Conformal dimensions using a large charge expansion

Conformal field theories (CFTs) are described by a set of dimensionless numbers referred to as conformal dimensions, which are difficult to compute. Recently it was proposed that conformal dimensions of certain large charge operators satisfy a simple relation with unknown coefficients. In this talk we explain our efforts to test this proposal and compute the unknown coefficients using Monte Carlo calculations. We focus on CFTs that arise at the O(2) and O(4) Wilson-Fisher fixed points as test cases. Since traditional Monte Carlo methods suffer from a severe signal-to-noise ratio problem in the large charge sectors, we use worldline formulations. In the O(2) case we show that the large charge expansion works very well even up to the smallest charge. In the O(4) case, the charged sectors are labeled by the two SU(2) representations (jL,jR). Here we introduce and study a drastically simplified alternate model, which we refer to as a "qubit model". We find that the (j,j) sector continues to show excellent agreement with the large charge expansion, again up to small values of j. We also present preliminary results on the behavior of the subleading (j,j-1) sector, which however suggests a less satisfying scenario.