The paper extends O(n) spectrum constraints to negative n via the O(n)-Sp(n) duality and derives closed-form two-loop anomalous dimensions for all phi^k operators from two known cases.
Does QFT make sense in non-integer dimensions?
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abstract
We revisit the old problem of analytically continuing QFTs to fractional dimension $d\in\mathbb C$. We observe that common theories like QCD and QED have branch cuts in the complex $d$ plane. In particular, many operators in their low-energy CFT have OPEs and scaling dimensions that jump as a function of $d$.
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Constraints on the $O(n)$ model from a negative number of flavors
The paper extends O(n) spectrum constraints to negative n via the O(n)-Sp(n) duality and derives closed-form two-loop anomalous dimensions for all phi^k operators from two known cases.