등각장론과 끈이론의 비섭동적 연구

다국어 초록 (Multilingual Abstract)

In this dissertation we discuss about some progress on understanding in super-conformal field theories and higher-spin theory.

We first study the basic properties of super-conformal symmetry in field theory and their implications on physical quantity. We review the AdS/CFT correspondence briefly and discuss
the strong/weak nature.

Main part consist of three part. In terms of AdS/CFT correspondence, we study the anomalous dimension of operators in N=4 SYM with large spin and R-charge in the symmetric representaion. Explicit calculation of energy spectrum of D-branes in terms of spin and charge is performed.
Secondly, we study the infra-red finiteness of scattering amplitude in ABJM theory. In terms of Kinishita-Lee-Nauenberg theorem, we calculated soft radiations and check the cancellations of leading order divergence between loop corrections and soft radiations.

Finally asymptotic symmetry in super-symmetric higher-spin theory in AdS_3. We found that shs^E(N|2,R) symmetry enhanced to the Super-W_infty algebra.

국문 초록 (Abstract)

이 논문에서는 초대칭 등각장론과 3차원 중력 이론에 대한 세 가지 분야의 연구를 한다.

4차원 시공간의 초대칭 등각장론에서 국소적 연산자의 scaling-dimension 을 홀로그래피 대응성을 이용하여 계산한다. 이를 통하여 섭동적 전개를 통해 발견된 스핀에 대한 로그 스케일링이 비섭동적 영역에서도 여전히 유효함을 확인한다.
또한 천-사이먼즈 초대칭 등각장론의 산란 진폭에 대한 발산 문제를 다룬다. 섭동 전개의 보정항에서 나타나는 적외선 영역에서의 발산이 Soft-Bremsstrahlung 의 보정항과 서로 상쇄되는 과정을 보인다.

마지막으로 높은 스핀 입자를 가지는 3차원의 중력이론에서 점근적 대칭성이 확장됨을 보인다. 안티 드 시터 공간에 대한 경계조건을 통해 점근적 대칭성이 수퍼-W 대칭성으로 주어짐을 확인한다.

목차 (Table of Contents)

• I Super-conformal symmetry and Duality 7
• 1 Introductions 8
• 2 (Super-)conformal eld theory 11
• 2.1 (Super-)conformal symmetry . . . . . . . . . . . . . . . . . . . . . . 12
• 2.2 N = 4 Super Yang-Mills theory in 4 dimension . . . . . . . . . . . . 21
• 2.3 N = 6 Chern-Simons matter theory in 3 dimension . . . . . . . . . . 23
• 3 Gauge gravity duality 25
• 3.1 Large N expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
• 3.2 AdS=CFT correspondence . . . . . . . . . . . . . . . . . . . . . . . . 26
• 3.3 Implications of Duality . . . . . . . . . . . . . . . . . . . . . . . . . . 28
• II Studies on Super-Conformal eld theories 30
• 4 Anomalous dimensions of N = 4 SYM 31
• 4.1 Spinning strings in AdS5 S5 . . . . . . . . . . . . . . . . . . . . . . 35
• 4.2 Spinning D-branes and higher representations . . . . . . . . . . . . . 39
• 5
• 5 Infra-red niteness in 3 dimensions 50
• 5.1 Scattering amplitudes of ABJM theory . . . . . . . . . . . . . . . . . 51
• 5.2 Kinoshita-Lee-Nauenberg Theorem . . . . . . . . . . . . . . . . . . . 54
• 5.3 IR niteness of ABJM theory . . . . . . . . . . . . . . . . . . . . . . 55
• III Studies on Higher-spin theories 64
• 6 Asymptotic symmetry of higher-spin gravity 65
• 6.1 Pure gravity in 3 dimension . . . . . . . . . . . . . . . . . . . . . . . 66
• 6.2 Higher-spin super-gravity . . . . . . . . . . . . . . . . . . . . . . . . 67
• IV Conclusions and outlook 89
• 7 Conclusions and outlook 90
• Appendices 93
• A Coordinates of AdS3 93
• B Asymptotic symmetry in HS theory 95
• B.1 Conventions and Notations . . . . . . . . . . . . . . . . . . . . . . . 95
• B.2 Matrix realization of osp(Nj2;R) superalgebra . . . . . . . . . . . . 96
• Bibliography 101
• 6