AGT relations for abelian quiver gauge theories on ALE spaces

We construct level one dominant representations of the affine Kac-Moody algebra $\widehat{\mathfrak{gl}}_k$ on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution $X_k$ of the $A_{k-1}$ toric singularity $\mathbb{C}^2/\mathbb{Z}_k$. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for $\widehat{\mathfrak{gl}}_k$, which proves the AGT correspondence for pure $\mathcal{N}=2$ $U(1)$ gauge theory on $X_k$. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition $\widehat{\mathfrak{gl}}_k\simeq \mathfrak{h}\oplus \widehat{\mathfrak{sl}}_k$, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra $\mathfrak{h}$ and primary fields of $\widehat{\mathfrak{sl}}_k$. We use these operators to prove the AGT correspondence for $\mathcal{N}=2$ superconformal abelian quiver gauge theories on $X_k$.Comment: 58 pages; v2: typos corrected, reference added; v3: Introduction expanded, minor corrections and clarifying remarks added throughout, references added and updated; Final version published in Journal of Geometry and Physic

Resurrecting the Dead Cone

The dead cone is a well-known effect in gauge theories, where radiation from a charged particle of mass m and energy E is suppressed within an angular size of m/E. This effect is universal as it does not depend on the spin of the particle nor on the nature of the gauge interaction. It is challenging to directly measure the dead cone at colliders, however, since the region of suppressed radiation either is too small to be resolved or is filled by the decay products of the massive particle. In this paper, we propose to use jet substructure techniques to expose the dead cone effect in the strong-force radiation pattern around boosted top quarks at the Large Hadron Collider. Our study shows that with 300/fb of 13-14 TeV collision data, ATLAS and CMS could obtain the first direct evidence of the dead cone effect and test its basic features.Comment: 12 pages, 12 figures; v2: references added; v3: approximate version to appear in PR

The Effects of Interactivity and Vividness of Functional Control in Changing Web Consumers\u27 Attitudes

The study proposed will investigate the effects of functional control on online consumers’ attitude formation. Functional control is an interactive interface feature that allows consumers to virtually try different functions of online products. An attitude formation model for analyzing and assessing the influences of functional control is proposed based on existing theories of vividness and interactivity, which are the two fundamental technological characteristics of functional control. The model suggests that functional control has direct effects on both attitudes toward online product presentation and attitudes toward products themselves, and that attitudes toward different online product presentation partly mediate the effects of functional control on attitudes toward products. A laboratory experiment has been designed to test the model. We expect that the results of the study will identify particular areas deserving attention for applying functional control to improve e-commerce environments

Metamemory or just Memory? Searching for the Neural Correlates of Judgments of Learning

Judgments of Learning (JOLs) are judgments of the likelihood of remembering recently studied material on a future test. Although JOLs have been extensively studied, particularly due to their important applications in education, relatively little is known about the cognitive and neural processes supporting JOLs and how these processes relate to actual memory processing. Direct access theories describe JOLs as outputs following direct readings of memory traces and hence predict that JOLs cannot be distinguished from objective memory encoding operations. Inferential theories, by contrast, claim JOLs are products of the evaluation of a number of cues, perceived by learners to carry predictive value. This alternative account argues that JOLs are made on the basis of multiple underlying processes, which do not necessarily overlap with memory encoding. In this thesis, the neural and cognitive bases of JOLs were examined in a series of four ERP experiments. Across experiments the study phase ERP data showed that JOLs produce neural activity that is partly overlapping with, but also partly distinct from, the activity that predicts successful memory encoding. Furthermore, the neural correlates of successful memory encoding appear sensitive to the requirements to make a JOL, emphasising the close interaction between subjective and objective measures of memory encoding. Finally, the neural correlates of both JOLs and successful memory encoding were found to vary depending on the nature of the stimulus materials, suggesting that both phenomena are supported by multiple cognitive and neural systems. Although the primary focus was on the study phase ERP data, the thesis also contains two additional chapters reporting the ERP data acquired during the test phases of three of the original experiments. These data, which examined the relative engagements of retrieval processes for low and high JOL items, suggest that encoding processes specifically resulting in later recollection (as opposed to familiarity) form one reliable basis for making JOLs. Overall, the evidence collected in this series of ERP experiments suggests that JOLs are not pure products of objective memory processes, as suggested by direct access theories, but are supported by neural systems that are at least partly distinct from those supporting successful memory encoding. These observations are compatible with inferential theories claiming that JOLs are supported by multiple processes that can be differentially engaged across stimulus contents