학위논문 (박사)-- 서울대학교 대학원 : 물리·천문학부 물리학전공, 2015. 8. 김석.This thesis aims at studying the higher dimensional quantum field theories, engi- neered from the string theory. These theories are genuinely strongly interactive, thus being difficult to be understood within the conventional QFT framework. In particular, I focus on those 5d / 6d QFTs which can be deformed to the weakly coupled 5d Yang-Mills theories, in which the deformation is caused either by a rel- evant operator or by a circle compactification. Instantons are crucial for observing the physics of 5d / 6d QFTs which correspond to the UV fixed points of certain 5d SYMs. In the first half of the thesis, I obtain the general expression for the instanton partition function of 5d SYMs and apply it to study the spectrum of various UV QFTs. The second half focuses on the 6d non-critical strings, which are key objects of 6d QFTs. Two types of 6d strings, M-strings and E-strings, are considered, for which the worldsheet gauge theories are explicitly developed.Abstract .......................... i
1 Introduction .......................... 1
2 Higher-dimensional QFTs .......................... 9
2.1 Six-dimensional theory .......................... 9
2.1.1 6d (2,0) theory .......................... 9
2.1.2 6d (1,0) theory .......................... 11
2.2 Five-dimensional theory ......................... 15
3 Instanton calculus in 5d gauge theory .......................... 19
3.1 Yang-Mills instantons .......................... 20
3.2 Instanton counting and Seiberg-Witten solution ........... 26
3.3 ADHM quantum mechanics ....................... 29
3.4 Exact computation of the 1d index................... 33
3.4.1 Rank-1 gauge group ....................... 36
3.4.2 Higher-rank gauge group .................... 42
3.5 Examples ................................. 49
3.5.1 N=1? theories.......................... 49
3.5.2 U(N) theories with matters and Chern-Simons term ...... 61
3.5.3 Sp(N)theories .......................... 64
4 Application of instanton calculus .......................... 69
4.1 6d (2,0) SCFT .............................. 69
4.2 U(N) theories for 5d SCFTs....................... 71
4.3 5d SCFT from D4-D8-O8 configuration ................ 74
4.3.1 Direct computations of the D0-D8-O8 indices ................. 80
4.3.2 Superconformal indices ..................... 81
4.4 6d (1,0) SCFT with E8 flavor symmetry................ 89
5 Non-critical strings in 6d QFTs ................. 95
5.1 M-strings in 6d (2,0) SCFT....................... 96
5.2 E-strings in 6d (1,0) E8 SCFT ..................... 99
5.2.1 The brane setup and the 2d (0,4) gauge theories ....... 100
5.2.2 E-string elliptic genera from 2d gauge theories ........ 111
5.2.3 Comparison with the instanton partition function ....... 135
A Characters of SO(2Nf) 141
B Modular forms and Jacobi forms 142
C Details of computation 147
C.1 Genus expansions of topological string amplitudes ................. 147
C.2 Exact properties of the E-string elliptic genus ................. 149
Bibliography ................. 163Docto
