About: Banks–Zaks fixed point

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In quantum chromodynamics (and also N = 1 super quantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (i.e. small enough to guarantee asymptotic freedom, depending on the number of colors), the theory can flow to an interacting conformal fixed point of the renormalization group. If the value of the coupling at that point is less than one (i.e. one can perform perturbation theory in weak coupling), then the fixed point is called a Banks–Zaks fixed point. The existence of the fixed point was first reported in 1974 by Belavin and Migdal and by Caswell, and later used by Banks and Zaks in their analysis of the phase structure of vector-like gauge theories with massless fermions. The name Caswell–Banks–Zaks fixed point is also used.

Attributes	Values
rdfs:label	Banks–Zaks fixed point (en)
rdfs:comment	In quantum chromodynamics (and also N = 1 super quantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (i.e. small enough to guarantee asymptotic freedom, depending on the number of colors), the theory can flow to an interacting conformal fixed point of the renormalization group. If the value of the coupling at that point is less than one (i.e. one can perform perturbation theory in weak coupling), then the fixed point is called a Banks–Zaks fixed point. The existence of the fixed point was first reported in 1974 by Belavin and Migdal and by Caswell, and later used by Banks and Zaks in their analysis of the phase structure of vector-like gauge theories with massless fermions. The name Caswell–Banks–Zaks fixed point is also used. (en)
dcterms:subject	Fixed points (mathematics) Gauge theories Quantum chromodynamics Supersymmetric quantum field theory Conformal field theory Renormalization group
Wikipage page ID	1965869 (xsd:integer)
Wikipage revision ID	1119140765 (xsd:integer)
Link from a Wikipage to another Wikipage	Beta function (physics) Fixed points (mathematics) Perturbation theory (quantum mechanics) Renormalization group Gauge theories Quantum chromodynamics Supersymmetric quantum field theory Color charge Super QCD Yang–Mills theory Alexander Belavin Conformal field theory Tom Banks (physicist) William E. Caswell Alexander Arkadyevich Migdal Fixed point (mathematics) Flavour (particle physics) Dirac fermion Quantum chromodynamics Asymptotic freedom Renormalization group Special unitary group
sameAs	Banks–Zaks fixed point Banks–Zaks fixed point Banks–Zaks fixed point
dbp:wikiPageUsesTemplate	dbt:ISBN dbt:Quantum-stub dbt:Reflist dbt:Short_description
has abstract	In quantum chromodynamics (and also N = 1 super quantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (i.e. small enough to guarantee asymptotic freedom, depending on the number of colors), the theory can flow to an interacting conformal fixed point of the renormalization group. If the value of the coupling at that point is less than one (i.e. one can perform perturbation theory in weak coupling), then the fixed point is called a Banks–Zaks fixed point. The existence of the fixed point was first reported in 1974 by Belavin and Migdal and by Caswell, and later used by Banks and Zaks in their analysis of the phase structure of vector-like gauge theories with massless fermions. The name Caswell–Banks–Zaks fixed point is also used. More specifically, suppose that we find that the beta function of a theory up to two loops has the form where and are positive constants. Then there exists a value such that : If we can arrange to be smaller than , then we have . It follows that when the theory flows to the IR it is a conformal, weakly coupled theory with coupling . For the case of a non-Abelian gauge theory with gauge group and Dirac fermions in the fundamental representation of the gauge group for the flavored particles we have where is the number of colors and the number of flavors. Then should lie just below in order for the Banks–Zaks fixed point to appear. Note that this fixed point only occurs if, in addition to the previous requirement on (which guarantees asymptotic freedom), where the lower bound comes from requiring . This way remains positive while is still negative (see first equation in article) and one can solve with real solutions for . The coefficient was first correctly computed by Caswell, while the earlier paper by Belavin and Migdal has a wrong answer. (en)
prov:wasDerivedFrom	wikipedia-en:Banks–Zaks_fixed_point?oldid=1119140765&ns=0
page length (characters) of wiki page	4815 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Banks–Zaks_fixed_point
is Link from a Wikipage to another Wikipage of	Beta function (physics) Index of physics articles (B) Infrared fixed point Alexander Belavin Tom Banks (physicist) Alexander Arkadyevich Migdal Banks-Zaks fixed point Conformal window
is Wikipage redirect of	Banks-Zaks fixed point Conformal window
is known for of	Tom Banks (physicist)
is known for of	Tom Banks (physicist)
is foaf:primaryTopic of	wikipedia-en:Banks–Zaks_fixed_point

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