A note on the large-c conformal block asymptotics and α-heavy operators

IF 2.5 3区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Nuclear Physics B Pub Date : 2024-11-17 DOI:10.1016/j.nuclphysb.2024.116741
Konstantin Alkalaev , Pavel Litvinov
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Abstract

We consider α-heavy conformal operators in CFT2 which dimensions grow as h=O(cα) with α being non-negative rational number and conjecture that the large-c asymptotics of the respective 4-point Virasoro conformal block is exponentiated similar to the standard case of α=1. It is shown that the leading exponent is given by a Puiseux polynomial which is a linear combination of power functions in the central charge with fractional powers decreasing from α to 0 according to some pattern. Our analysis is limited by considering the first six explicit coefficients of the Virasoro block function in the coordinate. For simplicity, external primary operators are chosen to be of equal conformal dimensions that, therefore, includes the case of the vacuum conformal block. The consideration is also extended to the 4-point W3 conformal block of four semi-degenerate operators, in which case the exponentiation hypothesis works the same way. Here, only the first three block coefficients can be treated analytically.
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关于大 C 保角块渐近和 α 重算子的说明
我们考虑了 CFT2 中的 α 重共形算子,其维度增长为 h=O(cα),其中 α 为非负有理数。我们猜想,与 α=1 的标准情况类似,各自的 4 点 Virasoro 共形块的大 C 渐近线是指数化的。结果表明,前导指数由普伊塞多项式给出,而普伊塞多项式是中心电荷幂函数的线性组合,其分数幂从 α 到 0 按某种规律递减。我们的分析仅限于考虑坐标中维拉索罗分块函数的前六个显式系数。为简单起见,外部主算子被选择为等保角维度,因此包括真空保角块的情况。我们也可以把考虑范围扩展到由四个半退化算子组成的 4 点 W3 共形块,在这种情况下,指数化假设也以同样的方式起作用。在这里,只有前三块系数可以进行分析处理。
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来源期刊
Nuclear Physics B
Nuclear Physics B 物理-物理:粒子与场物理
CiteScore
5.50
自引率
7.10%
发文量
302
审稿时长
1 months
期刊介绍: Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.
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