7 papers
Diagrammatic construction of GKZ systems for polygonal functions
K. B. Alkalaev, Semyon Mandrygin, Y. M. Zalishchansky
We investigate the recently introduced polygonal hypergeometric functions [arXiv:2502.12127, arXiv:2507.01904], which are conjectured to evaluate multipoint parametric one-loop con…
Thermal conformal partial waves from flat-space and defect CFT
K. B. Alkalaev, Semyon Mandrygin, Vladimir Samsonov
We establish a correspondence between conformal partial waves on flat, thermal, and defect backgrounds using the shadow formalism. We demonstrate that scalar one-point thermal bloc…
Multipoint conformal integrals in dimensions. Part II: Polygons and basis functions
K. B. Alkalaev, Semyon Mandrygin
We explicitly construct a class of multivariate generalized hypergeometric series which is conjectured in our previous paper [Alkalaev & Mandrygin 2025] to calculate multipoint one…
Multipoint conformal integrals in dimensions. Part I: Bipartite Mellin-Barnes representation and reconstruction
K. B. Alkalaev, Semyon Mandrygin
We propose a systematic approach to calculating -point one-loop parametric conformal integrals in dimensions which we call the reconstruction procedure. It relies on decompo…
One-point thermal conformal blocks from four-point conformal integrals
K. B. Alkalaev, Semyon Mandrygin
We develop the thermal shadow formalism to study the conformal blocks decomposition in -dimensional conformal field theory on , where t…
Torus shadow formalism and exact global conformal blocks
K. B. Alkalaev, Semyon Mandrygin
Using the shadow formalism we find global conformal blocks of torus CFT. It is shown that -point torus blocks in the ``necklace'' channel (a loop with legs) are expresse…
Torus conformal blocks and Casimir equations in the necklace channel
K. B. Alkalaev, Semyon Mandrygin, Mikhail Pavlov
We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of…