Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Yuji Tachikawa, , , ,
| Summary:
In the hope of providing some intellectual entertainment on April Fools’ day
of this dark year, we point out that some questions in quantum field theory are
undecidable in a precise mathematical sense. More concretely, it will be
demonstrated that there is no algorithm answering whether a given 2d
supersymmetric Lagrangian theory breaks supersymmetry or not. It will also be
shown that there is a specific 2d supersymmetric Lagrangian theory which breaks
supersymmetry if and only if the standard Zermelo-Fraenkel set theory with the
axiom of choice is consistent, which can never be proved or disproved as the
consequence of G"odel’s second incompleteness theorem. The article includes a
brief and informal introduction to the phenomenon of undecidability and its
previous appearances in theoretical physics.
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