Open fishchain in N = 4 Supersymmetric Yang-Mills Theory
Nikolay Gromov, Julius Julius, Nicolò Primi
Abstract
A bstract We consider a cusped Wilson line with J insertions of scalar fields in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM and prove that in a certain limit the Feynman graphs are integrable to all loop orders. We identify the integrable system as a quantum fishchain with open boundary conditions. The existence of the boundary degrees of freedom results in the boundary reflection operator acting non-trivially on the physical space. We derive the Baxter equation for Q-functions and provide the quantisation condition for the spectrum. This allows us to find the non-perturbative spectrum numerically.
Topics & Concepts
Integrable systemScalar (mathematics)Mathematical physicsBoundary value problemSpectrum (functional analysis)Feynman diagramOperator (biology)Boundary (topology)QuantumMathematicsPhysicsMathematical analysisQuantum mechanicsGeometryTranscription factorRepressorGeneChemistryBiochemistryBlack Holes and Theoretical PhysicsAlgebraic structures and combinatorial modelsNonlinear Waves and Solitons