Narrow Results

Deconstruction is a powerful means to explore the rich dynamics of gauge theories in four and higher dimensions. We demonstrate that gauge symmetry breaking in a compactified higher dimensional theory can be formulated via deconstructed 4D moose theory with spontaneous symmetry breaking and without boundary condition. The proper higher-D boundary conditions are automatically induced in the continuum limit rather than being imposed. We identify and analyze the moose theories which exhibit delayed unitarity violation (effective unitarity) as a collective effect of many gauge groups, without resorting to any known 5D geometry. Relevant phenomenological constraints are also addressed.

This paper contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.

We investigate 3D Yang-Mills theory coupled to an adjoint scalar, which can be regarded as a zeroth order approximation in (de)constructing 4D Yang-Mills theory. We develop a new algorithm to obtain the renormalized Hamiltonian with the Karabali-Nair variable, by carefully identifying finite local counterterms. We also discuss how this formalism can be applied to obtain glueball spectrum.

Truth is the telos of research — the ultimate treasure. All depends on it. However, it is often an elusive and difficult objective for the researcher. In a world of increasingly overwhelming levels of accessible information, false presumptions may often appear validated by those skilled at increasing the volume — fake news, special interests, all utilize their unique versions of “truth” toward enhancing their own interests. In the philosophical science of ontology, an unwavering quest for truth, much like that of reality, while ever evolving, serves as the bedrock of all research and theory. To that end, the self-correcting method in storytelling research is fast becoming a preferred methodology for researchers utilizing narratology, as it surpasses the limitations of the structured and semi-structured interrogatory-style dialogic in developing a deeper understanding of the whole story. This allows researchers to travel beyond the confines of the linear, structured investigation, offering admission into the deeper life of the story. Every story has its own continual, ever-expanding life force, comprising all the voices and influences melded from the past, present, and future. Built on the foundational work of Charles Sanders Peirce, through the use of induction, (later enhanced with abductive and deductive processes), the self-correcting method leads to a path of discovery by utilizing a broader, less constrictive, socio-narratology-based method that encourages interpretation through an abductive–inductive–deductive view of the conversational-based relationship. Developing further with the preliminary step of deconstructing the existing narrative, seeking antenarrative, and carefully considering the stories “around” the story being researched (which comprise the aggregated components of the whole), the resulting understanding provided to the researcher often invites entrance into the guarded domain of the study participant, gained only through thoughtful conversational interaction (not interrogation) based on an understanding between the researcher and the participants, as can only be built upon a foundation of mutual respect, honesty, and trust. There are inherent challenges to this methodology, the primary one being the necessity for skillful, nonspecific, indirect exchanges of dialogue required for the mastery of conversational storytelling interviews, while resisting the almost natural interrogatory interviewing tendency of many Western-trained researchers. There are countless stories living and evolving within every story, each with multiplicities interwoven that are inter-dimensionally dynamic with one another. With diligence and intuitive awareness of this, the use of self-correcting storytelling methodology serves researchers well in narratological studies.