More on the cubic versus quartic interaction equivalence in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> model
Oleg Antipin, Jahmall Bersini, Francesco Sannino, Zhi-Wei Wang, Chen Zhang
Abstract
We compute the scaling dimensions of a family of fixed-charge operators at the infrared fixed point of the $O(N)$ model featuring cubic interactions in $d=6\ensuremath{-}\ensuremath{\epsilon}$ for arbitrary $N$ to leading and subleading order in the charge but to all orders in the couplings. The results are used to analyze the conjectured equivalence with the $O(N)$ model displaying quartic interactions at its ultraviolet fixed point. This is performed by comparing the cubic model scaling dimensions against the known large $N$ results for the quartic model and demonstrating that they match. Our results reinforce the conjectured equivalence and further provide novel information on the finite $N$ physics stemming from the computations in the cubic model just below six dimensions.