Fermion bag approach to lattice field theories

We propose a new approach to the fermion sign problem in systems where there is a coupling U such that when it is infinite the fermions are paired into bosons, and there is no fermion permutation sign to worry about. We argue that as U becomes finite, fermions are liberated but are naturally confined to regions which we refer to as fermion bags. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three-dimensional massless lattice Thirring model as an example, we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find ν=0.87(2) and η=0.62(2). © 2010 The American Physical Society.

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.

Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

Integrating simultaneous prosocial and antisocial behavior into theories of collective action.

Trust and cooperation constitute cornerstones of common-pool resource theory, showing that "prosocial" strategies among resource users can overcome collective action problems and lead to sustainable resource governance. Yet, antisocial behavior and especially the coexistence of prosocial and antisocial behaviors have received less attention. We broaden the analysis to include the effects of both "prosocial" and "antisocial" interactions. We do so in the context of marine protected areas (MPAs), the most prominent form of biodiversity conservation intervention worldwide. Our multimethod approach relied on lab-in-the-field economic experiments (n = 127) in two MPA and two non-MPA communities in Baja California, Mexico. In addition, we deployed a standardized fishers' survey (n = 544) to verify the external validity of our findings and expert informant interviews (n = 77) to develop potential explanatory mechanisms. In MPA sites, prosocial and antisocial behavior is significantly higher, and the presence of antisocial behavior does not seem to have a negative effect on prosocial behavior. We suggest that market integration, economic diversification, and strengthened group identity in MPAs are the main potential mechanisms for the simultaneity of prosocial and antisocial behavior we observed. This study constitutes a first step in better understanding the interaction between prosociality and antisociality as related to natural resources governance and conservation science, integrating literatures from social psychology, evolutionary anthropology, behavioral economics, and ecology.

Do the Messages Matter? An Investigation of Classroom Messages and College Students’ Personal Theories about Education

Students hold a number of personal theories about education that influence motivation and achievement in the classroom: theories about their own abilities, knowledge, and the learning process. Therefore, college instructors have a great interest in helping to develop adaptive personal theories in their students. The current studies investigated whether specific messages that instructors send in college classroom might serve as a mechanism of personal theory development. Across 2 studies, 17 college instructors and 401 students completed surveys assessing their personal theories about education at the beginning and end of college courses. Students and instructors reported hearing and sending many messages in the classroom, including instructor help messages, conciliatory messages, uncertainty in the field messages, differential ability messages and generalized positive and negative feedback. Between-class and within-class differences in message reports were associated with students’ personal theories at the end of their courses, controlling for initial personal theories. Students’ initial personal theories were also related to the messages students reported hearing. The findings demonstrate the utility of assessing non-content messages in college classrooms as potential mechanisms for changing students’ personal theories in college. Implications for research and practice are discussed.

Grabbing Your Attention: The Impact of Finding a First Target in Multiple-Target Search

For over 50 years, the Satisfaction of Search effect, and more recently known as the Subsequent Search Miss (SSM) effect, has plagued the field of radiology. Defined as a decrease in additional target accuracy after detecting a prior target in a visual search, SSM errors are known to underlie both real-world search errors (e.g., a radiologist is more likely to miss a tumor if a different tumor was previously detected) and more simplified, lab-based search errors (e.g., an observer is more likely to miss a target ‘T’ if a different target ‘T’ was previously detected). Unfortunately, little was known about this phenomenon’s cognitive underpinnings and SSM errors have proven difficult to eliminate. However, more recently, experimental research has provided evidence for three different theories of SSM errors: the Satisfaction account, the Perceptual Set account, and the Resource Depletion account. A series of studies examined performance in a multiple-target visual search and aimed to provide support for the Resource Depletion account—a first target consumes cognitive resources leaving less available to process additional targets.

To assess a potential mechanism underlying SSM errors, eye movements were recorded in a multiple-target visual search and were used to explore whether a first target may result in an immediate decrease in second-target accuracy, which is known as an attentional blink. To determine whether other known attentional distractions amplified the effects of finding a first target has on second-target detection, distractors within the immediate vicinity of the targets (i.e., clutter) were measured and compared to accuracy for a second target. To better understand which characteristics of attention were impacted by detecting a first target, individual differences within four characteristics of attention were compared to second-target misses in a multiple-target visual search.

The results demonstrated that an attentional blink underlies SSM errors with a decrease in second-target accuracy from 135ms-405ms after detection or re-fixating a first target. The effects of clutter were exacerbated after finding a first target causing a greater decrease in second-target accuracy as clutter increased around a second-target. The attentional characteristics of modulation and vigilance were correlated with second- target misses and suggest that worse attentional modulation and vigilance are predictive of more second-target misses. Taken together, these result are used as the foundation to support a new theory of SSM errors, the Flux Capacitor theory. The Flux Capacitor theory predicts that once a target is found, it is maintained as an attentional template in working memory, which consumes attentional resources that could otherwise be used to detect additional targets. This theory not only proposes why attentional resources are consumed by a first target, but encompasses the research in support of all three SSM theories in an effort to establish a grand, unified theory of SSM errors.