[論文レビュー] The complex Liouville string

Scott Collier, Lorenz Eberhardt+2 more|arXiv (Cornell University)|Sep 25, 2024

Computational Physics and Python Applications被引用数 7

ひとこと要約

本論文は complex Liouville string を紹介し、それは二つの複素共役 Liouville CFT を結合して形成される solvable な worldsheet 理論であり、boundary observables と非摂動効果を含む双対描述を double-scaled two-matrix model によって確立し、de Sitter holography の解釈を与える。

ABSTRACT

We introduce the complex Liouville string, a solvable string theory defined by coupling two Liouville theories with complex conjugate central charges $c \in 13+i \mathbb{R}$ on the worldsheet. We compute its amplitudes from first principles and establish a duality with a double-scaled two-matrix integral. We also analyze general worldsheet boundaries and non-perturbative effects in the genus expansion. By expressing the complex Liouville string as a 2d dilaton gravity theory with a sine potential, we show that it admits both AdS$_2$ and dS$_2$ vacua.

研究の動機と目的

• Introduce the complex Liouville string (C̄LS) defined by c+ in 13+iR+ and c− in 13−iR+ coupled with bc ghosts.
• Compute string amplitudes from first principles via analytic bootstrap and DOZZ structure constants.
• Establish a dual description in terms of a double-scaled two-matrix integral and derive the associated spectral curve.
• Analyze general worldsheet boundaries, non-perturbative effects, and cosmological interpretations in de Sitter gravity.

提案手法

• Define the worldsheet theory as a combination of two Liouville CFTs with complex conjugate central charges.
• Use analytic bootstrap and resonance pole analysis to determine perturbative amplitudes A_{g,n}^{(b)}(p).
• Relate amplitudes to a double-scaled two-matrix model with spectral curve x(z) and y(z) given by (10).
• Apply topological recursion on the spectral curve to compute multi-resolvent quantities and map to A_{g,n}^{(b)} via (12).
• Express A_{g,n}^{(b)} in terms of stable graphs with vertex amplitudes V^{(b)}_{g_v,n_v} and momentum integrals as in (13).
• Incorporate worldsheet boundaries and ZZ-instantons through trumpet functions and non-perturbative completions (16).

実験結果

リサーチクエスチョン

• RQ1 Can the complex Liouville string amplitudes be determined from first principles using analytic bootstrap and DOZZ data?
• RQ2 What is the dual matrix model description of the C̄LS and its spectral curve structure?
• RQ3 How do general worldsheet boundaries and non-perturbative effects influence the genus expansion and holographic interpretation?
• RQ4 How do the amplitudes relate to de Sitter quantum gravity and cosmological correlators in dS3?
• RQ5 What is the role of ZZ-instantons and trumpet boundaries in non-perturbative completions of the theory?

主な発見

• A coherent definition of the complex Liouville string combining two Liouville CFTs with c±=13±iR and bc ghosts is given, with on-shell vertex operators V_p and a well-defined perturbative expansion.
• A dual description via a double-scaled two-matrix model is established, with a non-algebraic spectral curve x(z) = -2 cos(π b^{-1}√z), y(z) = 2 cos(π b√z).
• Leading eigenvalue density ρ_0(x) is obtained from the spectral curve and the associated topological recursion computes all A_{g,n}^{(b)} through the relation (12).
• String amplitudes satisfy symmetry relations, dilaton and higher equations of motion, and agree with worldsheet calculations in low genera (e.g., (0,4) and (1,1)).
• Non-perturbative effects are captured by ZZ-instantons with purely imaginary tensions, indicating oscillatory, not exponentially suppressed, corrections and a resurgence structure.
• A de Sitter gravity interpretation emerges, linking Liouville theory to dS3 quantum gravity and a de Sitter/matrix model holographic correspondence.