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arXiv · 1708.03740

Scaling dimensions in QED$_3$ from the $\epsilon$-expansion

Lorenzo Di Pietro·Emmanuel Stamou
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Abstract

We study the fixed point that controls the IR dynamics of QED in $d = 4 - 2\epsilon$. We derive the scaling dimensions of four-fermion and bilinear operators beyond leading order in $\epsilon$-expansion. For the four-fermion operators, this requires the computation of a two-loop mixing that was not known before. We then extrapolate these scaling dimensions to $d = 3$ to estimate their value at the IR fixed point of QED$_3$ as function of the number of fermions $N_f$. The next-to-leading order result for the four-fermion operators corrects significantly the leading one. Our best estimate at this order indicates that they do not cross marginality for any value of $N_f$, which would imply that they cannot trigger a departure from the conformal phase. For the scaling dimensions of bilinear operators, we observe better convergence as we increase the order. In particular, $\epsilon$-expansion provides a convincing estimate for the dimension of the flavor-singlet scalar in the full range of $N_f$.

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Lorenzo Di Pietro, Emmanuel Stamou. 2017-08-12. Scaling dimensions in QED$_3$ from the $\epsilon$-expansion. https://doi.org/10.1007/jhep12(2017)054

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