Paul Balduf#paperOfTheDay is "Bounding scalar operator dimensions in 4D CFT" from 2008.
A conformal field theory (#CFT ) is a #quantumFieldTheory that, in addition to the usual Lorentz symmetry, also has conformal #symmetry (a stronger version of scale invariance). This implies that the 2-point correlation function is a power law, i.e. instead of an arbitrary complicated function of distance, it is fully specified by knowing a single number, the operator's scaling dimension. Moreover, even the 3-point function is fixed once one knows the scaling dimensions of all three operators (where an operator is a polynomial in field variables and derivatives, evaluated at one point) involved in it. This illustrates the enormous importance that scaling dimensions of operators have in a CFT.
Secondly, a CFT allows for an operator product expansion (OPE), where one can rewrite a product of two operators at distinct spacetime points as an infinite sum of operators at only one of the points (morally analogous to a Taylor series for an ordinary function).
The most straightforward operator is the field variable itself. The present paper asks the question: When we know that the field has scaling dimension d, then what can we say about the scaling dimension of the leading operator that appears in the OPE of field x field? By combining the various structural features of the CFT, it turns out that one can find a strict upper bound to the possible scaling dimension of this operator.
The paper is relatively long, but very readable, since it includes detailed reviews and examples of how the various CFT constructions work. Beyond the actual result, it serves as a good introduction to CFT. #physics
https://iopscience.iop.org/article/10.1088/1126-6708/2008/12/031
A conformal field theory (#CFT ) is a #quantumFieldTheory that, in addition to the usual Lorentz symmetry, also has conformal #symmetry (a stronger version of scale invariance). This implies that the 2-point correlation function is a power law, i.e. instead of an arbitrary complicated function of distance, it is fully specified by knowing a single number, the operator's scaling dimension. Moreover, even the 3-point function is fixed once one knows the scaling dimensions of all three operators (where an operator is a polynomial in field variables and derivatives, evaluated at one point) involved in it. This illustrates the enormous importance that scaling dimensions of operators have in a CFT.
Secondly, a CFT allows for an operator product expansion (OPE), where one can rewrite a product of two operators at distinct spacetime points as an infinite sum of operators at only one of the points (morally analogous to a Taylor series for an ordinary function).
The most straightforward operator is the field variable itself. The present paper asks the question: When we know that the field has scaling dimension d, then what can we say about the scaling dimension of the leading operator that appears in the OPE of field x field? By combining the various structural features of the CFT, it turns out that one can find a strict upper bound to the possible scaling dimension of this operator.
The paper is relatively long, but very readable, since it includes detailed reviews and examples of how the various CFT constructions work. Beyond the actual result, it serves as a good introduction to CFT. #physics
https://iopscience.iop.org/article/10.1088/1126-6708/2008/12/031
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