In
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 natural phenomena. This is in contrast to experimental physics, which uses experim ...
, the Vafa–Witten theorem, named after
Cumrun Vafa
Cumrun Vafa ( fa, کامران وفا ; born 1 August 1960) is an Iranian-American theoretical physicist and the Hollis Professor of Mathematics and Natural Philosophy at Harvard University.
Early life and education
Cumrun Vafa was born in Tehran ...
and
Edward Witten
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...
, is a
theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of th ...
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. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
and
baryon number
In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as
::B = \frac\left(n_\text - n_\bar\right),
where ''n''q is the number of quarks, and ''n'' is the number of antiquarks. Bary ...
in vector-like gauge theories like
quantum chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the theory 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 ...
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 physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the for ...
References
*
*
Gauge theories
Theorems in quantum mechanics
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