arXiv subjects

V. S. Khiteev

Publications and source records attributed to V. S. Khiteev.

4 recordsLinked to original sources

arXiv2026

Wilson network expansion for four-point contact and exchange scalar Feynman diagrams in AdS$_2$

We derive new integral identities for AdS propagators and further develop the Wilson network expansion for AdS Feynman diagrams. In particular, we demonstrate that four-point contact and exchange scalar diagrams in two dimensions can be expanded into several infinite series of matrix elements of Wilson line network operators with running conformal weights. Each series is characterized by specific multi-trace operators associated with the external and intermediate edges of the corresponding graphs. The resulting expansions near the conformal boundary reproduce the well-known decompositions of the corresponding four-point Witten diagrams into conformal blocks.

hep-th↗

arXiv2025

Wilson network decomposition of AdS Feynman diagrams in two dimensions

We show that Feynman diagrams in AdS$_2$ space can be decomposed into infinite series of matrix elements of Wilson line network operators. The case of the 3-point scalar Feynman diagram with endpoints in the bulk is studied in detail. The resulting decomposition is similar to the conformal block decomposition of Witten diagrams, i.e. it comprises a single-trace term and infinite sums of double-trace terms. We derive a number of AdS propagator identities which relate the standard bulk-to-bulk propagators with the modified bulk-to-bulk propagators of two different types responsible for extracting single-trace and double-trace terms.

hep-th↗

arXiv2025

Holographic reconstruction for AdS Wilson line networks and scalar Witten diagrams

We find a holographic reconstruction formula for gravitational Wilson line network operators in AdS$_2$ evaluated between Ishibashi states of the algebra $sl(2,\mathbb{R})$. It is given in integral form where the integrand is the global conformal block multiplied by a smearing function which is the product of the scalar bulk-to-boundary propagators. The integral can be explicitly calculated as multidimensional series of which arguments are rational functions of endpoint coordinates. In the case of two and three endpoints the resulting expressions allow one to establish a number of relations between the gravitational Wilson line networks and Witten diagrams for massive scalar fields in AdS$_2$.

hep-th↗

arXiv2023

Wilson networks in AdS and global conformal blocks

We develop the relation between gravitational Wilson line networks, defined as a particular product of Wilson line operators averaged over the cap states, and conformal correlators in the context of the AdS$_2$/CFT$_1$ correspondence. The $n$-point $sl(2, \mathbb{R})$ comb channel global conformal block in CFT$_1$ is explicitly calculated by means of the extrapolate dictionary relation from the gravitational Wilson line network with $n$ boundary endpoints stretched in AdS$_2$. Remarkably, the Wilson line calculation directly yields the conformal block in a particularly simple form which up to the leg factor is given by the comb function of cross-ratios. It is also found that the comb channel structure constants are expressed in terms of factorials and triangle functions of conformal weights whose form determines fusion rules for a given 3-valent vertex. We obtain analytic expressions for the Wilson line matrix elements in AdS$_2$ which are building blocks of the Wilson line networks. We analyze general cap states and specify those which lead to asymptotic values of the Wilson line networks interpreted as boundary correlators of CFT$_1$ primary operators. The cases of (in)finite-dimensional $sl(2, \mathbb{R})$ modules carried by Wilson lines are treated on equal footing that boils down to consideration of singular submodules and their contributions to the Wilson line matrix elements.

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