Commutative Quantum Operator Algebras

A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is not commutativity in any ordinary sense, but it is clearly the correct generalization to the quantum context. The main purpose of the current paper is to begin laying the foundations for a complete mathematical theory of {\it commutative quantum operator algebras.} We give proofs of most of the relevant results announced in \cite{LZ10}, and we carry out some calculations with sufficient detail to enable the interested reader to become proficient with the algebra of commuting quantum operators.Comment: 22 pages, Late

The 125 GeV Higgs and Electroweak Phase Transition Model Classes

Recently, the ATLAS and CMS detectors have discovered a bosonic particle which, to a reasonable degree of statistical uncertainty, fits the profile of the Standard Model Higgs. One obvious implication is that models which predict a significant departure from Standard Model phenomenology, such as large exotic (e.g., invisible) Higgs decay or mixing with a hidden sector scalar, are already ruled out. This observation threatens the viability of electroweak baryogenesis, which favors, for example, a lighter Higgs and a Higgs coupled to or mixed with light scalars. To assess the broad impact of these constraints, we propose a scheme for classifying models of the electroweak phase transition and impose constraints on a class-by-class basis. We find that models, such as the MSSM, which rely on thermal loop effects are severely constrained by the measurement of a 125 GeV Higgs. Models which rely on tree-level effects from a light singlet are also restricted by invisible decay and mixing constraints. Moreover, we find that the parametric region favored by electroweak baryogenesis often coincides with an enhanced symmetry point with a distinctive phenomenological character. In particular, enhancements arising through an approximate continuous symmetry are phenomenologically disfavored, in contrast with enhancements from discrete symmetries. We also comment on the excess of diphoton events observed by ATLAS and CMS. We note that although Higgs portal models can accommodate both enhanced diphoton decay and a strongly first order electroweak phase transition, the former favors a negative Higgs portal coupling whereas the latter favors a positive one, and therefore these two constraints are at tension with one another.Comment: 35 pages, 7 figure

Strongly First Order Phase Transitions Near an Enhanced Discrete Symmetry Point

We propose a group theoretic condition which may be applied to extensions of the Standard Model in order to locate regions of parameter space in which the electroweak phase transition is strongly first order, such that electroweak baryogenesis may be a viable mechanism for generating the baryon asymmetry of the universe. Specifically, we demonstrate that the viable corners of parameter space may be identified by their proximity to an enhanced discrete symmetry point. At this point, the global symmetry group of the theory is extended by a discrete group under which the scalar sector is non-trivially charged, and the discrete symmetry is spontaneously broken such that the discrete symmetry relates degenerate electroweak preserving and breaking vacua. This idea is used to investigate several specific models of the electroweak symmetry breaking sector. The phase transitions identified through this method suggest implications for other relics such as dark matter and gravitational waves.Comment: 17 pages, 4 figure

Algebraic and geometric structures in string backgrounds

We give a brief introduction to the study of the algebraic structures -- and their geometrical interpretations -- which arise in the BRST construction of a conformal string background. Starting from the chiral algebra \cA of a string background, we consider a number of elementary but universal operations on the chiral algebra. From these operations we deduce a certain fundamental odd Poisson structure, known as a Gerstenhaber algebra, on the BRST cohomology of \cA. For the 2D string background, the correponding G-algebra can be partially described in term of a geometrical G-algebra of the affine plane \bC^2. This paper will appear in the proceedings of {\it Strings 95}

Twenty putative palmitoyl-acyl transferase genes with distinct expression patterns in Arabidopsis thaliana

Palmitoylation is a reversible posttranslational addition of palmitate to cysteine residues in proteins through a thioester bond by a family of DHHC (Asp-His-His-Cys) palmitoyltransferases (PATs) involved in cellular signaling, membrane trafficking, and synaptic transmission. There are 20 genes containing DHHC domain predicted to encode putative palmitoyltransferase in Arabidopsis thaliana genome. However, little is known about their characteristics such as genetic relationship and expression profile. Here, we present an overview of the putative PAT genes in A. thaliana focusing on their phylogeny, gene structure and expression profiles in different tissues and under different stresses. Besides conserved DHHC domain, the identity of their cDNA sequences was from 30 to 60%. Temprospatial expression profile of each putative gene of the entire PAT family showed that nineteen of twenty putative PAT members differently expressed in flowers, leaves, stems, roots, seedlings, young and old siliques except At2g40990. Among these nineteen expressed putative PATs, some members expressed at very high levels in certain tissue and some exhibited more even distribution in different tissues. This is the first report on the expression patterns of all these putative PAT genes, which will provide important fundamental data for further identification of their biological functions.Key words: Palmitoylation, palmitoyltransferase, Arabidopsis thaliana, expression pattern