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Vacuum Condensates on the Coulomb Branch
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Vacuum Condensates on the Coulomb Branch
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We study correlation functions on the Coulomb branch of planar $\mathcal{N} = 4$ super-Yang- Mills theory (SYM), and their relationship with integrability, the operator product expansion (OPE), the sum rule, the large charge expansion, and holography. First, we compute one-point functions of arbitrary scalar operators at weak coupling and derive a compact spin-chain representation. We next study the two-point functions of chiral primaries at one loop and find that the radius of convergence of OPE in position space is infinite. We estimate the asymptotic growth of the OPE data based on this finding. Finally, we propose a concrete nonperturbative formula that connects the correlation functions on the Coulomb branch with the correlation functions with large charge insertions at the conformal point and provide a holographic interpretation based on a large D3-brane in AdS. The formula extends the known connection between the large charge sector and the Coulomb branch for rank-1 theories to the large $N$ limit.
Forward citations
Cited by 5 Pith papers
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Integrable chiral and achiral n-site boundary states of the ABJM spin chain are obtained by solving KT-relations for elementary blocks and K(u), with nontrivial solutions for even n and operator-valued 1-site Clifford pairs.
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Chiral Integrable Boundary States of ABJM Spin Chain from Reflection Equations
A framework is proposed for 2n-site chiral integrable matrix product states in the ABJM spin chain from reflection equations, with exact overlap formulas for four-site states and numerical checks of subspaces.
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Wilson loops on the Coulomb branch of $N=4$ super-Yang-Mills
Holographic minimal-surface calculation maps the Gross-Ooguri phase transition for circular Wilson loops on the Coulomb branch and indicates tree-level exactness for the straight line.
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