Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Physical and Genetic Analysis of the CUP1 Tandem Array in the Yeast Saccharomyces cerevisiae

The genomes of many strains of baker’s yeast, Saccharomyces cerevisiae, contain multiple repeats of the copper-binding protein Cup1. Cup1 is a member of the metallothionein family, and is found in a tandem array on chromosome VIII. In this thesis, I describe studies that characterized these tandem arrays and their mechanism of formation across diverse strains of yeast. I show that CUP1 arrays are an illuminating model system for observing recombination in eukaryotes, and describe insights derived from these observations.

In our first study, we analyzed 101 natural isolates of S. cerevisiae in order to examine the diversity of CUP1-containing repeats across different strains. We identified five distinct classes of repeats that contain CUP1. We also showed that some strains have only a single copy of CUP1. By comparing the sequences of all the strains, we were able to elucidate the mechanism of formation of the CUP1 tandem arrays, which involved unequal non-homologous recombination events starting from a strain that had only a single CUP1 gene. Our observation of CUP1 repeat formation allows more general insights about the formation of tandem repeats from single-copy genes in eukaryotes, which is one of the most important mechanisms by which organisms evolve.

In our second study, we delved deeper into our mechanistic investigations by measuring the relative rates of inter-homolog and intra-/inter-sister chromatid recombination in CUP1 tandem arrays. We used a diploid strain that is heterozygous both for insertion of a selectable marker (URA3) inside the tandem array, and also for markers at either end of the array. The intra-/inter-sister chromatid recombination rate turned out to be more than ten-fold greater than the inter-homolog rate. Moreover, we found that loss of the proteins Rad51 and Rad52, which are required for most inter-homolog recombination, did not greatly reduce recombination in the CUP1 tandem repeats. Additionally, we investigated the effects of elevated copper levels on the rate of each type of recombination at the CUP1 locus. Both types of recombination are increased at high concentrations of copper (as is known to be the case for CUP1 transcription). Furthermore, the inter-homolog recombination rate at the CUP1 locus is higher than the average over the genome during mitosis, but is lower than the average during meiosis.

The research described in Chapter 2 is published in 2014.