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Huge BPS Operators and Fluid Dynamics in $\mathcal{N}=4$ SYM
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abstract
In the bulk dual of holography, huge operators correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the correlation function of three such huge operators when they are given by $1/2$ BPS operators in $\mathcal{N}=4$ SYM theory, dual to IIB Strings in $AdS_5 \times S^5$. We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we translate these matrix model expressions into a $1+1$ dimensional hydrodynamical fluid problem. This fluid is integrable thus unveiling a novel integrable sector of the $AdS/CFT$ duality in a full fledged gravitational regime, very far from the usual free string planar regime where integrability reigns supreme. We explain how an adiabatic deformation method can be developed to yield the solution to an integrable discrete formulation of these fluids -- the rational Calogero-Moser Model -- so we can access the general three point correlation functions of generic huge $1/2$-BPS operators. Everything will be done on the gauge theory side of the duality. It would be fascinating to find the holographic dual of these matrix models and fluids.
Forward citations
Cited by 4 Pith papers
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On the strong coupling limit of Yang-Mills matrix models
In mass-deformed Yang–Mills matrix models, strong-coupling commutativity sets in at or above the critical fermion count N_c = 2(D−2), with the supersymmetric models sitting at the critical boundary where huge-operator...
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Holographic two-point functions of heavy operators revisited
Holographic two-point functions of heavy operators are reproduced by adding boundary terms to the D3-brane action and by the Gibbons-Hawking-York term in LLM backgrounds, but only in coordinate dependence and without ...
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Berry Picking: Random Wave Chaos Hierarchy for BPS Microstate Geometries
Wave chaos in BPS microstate geometries strengthens toward black-hole-like throats while geodesic chaos weakens, and weak-coupling CFT Renyi entropies do not share that bulk hierarchy.
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Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials
New superintegrability formulas are proposed for eigenvalue models built on multivariate Meixner-Pollaczek and Wilson measures, with the Wilson case left partly conjectural.
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