Triangle Seminars
Wednesday, 12 Mar 2025
Yangian symmetry, GKZ equations and integrable Feynman graphs
📍 London
Fedor Levkovich-Maslyuk
(City University London)
Abstract:
We extend the powerful property of Yangian invariance to a new large class of conformally invariant multi-loop Feynman integrals. This leads to new highly constraining differential equations for them, making integrability visible at the level of individual Feynman graphs. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. The graphs we consider determine correlators in the recently proposed "loom" fishnet CFTs. The construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs. We also relate these equations in certain cases to famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators, opening the way to using new powerful solution methods.
We extend the powerful property of Yangian invariance to a new large class of conformally invariant multi-loop Feynman integrals. This leads to new highly constraining differential equations for them, making integrability visible at the level of individual Feynman graphs. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. The graphs we consider determine correlators in the recently proposed "loom" fishnet CFTs. The construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs. We also relate these equations in certain cases to famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators, opening the way to using new powerful solution methods.
Posted by: andrea
Thursday, 13 Mar 2025
(Super)blocks, free block coefficients, and applications to N=4 SYM at strong coupling
📍 London
Paul Heslop
(Durham University)
Abstract:
Recently a formula for free theory (super)block coefficients in many SCFTs was first guessed and then proved https://arxiv.org/abs/2502.14077. I will describe this result and summarise some of the background to it, involving a number of beautiful relations between superblocks, symmetric polynomials, superJacobi polynomials, Heckman Opdam hypergeometric functions, Calogero Sutherland Moser wave functions and Cauchy identities. I will also give a new application to strong coupling N=4 SYM.
Recently a formula for free theory (super)block coefficients in many SCFTs was first guessed and then proved https://arxiv.org/abs/2502.14077. I will describe this result and summarise some of the background to it, involving a number of beautiful relations between superblocks, symmetric polynomials, superJacobi polynomials, Heckman Opdam hypergeometric functions, Calogero Sutherland Moser wave functions and Cauchy identities. I will also give a new application to strong coupling N=4 SYM.
Posted by: QMW