고차원에서 정의된 양자장론에 관한 정량적 이해

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

Photochemical Pump and NMR Probe to monitor the formation and kinetics of hyperpolarized metal dihydrides

On reaction of IrI(CO)(PPh 3) 21with para-hydrogen(p-H 2),Ir(H) 2I(CO)(PPh 3) 22 is formed which exhibits strongly enhanced 1H NMR signals for its hydride resonances. Complex 2 also shows similar enhancement of its NMR spectra when it is irradiated under p-H 2. We report the use of this photochemical reactivity to measure the kinetics of H 2 addition by laser-synchronized reactions in conjunction with NMR. The single laser pulse promotes the reductive elimination of H 2 from Ir(H) 2I(CO)(PPh 3) 22 in C 6D 6 solution to form the 16-electron precursor 1, back reaction with p-H 2 then reforms 2 in a well-defined nuclear spin-state. The build up of this product can be followed by incrementing a precisely controlled delay (τ), in millisecond steps, between the laser and the NMR pulse. The resulting signal vs. time profile shows a dependence on p-H 2 pressure. The plot of k obs against p-H 2 pressure is linear and yields the second order rate constant, k 2, for H 2 addition to 1 of (3.26 ± 0.42) × 10 2 M −1 s −1. Validation was achieved by transient-UV-vis absorption spectroscopy which gives k 2 of (3.06 ± 0.40) × 10 2 M −1 s −1. Furthermore, irradiation of a C 6D 6 solution of 2 with multiple laser shots, in conjunction with p-H 2 derived hyperpolarization, allows the detection and characterisation of two minor reaction products, 2a and 3, which are produced in such low yields that they are not detected without hyperpolarization. Complex 2a is a configurational isomer of 2, while 3 is formed by substitution of CO by PPh

Entropy of Pairs of Dual Attractors in 6D/7D

We study the attractor mechanism of dual pairs of black brane bounds in N=2 supergravity in six and seven dimensions. First, we consider the effective potentials of the 6D and 7D black branes as well as their entropies. The contribution coming from the SO(1,1) factor of the moduli spaces M_{6D} and M_{7D} of these theories is carefully analyzed and it is used to motivate the study of the dual black branes bounds; which in turn allow to fix the critical value of the dilaton at horizon. The attractor eqs of the black branes and the bound pairs are derived by combining the criticality conditions of the corresponding effective potentials and the Lagrange multiplier method capturing constraints eqs on the fields moduli.Comment: 55 pages, 2 figures, To appear in JHE

Warped compactification on curved manifolds

The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity. In this context, Douglas and Kallosh recently pointed out that a compact internal space with negative curvature could help to construct four-dimensional de Sitter solutions only if the extra dimensions are strongly warped or there are large stringy corrections. That is, the problem of finding 4-dimensional de Sitter solutions is well posed, if all extra dimensions are physically compact, which is called a no-go theorem. Here, we show that the above conclusion does not extend to a general class of warped compactifications in classical supergravity that allow a non-compact direction or cosmological solutions for which the internal space is asymptotic to a cone over a product of compact Einstein spaces or spheres. For clarity, we present classical solutions that compactify higher-dimensional spacetime to produce a Robertson--Walker universe with de Sitter-type expansion plus one extra non-compact direction. Such models are found to admit both an effective four-dimensional Newton constant that remains finite and a normalizable zero-mode graviton wavefunction. We also exhibit the possibility of obtaining 4D de Sitter solutions by including the effect of fluxes (p-form field strengths).Comment: 24 pages, 1 figure; v5 significant changes in the presentation, published (journal) versio

Gravitational Forces on a Codimension-2 Brane

We compute the gravitational response of six dimensional gauged, chiral supergravity to localized stress energy on one of two space-filling branes, including the effects of compactifying the extra dimensions and brane back-reaction. We find a broad class of exact solutions, including various black-brane solutions. Several approximate solutions are also described, such as the near-horizon geometry of a small black hole which is argued to be approximately described by a 6D Schwarzschild (or Kerr) black hole, with event horizon appropriately modified to encode the brane back-reaction. The general linearized far-field solutions are found in the 4D regime very far from the source, and all integration constants are related to physical quantities describing the branes and the localized energy source. The localized source determines two of these, corresponding to the source mass and the size of the strength of a coupling to a 4D scalar mode whose mass is parametrically smaller than the KK scale. At large distances the solutions agree with those of 4D general relativity, but for an intermediate range of distances (larger than the KK scale) the solutions better fit a Brans-Dicke theory. For a realistic choice of parameters the KK scale could lie at a micron, while the crossover to Brans-Dicke behaviour could occur at around 10 microns. While allowed by present data this points to potentially measurable changes to Newton's Law arising at distances larger than the KK scale.Comment: 31 pages + appendices, 2 figure

Towards the Classification of Non-Marginal Bound States of M-branes and Their Construction Rules

We present a systematic analysis of possible bound states of M-brane solutions (including waves and monopoles) by using the solution generating technique of reduction of M-brane to 10 dimensions, use of T-duality and then lifting back to 11 dimensions. We summarize a list of bound states for one- and two-charge cases including tilted brane solutions. Construction rules for these non-marginal solutions are also discussed.Comment: Latex, 37 page

Six-dimensional localized black holes: numerical solutions

To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature $\mathcal{T} \approx 1/2\pi \ell$, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes.Comment: 17 pages, 9 figures, RevTeX4, typos correcte

Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM

We study near-horizon limits of near-extremal charged black hole solutions to five-dimensional $U(1)^3$ gauged supergravity carrying two charges, extending the recent work of Balasubramanian et.al. We show that there are two near-horizon decoupling limits for the near-extremal black holes, one corresponding to the near-BPS case and the other for the far from BPS case. Both of these limits are only defined on the 10d IIB uplift of the 5d black holes, resulting in a decoupled geometry with a six-dimensional part (conformal to) a rotating BTZ X $S^3$. We study various aspects of these decoupling limits both from the gravity side and the dual field theory side. For the latter we argue that there should be two different, but equivalent, dual gauge theory descriptions, one in terms of the 2d CFT's dual to the rotating BTZ and the other as certain large R-charge sectors of d=4,N =4 U(N) SYM theory. We discuss new BMN-type sectors of the N=4 SYM in the $N\to\infty$ limit in which the engineering dimensions scale as $N^{3/2}$ (for the near-BPS case) and as $N^2$ (for the far from BPS case).Comment: 44 pages, references added, minor change