請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98785完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 黃宇廷 | zh_TW |
| dc.contributor.advisor | Yu-Tin Huang | en |
| dc.contributor.author | 李紹誠 | zh_TW |
| dc.contributor.author | Shao-Cheng Lee | en |
| dc.date.accessioned | 2025-08-19T16:11:36Z | - |
| dc.date.available | 2025-08-20 | - |
| dc.date.copyright | 2025-08-19 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-08-12 | - |
| dc.identifier.citation | Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B, 241(2):333–380, 1984.
C. Banerjee, Z. Chen, and N. Noman. Improved soft actor-critic: Mixing prioritized off- policy samples with on-policy experiences. IEEE Transactions on Neural Networks and Learning Systems, 35(3):3121–3129, 2022. V. Benedetti, H. Casini, and J. M. Magan. Selection rules for RG flows of minimal models. Phys. Rev. D, 111(6):065024, 2025. H. Chen, C. Hussong, J. Kaplan, and D. Li. A Numerical Approach to Virasoro Blocks and the Information Paradox. JHEP, 09:102, 2017. P. Di Francesco, P. Mathieu, and D. Senechal. Conformal Field Theory. Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997. P. H. Ginsparg. APPLIED CONFORMAL FIELD THEORY. In Les Houches Summer School in Theoretical Physics: Fields, Strings, Critical Phenomena, 9 1988. T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In International conference on machine learning, pages 1861–1870. Pmlr, 2018. G. Kántor, V. Niarchos, and C. Papageorgakis. Conformal bootstrap with reinforcement learning. Phys. Rev. D, 105(2):025018, 2022. A. Laio, U. L. Valenzuela, and M. Serone. Monte Carlo approach to the conformal bootstrap. Phys. Rev. D, 106(2):025019, 2022. A. Liu, D. Simmons-Duffin, N. Su, and B. C. van Rees. Skydiving to Bootstrap Islands. 7 2023. X. Ma, J. Chen, L. Xia, J. Yang, Q. Zhao, and Z. Zhou. Dsac: Distributional soft actor-critic for risk-sensitive reinforcement learning. Journal of Artificial Intelligence Research, 83, 2025. D. Mazac and M. F. Paulos. The analytic functional bootstrap. Part II. Natural bases for the crossing equation. JHEP, 02:163, 2019. E. Perlmutter. Virasoro conformal blocks in closed form. JHEP, 08:088, 2015. D. Poland, S. Rychkov, and A. Vichi. The Conformal Bootstrap: Theory, Numerical Techniques, and Applications. Rev. Mod. Phys., 91:015002, 2019. D. Simmons-Duffin. A Semidefinite Program Solver for the Conformal Bootstrap. JHEP, 06:174, 2015. D. Simmons-Duffin. The Conformal Bootstrap. In Theoretical Advanced Study Institute in Elementary Particle Physics:New Frontiers in Fields and Strings, pages 1–74, 2017. A. B. Zamolodchikov. CONFORMAL SYMMETRY IN TWO-DIMENSIONS: AN EXPLICIT RECURRENCE FORMULA FOR THE CONFORMAL PARTIAL WAVE AMPLITUDE. Commun. Math. Phys., 96:419–422, 1984. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98785 | - |
| dc.description.abstract | 在本篇文章中，我們提出一種數值方法用於共形自舉。首先，我們利用交叉對稱方程式計算給定的共形譜中的算符乘積展開係數，這些係數在不同交叉比的取樣下所形成的統計分布提供了一個衡量交叉對稱滿足程度的指標。基於此統計量，我們建構一個獎勵函數並通過遺傳演算法在給定的範圍裡搜尋能夠最大化該獎勵的共形譜。重要的是，此方法並不依賴單位性的假設。我們在中央荷小於 1的共形模型 (最小模型) 上驗證了此方法的有效性，所有找到的最佳解皆能對應到已知的最小模型。本方法本質上是透過線性變數的統計行為，來求解具非線性限制的方程組，其概念可推廣至更廣泛的自舉問題。 | zh_TW |
| dc.description.abstract | In this thesis, we introduce a numerical approach to bootstrapping the spectrum of general conformal field theories (CFT). Starting with a given spectrum we use crossing equations to compute the OPE coefficients. The statistical distribution of the latter, from sampling over cross-ratios, provides a robust measure of how close crossing symmetry is being solved. We define a reward function based on the statistics and utilize genetic algorithm to search for spectrum that optimize the reward. Importantly, the setup does not require unitarity. We demonstrate the utility of this approach on Virasoro blocks with c < 1, where all optimized points can be identified with known minimal models. This method of solving constrained equations of non-linear variables utilizing the statistics of linear variables can be applied to broader bootstrap problems. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-08-19T16:11:35Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-08-19T16:11:36Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員審定書 i
致謝 iii 摘要 v Abstract vii 目次 ix 圖次 xi 表次 xiii 第一章 Introduction 1 1.1 Motivation and Objectives 1 1.2 Summary of this work 2 第二章 Overviews of Conformal field theory, Minimal models and Conformal bootstrap 5 2.1 Conformal Symmetry in Two Dimensions 5 2.2 Basic Structure of 2D Conformal Field Theories 8 2.3 Minimal Models 13 2.4 Conformal bootstrap 17 第三章 Standard Deviation Method for Truncated Crossing Equation Consistency 21 3.1 Limitations of Crossing Symmetry Alone 21 3.2 Statistical Structure of the Truncated Crossing Equation 22 3.2.1 Solving Squared OPE Coefficients via Pseudo-Inverse 23 3.2.2 Standard deviation measurement of OPE Coefficient Distributions . 25 3.3 Reliability Test of Reward Signal 27 第四章 Searching algorithm for c < 1 CFTs 37 第五章 Optimization Method 43 5.1 Genetic algorithm for Reward optimization 43 5.2 Results 44 5.2.1 Search in (c, hϕ, hint) parameter space 44 5.2.2 Fusion sub-algebra construction from Primary Subsets 46 5.3 Exploratory Use of Reinforcement Learning 52 第六章 Conclusion and Outlook 57 6.1 Conclusion 57 6.2 Outlook 58 參考文獻 59 附錄 A — Virasoro conformal blocks construction 61 附錄 B — Global conformal block re-expansion 65 附錄 C — Background on RL Algorithms and Techniques 67 | - |
| dc.language.iso | en | - |
| dc.subject | 交叉對稱 | zh_TW |
| dc.subject | 共形自舉 | zh_TW |
| dc.subject | 標準差 | zh_TW |
| dc.subject | 最小模型 | zh_TW |
| dc.subject | Standard deviation | en |
| dc.subject | Conformal bootstrap | en |
| dc.subject | Minimal models | en |
| dc.subject | Crossing symmetry | en |
| dc.title | 非單位共形自舉的數值最佳化方法 | zh_TW |
| dc.title | Numerical optimization for non-unitary Conformal bootstrap | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 程之寧;陳柏中 | zh_TW |
| dc.contributor.oralexamcommittee | Miranda Cheng;Po-Chung Chen | en |
| dc.subject.keyword | 共形自舉,交叉對稱,標準差,最小模型, | zh_TW |
| dc.subject.keyword | Conformal bootstrap,Crossing symmetry,Standard deviation,Minimal models, | en |
| dc.relation.page | 69 | - |
| dc.identifier.doi | 10.6342/NTU202503813 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2025-08-14 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| dc.date.embargo-lift | 2025-08-20 | - |
| 顯示於系所單位： | 物理學系 | |
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