Banks-Zaks fixed point
Encyclopedia
In quantum chromodynamics
(and also N = 1 superquantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (that is small enough to guarantee asymptotic freedom), 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, then the fixed point is called a Banks–Zaks fixed point.
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 the theory in the IR is a conformal, weakly coupled theory with coupling 
.
For the case of QCD the number of flavors,
, should lie just below 
, where 
is the number of colors, in order for the Banks–Zaks fixed point to appear.
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
(and also N = 1 superquantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (that is small enough to guarantee asymptotic freedom), the theory can flow to an interacting conformal fixed point
Fixed point (mathematics)
In mathematics, a fixed point of a function is a point that is mapped to itself by the function. A set of fixed points is sometimes called a fixed set...
of the renormalization group
Renormalization group
In theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...
. If the value of the coupling at that point is less than one, then the fixed point is called a Banks–Zaks fixed point.
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 the theory in the IR is a conformal, weakly coupled theory with coupling .For the case of QCD the number of flavors,
, should lie just below , where is the number of colors, in order for the Banks–Zaks fixed point to appear.