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theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...
, the Vafa–Witten theorem, named after Cumrun Vafa and
Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...
, is a
theorem In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...
that shows that vector-like global symmetries (those that transform as expected under reflections) such as
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin. Isospin symmetry is a subset of the flavour symmetr ...
and baryon number in vector-like gauge theories like
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of ...
cannot be spontaneously broken as long as the theta angle is zero. This theorem can be proved by showing the exponential fall off of the propagator of fermions.


See also

*
F-theory In theoretical physics, F-theory is a branch of string theory developed by Iranian-American physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in ...


References

* * Gauge theories Theorems in quantum mechanics {{quantum-stub