Scaling dimension

In theoretical physics, the scaling dimension, or simply dimension, of a local operator in a quantum field theory characterizes the rescaling properties of the operator under spacetime dilations x\to \lambda x. If the quantum field theory is scale invariant, scaling dimensions of operators are fixed numbers, otherwise they are functions of the distance scale. Scale-invariant quantum field theory In a scale invariant quantum field theory, by definition each operator O acquires under a dilation x\to \lambda x a factor \lambda^{-\Delta}, where \Delta is a number called the scaling dimension of O. This implies in particular that the two point correlation function \langle O(x) O(0)\rangle depends on the distance as (x^2)^{-\Delta}. More generally, correlation functions of several local operators must depend on the distances in such a way that \langle O_1(\lambda x_1) O_2(\lambda x_2)\ldots\rang

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The scaling dimensions of charged operators in conformal field theory were recently computed in a large charge expansion. We verify this expansion in a dual AdS model. Specifically, we numerically construct solitonic boson star solutions of Einstein-Maxwell-Scalar theory in AdS4 and find that its mass at large charge reproduces the universal form of the lowest operator dimension in the large U(1) charge sector of the dual 2+1 dimensional CFT.

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