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.