Two and four-loop β\beta-functions of rank 4 renormalizable tensor field theories

A recent rank 4 tensor field model generating 4D simplicial manifolds has been proved to be renormalizable at all orders of perturbation theory [arXiv:1111.4997 [hep-th]]. The model is built out of $\phi^6$ ($\phi^6_{(1/2)}$), $\phi^4$ ($\phi^4_{(1)}$) interactions and an anomalous term ($\phi^4_{(2)}$). The $\beta$-functions of this model are evaluated at two and four loops. We find that the model is asymptotically free in the UV for both the main $\phi^6_{(1/2)}$ interactions whereas it is safe in the $\phi^4_{(1)}$ sector. The remaining anomalous term turns out to possess a Landau ghost.Comment: 31 pages, 31 figures; improved versio

Equivalent Fixed-Points in the Effective Average Action Formalism

Starting from a modified version of Polchinski's equation, Morris' fixed-point equation for the effective average action is derived. Since an expression for the line of equivalent fixed-points associated with every critical fixed-point is known in the former case, this link allows us to find, for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3: published in J. Phys. A - minor change

On the Effective Action of Noncommutative Yang-Mills Theory

We compute here the Yang-Mills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar field theory with harmonic term, minimally coupled to an external gauge potential. We also explain the special regularisation scheme chosen here and give some links to the Schwinger parametric representation. Finally, we discuss the results obtained: a noncommutative possibly renormalisable Yang-Mills theory.Comment: 19 pages, 6 figures. At the occasion of the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France). To appear in J. Phys. Conf. Se

Noncommutative Induced Gauge Theory

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the one-loop Yang-Mills-type effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action involves, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative $\phi^4$-theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.Comment: 20 pages, 6 figure

Pathologic tearfulness after limbic encephalitis: A novel disorder and its neural basis

Objective We investigated the nature and neural foundations of pathologic tearfulness in a uniquely large cohort of patients who had presented with autoimmune limbic encephalitis (aLE). Methods We recruited 38 patients (26 men, 12 women; median age 63.06 years; interquartile range [IQR] 16.06 years) in the postacute phase of aLE who completed questionnaires probing emotion regulation. All patients underwent structural/functional MRI postacutely, along with 67 age- and sex-matched healthy controls (40 men, 27 women; median age 64.70 years; IQR 19.87 years). We investigated correlations of questionnaire scores with demographic, clinical, neuropsychological, and brain imaging data across patients. We also compared patients diagnosed with pathologic tearfulness and those without, along with healthy controls, on gray matter volume, resting-state functional connectivity, and activity. Results Pathologic tearfulness was reported by 50% of the patients, while no patient reported pathologic laughing. It was not associated with depression, impulsiveness, memory impairment, executive dysfunction in the postacute phase, or amygdalar abnormalities in the acute phase. It correlated with changes in specific emotional brain networks: volume reduction in the right anterior hippocampus, left fusiform gyrus, and cerebellum, abnormal hippocampal resting-state functional connectivity with the posteromedial cortex and right middle frontal gyrus, and abnormal hemodynamic activity in the left fusiform gyrus, right inferior parietal lobule, and ventral pons. Conclusions Pathologic tearfulness is common following aLE, is not a manifestation of other neuropsychiatric features, and reflects abnormalities in networks of emotion regulation beyond the acute hippocampal focus. The condition, which may also be present in other neurologic disorders, provides novel insights into the neural basis of affective control and its dysfunction in disease

Laplacians on discrete and quantum geometries

We extend discrete calculus for arbitrary ($p$-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries.Comment: 43 pages, 2 multiple figures. v2: discussion improved, references added, minor typos correcte

Spatial and contextual long-term and working memory in ageing and disease

Initially thought to be two independent memory systems, working memory (WM) and long-term memory (LTM) both present associative features controlled by the medial temporal lobe (MTL). Despite their similarities, the two memory systems have mostly been explored and compared using distinct methods and measures. Considering their differences and their correspondences, this thesis focuses on spatial associative WM and LTM performance in healthy ageing and in the presence of MTL impairment. The studies presented investigate the mechanisms of the two memory systems, their interplay, and the modulatory relationship between them and attention, using analogous tasks and equivalent behavioural measures. Specifically, Chapter 2 explores if retro-cueing benefits, previously observed in WM, extend to LTM retrieval, and whether this could represent a means of ameliorating age-related LTM impairment. Next, in Chapter 3, I compare the performance of young and older healthy adults in a spatial memory task on two devices – a personal computer and an immersive VR device – to test whether old adults benefit from an increased level of immersion and determine the optimal methods of measuring spatial memory. In the second study, I use a navigation-based memory task measuring WM and LTM, to investigate their patterns of use and interplay that might change with ageing. Lastly, Chapter 4 relies on the same task and aims to analyse patterns of performance modulated by different levels of MTL impairment in old healthy adults and individuals with limbic encephalitis. The results propose that WM and LTM show age-related associative deficits and that their interplay is preserved in ageing, despite old adults’ increased forgetting. Additionally, they suggest that WM and LTM may rely on different retro-cueing mechanisms. Lastly, the most noteworthy outcomes are the tasks developed to measure spatial associative memory of different timespans in equivalent ways, using analogous steps and stimuli, which can become great tools in the research of WM and LTM retrieval processes