General Properties of Multiscalar RG Flows in d=4-\varepsilon

Wednesday, 24 October, 2018

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Fixed points of scalar field theories with quartic interactions in d=4-\varepsilon dimensions are considered in full generality. For such theories it is known that there exists a scalar function A of the couplings through which the leading-order beta-function can be expressed as a gradient. It is here proved that the fixed-point value of A is bounded from below by a simple expression linear in the dimension of the vector order parameter, N. Saturation of the bound requires a marginal deformation, and is shown to arise when fixed points with the same global symmetry coincide in coupling space. Several general results about scalar CFTs are discussed, and a review of known fixed points is given.


Slava Rychkov
Andreas Stergiou