UTC), posted by SE-user Jules Lamers

commented Mar 9, 2022 by Jules Lamers (0 points) [ no revision ]

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.

This post imported from StackExchange MathOverflow at 2023-11-25 20:57 (UTC), posted by SE-user markvs

commented Mar 9, 2022 by markvs (0 points) [ no revision ]

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