arXiv 2201.044912022-01hep-thgr-qcmath-phmath.CAmath.MP

Irregular Liouville correlators and connection formulae for Heun functions

Giulio Bonelli, Cristoforo Iossa, Daniel Panea Lichtig, Alessandro Tanzini

备注：: 61 pages, many diagrams, 2 figures, huge list of symbols, comments welcome
DOI：: 10.1007/s00220-022-04497-5

英文摘要：

We perform a detailed study of a class of irregular correlators in Liouville Conformal Field Theory, of the related Virasoro conformal blocks with irregular singularities and of their connection formulae. Upon considering their semi-classical limit, we provide explicit expressions of the connection matrices for the Heun function and a class of its confluences. Their calculation is reduced to concrete combinatorial formulae from conformal block expansions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

New indefinite integrals of confluent Heun functions

We obtain some new formulae to compute the first derivative of confluent and biconfluent Heun functions under the minimal assumption of fixing only one parameter. These results together with the Lagrangian formulation of a general homogeneous linear ordinary differential equation allow to construct several new indefinite integrals for the confluent, biconfluent, doubly confluent, and triconfluent Heun functions.

2018-10-13hep-thmath-phmath.CA

Kerr-Newman-de Sitter黑洞的准正规模：来自Heun连接公式

Quasinormal modes of Kerr-Newman-de Sitter black holes from Heun connection formulae

Toyota Technological Institute（丰田技术研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；Tokyo Metropolitan University（东京都立大学）；Nagoya University（名古屋大学）

本文利用Heun连接公式解析研究Kerr-Newman-de Sitter时空的准正规模，推导出小宇宙学常数、近极端和近Nariai极限下的谱及非整数幂修正。

2026-09-17astro-ph.HEgr-qchep-th

AdS/CFT中的精确低温格林函数：从Heun方程到合流Heun方程

Exact low-temperature Green's functions in AdS/CFT: From Heun to confluent Heun

本研究借助Heun连接问题的最新进展，微扰求解得到RN-AdS₅黑膜对偶CFT₄中低温带电标量算符关联函数的精确表达式，提取了全息超导体临界温度与拟正模色散关系，且与数值结果精确吻合。

2024-12-12cond-mat.str-elgr-qchep-th

Exact thermal correlators of holographic $CFT$s

We compute the exact retarded Green's functions in thermal $CFT$s with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in $AdS$ spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville $CFT$. The connection formulae associated…

2023-02-24cond-mat.str-elgr-qchep-th

带二级退化场插入的5点Liouville共形块的精确表达式

Exact expressions for the 5-Point Liouville conformal block with a level-two degenerate field insertion

Yerevan Physics Institute（埃里温物理研究所）

本文通过简化递推关系并给出归纳证明，用单个超几何函数精确表示带二级退化场的5点Liouville共形块，并在准经典极限下恢复Heun方程的有效表示。

2026-09-18hep-th

Riemann-Hilbert treatment of Liouville theory on the torus

We apply a perturbative technique to study classical Liouville theory on the torus. After mapping the problem on the cut-plane we give the perturbative treatment for a weak source. When the torus reduces to the square the problem is exactly soluble by means of a quadratic transformation in terms of hypergeometric functions. We give general formulas for the deformation of a torus and apply them to the case of the deformation of the square. One can compute the Heun parameter to first order and express the solution in terms of quadratures. In addition we give in terms of quadratures of hypergeome…

2010-12-05hep-th

更多相关论文收起更多论文

Riemann-Hilbert treatment of Liouville theory on the torus: The general case

We extend the previous treatment of Liouville theory on the torus, to the general case in which the distribution of charges is not necessarily symmetric. This requires the concept of Fuchsian differential equation on Riemann surfaces. We show through a group theoretic argument that the Heun parameter and a weight constant are sufficient to satisfy all monodromy conditions. We then apply the technique of differential equation on a Riemann surface to the two point function on the torus in which one source is arbitrary and the other small. As a byproduct we give in terms of quadratures the exact …

2011-05-06hep-th

Entanglement Renyi entropy of two disjoint intervals for large $c$ Liouville field theory

Entanglement entropy (EE) is a quantitative measure of the effective degrees of freedom and the correlation between the sub-systems of a physical system. Using the replica trick, we can obtain the EE by evaluating the entanglement Renyi entropy (ERE). The ERE is a $q$-analogue of the EE and expressed by the $q$ replicated partition function. In the semi-classical approximation, it is apparently easy to calculate the EE because the classical action represents the partition function by the saddle point approximation and we do not need to perform the path integral for the evaluation of the partit…

2022-09-30hep-th

双曲 $CFT$s 的全息热关联函数

Holographic Thermal Correlators for Hyperbolic $CFT$s

本文利用全息方法，将标量场波动方程重写为 Heun 方程，并通过 Liouville 理论中的交叉对称性获得连接公式，从而精确计算了双曲 CFT 中标量算子的推迟热 Green 函数。

2023-11-26hep-th

爆破边缘：Lamé 方程的连接公式与稳定性图

Blowing-up the edge: connection formulae and stability chart of the Lamé equation

本文通过超对称规范理论与二维共形场论研究周期谱问题，提出用爆破方程极限重求和半经典 Virasoro 块的新方法，并精确刻画了 Lamé 方程等量子可积系统的稳定性图与连接问题。

2025-07-07hep-thmath-phmath.MP

Confluent conformal blocks and the Teukolsky master equation

Quasinormal modes of usual, four dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation. In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert problem, which was recently solved in terms of the Painlevé V transcendent. We use this formulation to generate the small-frequency expansion for the angular spheroidal harmonic eigenvalue, and derive conditions on the monodromy properties for the radial modes. Using exponentiation, we relate the accessory parameter to a semi-classical conformal description …

2022-05-25gr-qchep-th

不规则 Fibonacci 共形块

Irregular Fibonacci Conformal Blocks

本工作研究了插入 3 阶退化场的不规则 Liouville 共形块，推导了相应的 3 阶 BPZ 方程，利用 Lefschetz thimbles 构造积分表示并证明其满足该方程，最后证明在半经典极限下可用 Heun 函数表达且行为与共形权重一致。

2023-11-22hep-th

Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT

All types of 4-point spheric conformal blocks in both sectors of N=1 superconformal field theory are introduced and analyzed. The elliptic recurrence formulae are derived for all the types of blocks not previously discussed in the literature. The results are used for numerical verification of the crossing symmetry of some 4-point functions in the N=1 superconformal Liouville field theory.

2011-03-12hep-th

SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with c < 1 matter

We consider BRST quantized 2D gravity coupled to conformal matter with arbitrary central charge $c^M = c(p,q) < 1$ in the conformal gauge. We apply a Lian-Zuckerman $SO(2,\bbc)$ ($(p,q)$ - dependent) rotation to Witten's $c^M = 1$ chiral ground ring. We show that the ring structure generated by the (relative BRST cohomology) discrete states in the (matter $\otimes$ Liouville $\otimes$ ghosts) Fock module may be obtained by this rotation. We give also explicit formulae for the discrete states. For some of them we use new formulae for $c <1$ Fock modules singular vectors which we present in term…

1992-01-29hep-thmath.RT

Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation

In this work the correspondence between the semiclassical limit of the DOZZ quantum Liouville theory on the torus and the Nekrasov-Shatashvili limit of the N=2* (Omega-deformed) U(2) super-Yang-Mills theory is used to propose new formulae for the accessory parameter of the Lame equation. This quantity is in particular crucial for solving the problem of uniformization of the one-punctured torus. The computation of the accessory parameters for torus and sphere is an open longstanding problem which can however be solved if one succeeds to derive an expression for the so-called classical Liouville…

2014-04-02hep-th

A Study of Two Dimensional String Theory (PhD Thesis)

This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. Introductions to both the Liouville model and its matrix model formulation are included. In particular the special states are discussed. Some calculations of partition functions on genus one using field theory techniques are given. Nonperturbative issues and string theory at finite radius are discussed. Zero momentum correlation functions are calculated using the matrix model. One important result is a set of recursion relations. The treatment is extended to nonzero momentum. …

1992-05-18hep-th