Coulomb Branch and Integrability

2025/06/08 by Frank Coronado, Coronado, Frank, Shota Komatsu +3 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2506.07222

openalex publication_date 2025/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study one-point functions of non-BPS single-trace operators on the Coulomb branch of planar N=4 supersymmetric Yang-Mills theory. Holography relates them to overlaps between on-shell closed string states and a boundary state describing a probe D3-brane in AdS₅× S⁵. Assuming that the D-brane preserves integrability, we formulate and solve integrable bootstrap equations satisfied by the boundary state at finite 't Hooft coupling. This leads to a closed-form determinant expression for one-point functions at finite coupling, valid for sufficiently long operators. We test the result against direct field theory computations at tree level and one loop, finding perfect agreement.

Citations

• Derivations for the MPS overlap formulas of rational spin chains
• Symplectic Grassmannian description of the Coulomb branch three and four point amplitudes
• Integrable Corners in the Space of Gukov-Witten Surface Defects
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• The spectrum of defect ABJM theory
• 't Hooft loops in N=4 super-Yang-Mills
• Exact overlaps for "all" integrable matrix product states of rational spin chains
• Dual overlaps and finite coupling 't Hooft loops
• Moduli Spaces in CFT: Large Charge Operators
• Moduli Spaces in CFT: Bootstrap Equation in a Perturbative Example
• Vacuum Condensates on the Coulomb Branch
• Coulomb Branch Amplitudes from a Deformed Amplituhedron Geometry
• 't Hooft loops and integrability
• Double excitations in the AdS(5)/CFT(4) integrable system and the Lagrange operator
• Overlaps and Fermionic Dualities for Integrable Super Spin Chains
• Lectures on Three-point Functions in N=4 Supersymmetric Yang-Mills Theory
• Asymptotic Four Point Functions
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4\n super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• The dilatation operator of conformal super-Yang–Mills theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• How Algebraic Bethe Ansatz works for integrable model
• Supersymmetric Yang-Mills theories

Cited by

• Wilson loops on the Coulomb branch of N=4 super-Yang-Mills
• String Integrability on the Coulomb Branch

Related

• String Integrability on the Coulomb Branch
• Vacuum Condensates on the Coulomb Branch
• One-point functions in AdS/dCFT: MPS and twisted Yangian
• Wilson loops on the Coulomb branch of N=4 super-Yang-Mills
• Bootstrapping N = 4 sYM correlators using Integrability and Localization