SciPost Phys. 12, 055 (2022) ·
published 9 February 2022

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We study correlation functions of Dbranes and a supergravity mode in AdS, which are dual to structure constants of two subdeterminant operators with large charge and a BPS singletrace operator. Our approach is inspired by the large charge expansion of CFT and resolves puzzles and confusions in the literature on the holographic computation of correlation functions of heavy operators. In particular, we point out two important effects which are often missed in the literature; the first one is an average over classical configurations of the heavy state, which physically amounts to projecting the state to an eigenstate of quantum numbers. The second one is the contribution from wave functions of the heavy state. To demonstrate the power of the method, we first analyze the threepoint functions in $\mathcal{N}=4$ super YangMills and reproduce the results in field theory from holography, including the cases for which the previous holographic computation gives incorrect answers. We then apply it to ABJM theory and make solid predictions at strong coupling. Finally we comment on possible applications to states dual to black holes and fuzzballs.
SciPost Phys. 7, 065 (2019) ·
published 26 November 2019

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The existence of higherspin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question of whether classicallyconserved local higherspin currents in twodimensional sigma models survive quantization. We define an integrability index $\mathcal{I}(J)$ for each spin $J$, with the property that $\mathcal{I}(J)$ is a lower bound on the number of quantum conserved currents of spin $J$. In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins. We apply our techniques to the $\mathbb{CP}^{N1}$ model, the $O(N)$ model, and the flag sigma model $\frac{U(N)}{U(1)^{N}}$. For the $O(N)$ model, we establish the existence of a spin6 quantum conserved current, in addition to the wellknown spin4 current. The indices for the $\mathbb{CP}^{N1}$ model for $N>2$ are all nonpositive, consistent with the fact that these models are not integrable. The indices for the flag sigma model $\frac{U(N)}{U(1)^{N}}$ for $N>2$ are all negative. Thus, it is unlikely that the flag sigma models are integrable.