In this thesis the proposed exact results for low energy effective N = 2 supersymmetric SU(N) Yang-Mills gauge theory coupled to Nf fundamental matter multiplets in four dimensions are considered. The proposed exact results are based upon the work of Seiberg and Witten for low energy effective four dimensional M = 2 supersymmetric SU[2) Yang-Mills gauge theory coupled to Nf fundamental matter multiplets. The testing and matching of the proposed exact results via supersymmetric instanton calculus are the motivation for two studies. Firstly, we study the ADHM construction of instantons for gauge groups U(N) and SU(2) and for topological charge two and three. The ADHM constraints which implicitly specify instanton gauge field configurations are solved for the explicit exact general form of instantons with topological charge two and gauge group U[N). This is the first explicit and general multi-instanton configuration for the unitary gauge groups. The U[N) ADHM two-instanton configuration may be used in further tests and matching of the proposed exact results in low energy effective M =2 supersymmetric SU(iV) Yang-Mills gauge theories by comparison with direct instanton calculations. Secondly, a one-instanton level test is performed for the reparameterization scheme proposed by Argyres and Pelland matching the conjectured exact low energy results and instanton predictions for the instanton contributions to the prepotential of low energy effective M = 2 supersymmetric SU [N) Yang-Mills gauge theory with Nf = 2N mass-less fundamental matter multiplets. The constants within the reparameterization scheme which ensure agreement between the exact results and the instanton predictions for general N > 1 are derived for the entire quantum moduli space. This constitutes a non-trivial test of the proposed reparameterization scheme, which eliminates the discrepancies arising when the two sets of results are compared.

This work details how to use the Point-Particle Effective Field Theory (PPEFT) framework to make predictions for the nuclear-size contributions to spectroscopic transitions of atoms without the overbearing large uncertainties generally associated with such effects. After a lightning review of Quantum Field Theories, Effective Field Theories and their model-building algorithms, the backbones of the PPEFT formalism are laid down by considering the low-energy effective theories of lumps. Then, by drawing an analogy between a certain type of lumps and a freely propagating point-particle we build a PPEFT for nuclei, which we gradually couple to gauge and fermionic fields. We find that the consequences of having a nucleus in our theory are captured by a set of new near-nucleus boundary conditions its action implies for the surrounding fields, set up on a Gaussian spherical boundary with arbitrary radius, $\epsilon$. Afterwards, we use this formalism to derive the effects of the finite size of the nucleus on bound-state energies in terms of Renormalization Group (RG)-invariant parameters that characterize the running of the PPEFT couplings in $\epsilon$, implied by these new boundary conditions in order to keep physical quantities independent of this fictitious scale. Surprisingly, when comparing to formulae from the literature that express these same energy shifts in terms of nuclear moments there always appear to be fewer RG-invariants than moments. By fitting these handful of parameters using experimental data we then reduce the errors in nuclear-size effect predictions for other transitions by writing them in terms of differences between spectroscopic measurements and their corresponding energy differences predicted by those bound-state Quantum Electrodynamics calculations that assume nuclei to be point-like. Finally, we apply this algorithm to the systems: ${}^4_2 {\rm He}^+$, $\mu \, {}^4_2 {\rm He}^+$, H, and $\mu$H, where we make such predictions. / Thesis / Doctor of Philosophy (PhD) / The finite size of the nucleus shifts the bound-state energy of electrons (or muons) in atoms. Although these effects had been captured through a large number of nuclear-model independent ``nuclear moments'' closely related to the extent of the nucleus in the past, they introduce large uncertainties into theoretical predictions, which hinders testing fundamental subatomic processes in spectroscopic measurements. In this work it is shown that there is a more manageable number of parameters that control these effects because the above moments always appear in specific combinations. This allows for trading these combinations for differences between experimental values and their theoretically expected ones that assume the nucleus to have no size, which is the key in making predictions for atomic transitions that do not suffer from the large nuclear errors. A large set of such predictions are made for Hydrogen and the principles are applied to its muonic cousin as well.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19496号 / 理博第4156号 / 新制||理||1597(附属図書館) / 32532 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 笹倉 直樹, 教授 田中 貴浩, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM