Twisted Gauge Theory Model of Topological Phases in Three Dimensions

We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\mathbb{Z})$ generators as the modular $S$ and $T$ matrices of the ground states, which yield a set of topological quantum numbers classified by $\omega$ and quantities derived from $\omega$. Our model fulfills a Hamiltonian extension of the $3+1$-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group $G$. This work is presented to be accessible for a wide range of physicists and mathematicians.Comment: 37 pages, 9 figures, 4 tables; revised to improve the clarity; references adde

Effective Theory of Braid Excitations of Quantum Geometry in terms of Feynman Diagrams

We study interactions amongst topologically conserved excitations of quantum theories of gravity, in particular the braid excitations of four-valent spin networks. These have been shown previously to propagate and interact under evolution rules of spin foam models. We show that the dynamics of these braid excitations can be described by an effective theory based on Feynman diagrams. In this language, braids which are actively interacting are analogous to bosons, in that the topological conservation laws permit them to be singly created and destroyed. Exchanges of these excitations give rise to interactions between braids which are charged under the topological conservation rules.Comment: 23 pages, 7 figures. Accepted by Nucl. Phys.

Function annotation of hepatic retinoid x receptor α based on genome-wide DNA binding and transcriptome profiling.

BackgroundRetinoid x receptor α (RXRα) is abundantly expressed in the liver and is essential for the function of other nuclear receptors. Using chromatin immunoprecipitation sequencing and mRNA profiling data generated from wild type and RXRα-null mouse livers, the current study identifies the bona-fide hepatic RXRα targets and biological pathways. In addition, based on binding and motif analysis, the molecular mechanism by which RXRα regulates hepatic genes is elucidated in a high-throughput manner.Principal findingsClose to 80% of hepatic expressed genes were bound by RXRα, while 16% were expressed in an RXRα-dependent manner. Motif analysis predicted direct repeat with a spacer of one nucleotide as the most prevalent RXRα binding site. Many of the 500 strongest binding motifs overlapped with the binding motif of specific protein 1. Biological functional analysis of RXRα-dependent genes revealed that hepatic RXRα deficiency mainly resulted in up-regulation of steroid and cholesterol biosynthesis-related genes and down-regulation of translation- as well as anti-apoptosis-related genes. Furthermore, RXRα bound to many genes that encode nuclear receptors and their cofactors suggesting the central role of RXRα in regulating nuclear receptor-mediated pathways.ConclusionsThis study establishes the relationship between RXRα DNA binding and hepatic gene expression. RXRα binds extensively to the mouse genome. However, DNA binding does not necessarily affect the basal mRNA level. In addition to metabolism, RXRα dictates the expression of genes that regulate RNA processing, translation, and protein folding illustrating the novel roles of hepatic RXRα in post-transcriptional regulation