臺灣博碩士論文加值系統

在這篇論文裡，我們首先複習了關於保角場論和反迪希特時空中的高自旋場論。 然後複習了測地線的維騰圖[2]，被提出是純量保角部分震幅的對偶透過算符乘 積展開的方式來看在這階段結束前我們嚴格的計算出了自然的基底對於所有的 四點測地線的維騰圖，研究了他們是如何被黏在一起透過積分的奇點結構，這 讓我們嚴格的構造出純量保角部分震幅的對偶,當外角具有自旋非零的時候。除 此之外，我們研究了對於傳播子的分裂表示法去展現一般的維騰圖對於任意傳 播的自旋，可以被系統性的分解成許多測地線的維騰圖。最後我們做了一些論 述關於外角傳播子具有自旋的情況。

In this thesis, first we review the basic knowledge about the conformal field theory and the AdS higher spin theory. Then we revisit the so-called “Geodesic Witten Diagrams” (GWDs) [2], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related “split representation” for the bulk to bulk spinning propagator, to demonstrate how ordinary Witten diagram with arbitrary spin exchange, can be systematically decomposed into GWDs. We also comment how to generalize to spinning cases.

1 Introduction 5
2 Basic review of Conformal field theory 8
2.1 ConformalSymmetryAndCorrelation 8
2.1.1 Correlation functions of primary operators and Embedding
Formalism 10
2.1.2 Operator product expansion 12
2.2 ScalarAndSpinningConformalBlocks 15
2.2.1 Spinning Conformal Blocks And Three Point Functions 16
2.3 ConformalBootstrap 20
3 Scalar Four Point Geodesic Witten Diagrams Revisited 23
3.1 Embedding Formalism for AdS And Split Representation 23
3.2 Three point Witten Diagrams In Higher-Spin Theory 31
3.3 Scalar Four Point Geodesic Witten Diagrams Revisited . 34
4 Spinning Conformal Partial Waves from Anti-de Sitter Space 41
4.1 GeodesicInteraction 41
4.1.1 The(l1,l2,0)Case 45
4.1.2 The(1,1,2)Case. 45
5 Decomposition of Witten Diagrams via Split Representation 50
5.1 Decomposition of Witten Diagrams for External Scalars 50
5.2 Comments on Fields with Spins 58
6 Conclusion and Future Direction 60
6.1 Conclusion. 60
6.2 FutureDirection 60
6.2.1 Consider Mixed Tensor 60
6.2.2 FermionAndParityOddInteractions 61
6.2.3 AddingLoops 61

A Appendix: Integrals for Three Point Geodesic Witten Diagrams 62
A.1 ScalarIntegral 62
A.2 Spin-lIntegral 63
B Integrals for Three Point Normal Witten Diagrams 65
C Rewriting tensor structures and some useful identities 67
D Explicit Calculations for l1, l2, 0 And 1, 1, 2 Examples 70
D.1 (l1,l2,0)70
D.2 (1,1,2) 71
Reference 72

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