Negative anomalous dimensions in N=4 SYM

Abstract

We elucidate aspects of the one-loop anomalous dimension of $so(6)$-singlet multi-trace operators in $\mathcal{N}=4SU(N_c)$ SYM at finite $N_c$. First, we study how $1/N_c$ corrections lift the large $N_c$ degeneracy of the spectrum, which we call the operator submixing problem. We observe that all large $N_c$ zero modes acquire non-positive anomalous dimension starting at order $1/N_c^2$, and they mix only among the operators with the same number of traces at leading order. Second, we study the lowest one-loop dimension of operators of length equal to $2N_c$. The dimension of such operators becomes more negative as $N_c$ increases, which will eventually diverge in a double scaling limit. Third, we examine the structure of level-crossing at finite $N_c$ in view of unitarity. Finally we find out a correspondence between the large $N_c$ zero modes and completely symmetric polynomials of Mandelstam variables.

34+31 pages, many figures, a Mathematica file attached, v2: typos corrected, references added, section 5 revised, v3: revised Section 4 on correlators, and small details

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• Simplifying large spin bootstrap in Mellin space
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Flavour singlets in gauge theory as Permutations
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