An all order exact result for the anomalous dimension of the scalar primary in Chern Simons Vector Models

Abstract

We present a conjecture for the leading $1/N$ anomalous dimension of the scalar primary operator in $U(N{)}_k$ Chern-Simons theories coupled to a single fundamental field, to all orders in the t'Hooft coupling $\lambda =\frac{N}{k}$. Following this we compute the anomalous dimension of the scalar in a Regular Bosonic theory perturbatively at two-loop order and demonstrate that matches exactly with the result predicted by our conjecture. We also show that our proposed expression for the anomalous dimension is consistent with all other existing two-loop perturbative results, which constrain its form at both weak and strong coupling thanks to the bosonization duality. Furthermore, our conjecture passes a novel non-trivial all loop test which provides a strong evidence for its consistency.

arXiv comment11 pages two column format, 6 figures

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• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Chern-Simons dualities with multiple flavors at large $N$
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
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• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$