de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs
Livia Ferro, Tomasz Lukowski, Lecheng Ren, Marcus Spradlin, Anastasia Volovich + 2 more
TLDR
This paper provides an explicit formula for the cosmological wavefunction in de Sitter space using quadrangular polylogarithms for chain graphs.
Key contributions
- Presents an explicit formula for the n-site chain graph contribution to the de Sitter cosmological wavefunction.
- Leverages total compatibility with the A_{2n-2} cluster algebra for the function's symbol.
- Utilizes Rudenko's quadrangular polylogarithms as a complete basis for these functions.
- Proves the formula by linking recursive differential equations to a coproduct formula.
Why it matters
This paper offers a concrete mathematical tool for calculating cosmological wavefunctions in de Sitter space. By leveraging quadrangular polylogarithms and cluster algebras, it provides a novel approach to complex theoretical physics problems, potentially simplifying future calculations.
Original Abstract
We present an explicit formula for the $n$-site chain graph contribution to the cosmological wavefunction for conformally coupled $φ^3$ theory in de Sitter space. Our result relies on the recent finding that the symbol of this function satisfies total compatibility with respect to the $A_{2n-2}$ cluster algebra, and that Rudenko's quadrangular polylogarithms provide, by construction, a complete basis for such functions. We prove our formula by directly relating a recursive set of differential equations satisfied by these wavefunction coefficients to a recursive coproduct formula for quadrangular polylogarithms.
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