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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 黃宇廷 | zh_TW |
| dc.contributor.advisor | Yu-Tin Huang | en |
| dc.contributor.author | 郭家愷 | zh_TW |
| dc.contributor.author | Chia-Kai Kuo | en |
| dc.date.accessioned | 2024-05-02T16:07:58Z | - |
| dc.date.available | 2024-05-03 | - |
| dc.date.copyright | 2024-05-01 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-04-17 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92598 | - |
| dc.description.abstract | 在本篇論文中，我們討論如何計算高點ABJM圈振幅的方法，並引入了正幾何的架構到這個理論。
在第一部分中，我們以八點振幅為例，計算一圈、兩圈振幅，所使用的方法可以直接推廣到更高點的圈振幅。我們首先利用廣義么正性和發散限制條件，確定了該理論的一圈和兩圈被積函數。隨後，我們計算這些被積函數積分後的結果，得到完整的一圈和兩圈八點振幅。 在第二部分中，我們引進並研究了與ABJM振幅和它的正幾何。我們先在動量空間定義他的樹正幾何，接著在動量扭空間將樹正幾何推廣到圈正幾何。我們引進新的正幾何與$\\cal{N}=$4 超對稱楊-米爾斯理論的正幾何有非常簡單的關係：對所有相鄰扭量加上辛條件，並將所有扭量括號由正號改成負號。 | zh_TW |
| dc.description.abstract | In this thesis, we discuss methods for calculating the higher-point ABJM loop amplitudes and introduce the positive geometry framework into this theory.
In the first part, we take the eight-point amplitude as an example and calculate the one-loop and two-loop amplitudes. The methods used can be directly extended to higher-point loop amplitudes. We first determine the one-loop and two-loop integrands of the theory using generalized unitarity and IR constraints. Then, we compute these integrands to derive complete one- and two-loop eight-point amplitudes. In the second part, we introduce the positive geometry associated with ABJM amplitudes. We first define its tree-level geometry in momentum space and then extend it to loop-level in momentum twistor space. The new positive geometry has a very simple relationship with one of $\\cal{N}=$4 super Yang-Mills theory: imposing symplectic conditions on all adjacent twistors and changing the sign of all twistor brackets from positive to negative. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-05-02T16:07:57Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-05-02T16:07:58Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix I Introduction 1 II Scattering Amplitudes in ABJM Theory 7 Chapter 1 Tree Amplitudes and Loop Integrands in ABJM 9 1.1 Tree-level amplitudes . . . . . . . . . . . . . . . . 9 1.2 The one-loop eight-point integrand . . . . . . . . . 16 1.2.1 Maximal cuts constraint . . . . . . . . . . . . . 17 1.2.2 The complete one-loop eight-point integrand . . . .18 1.3 The two-loop eight-point integrand . . . . . . . . . 21 1.3.1 Generalized unitarity and IR constraint . . . . . 24 1.3.2 The complete two-loop eight-point integrand . . . .36 Chapter 2 The Integrated Loop Amplitudes in ABJM 41 2.1 The one-loop eight-point amplitudes . . . . . . . . .41 2.2 The two-loop eight-point amplitude . . . . . . . . . 43 2.2.1 The computation of two-loop integrals . . . . . . 44 2.2.2 The integrated result . . . . . . . . . . . . .. . 61 2.2.3 Consistency checks and analytic structure . . . . .65 III Positive Geometry in ABJM Theory 73 Chapter 3 Geometry of Tree Amplitudes 75 3.1 Momentum space geometry: orthogonal momentum amplituhedron .76 3.1.1 Definition: maps from OG+ . . . . . . . . . . . . . . . 76 3.1.2 Reduced SUSY amplitudes as canonical form . . . . . . . . 79 3.2 Twistor-string map and the pushforward . . . . . . . . . . 82 Chapter 4 Geometry of Loop Integrands 95 4.1 Momentum twistor geometry: ABJM amplituhedron . . . . . . . 96 4.1.1 Positive kinematic . . . . . . . . . . . . . . . . . . . .96 4.1.2 Definition of loop geometry . . . . . . . . . . . . . . 100 4.2 Loop integrands from positive geometry . . . . . . . . . . 107 4.2.1 Chambers and one-loop integrands . . . . . . . . . . . . 107 4.2.2 Higher loops and bipartite negative geometries . . . . . 125 4.3 Beyond positive solutions and parity action . . . . . . . .134 References 145 | - |
| dc.language.iso | en | - |
| dc.subject | 圈振幅 | zh_TW |
| dc.subject | ABJM 理論 | zh_TW |
| dc.subject | 正幾何 | zh_TW |
| dc.subject | Positive Geometry | en |
| dc.subject | ABJM Theory | en |
| dc.subject | Loop Amplitudes | en |
| dc.title | ABJM 圈振幅及其正幾何 | zh_TW |
| dc.title | Loop Amplitudes of ABJM and Its Positive Geometry | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 博士 | - |
| dc.contributor.coadvisor | 何頌 | zh_TW |
| dc.contributor.coadvisor | Song He | en |
| dc.contributor.oralexamcommittee | 川合光;沈家賢;丹尼爾包曼;詹傳宗;賀培銘 | zh_TW |
| dc.contributor.oralexamcommittee | Hikaru Kawai;Chia-Hsien Shen;Daniel Baumann;Chuan-Tsung Chan;Pei-Ming Ho | en |
| dc.subject.keyword | ABJM 理論,圈振幅,正幾何, | zh_TW |
| dc.subject.keyword | ABJM Theory,Loop Amplitudes,Positive Geometry, | en |
| dc.relation.page | 150 | - |
| dc.identifier.doi | 10.6342/NTU202400860 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2024-04-17 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| 顯示於系所單位： | 物理學系 | |
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