Abstract
We present a direct Monte-Carlo determination of the scaling dimension of a topological defect operator in the infrared fixed point of a three-dimensional interacting quantum field theory. For this, we compute the free energy to introduce the background gauge field of the $Q=1$ monopole-antimonopole pair in three-dimensional non-compact QED with $N=2,4$ and $12$ flavors of massless two-component fermions, and study its asymptotic logarithmic dependence on the monopole-antimonopole separation. We estimate the scaling dimension in the $N=12$ case to be consistent with the large-$N$ (free fermion) value. We find the deviations from this large-$N$ value for $N=2$ and $4$ are positive but small, implying that the higher order corrections in the large-$N$ expansion become mildly important for $N=2,4$.
Highlights
Conformal field theories in three dimensions, and renormalization group flows from one fixed point to another induced by the introduction of relevant operators at fixed points have been investigated over the last few years
We presented an ab initio lattice computation of the monopole correlator in N 1⁄4 2, 4 and 12 flavor massless QED3 by using the background field method
To avoid the overlap problem which would make the computation of ratio of partition functions with and without a monopole-antimonopole background field, we slowly increased the value of monopole flux from 0 to integer Q
Summary
Conformal field theories in three dimensions, and renormalization group flows from one fixed point to another induced by the introduction of relevant operators at fixed points have been investigated over the last few years. Crucial to this inference is that the monopoles in a gauge theory with N massless fermions break UðNÞ global flavor symmetry to UðN=2Þ × UðN=2Þ symmetry [4,19,20] Such an approach further assumes that (1) both compact and noncompact QED3 flow to the same infrared fixed point for. Independent of the choice of Wg, we can always restrict the above integral over all θμðxÞ to be from −π to π by summing Wg over all possible nμðxÞ for different x and μ In this way, the underlying gauge group is always U(1) owing to the usage of the compact links UμðxÞ in the Dirac operator, and magnetic monopoles are well defined in these theories. The details pertaining to the construction of the background field AQμ Qcan be found in [37]
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