Topological quantum field theory and four-manifolds

I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of non-simply connected manifolds, and for generalizations of these invariants to the gauge group SU(N); (b) compactifications to lower dimensions, and relations with three-manifold topology and with intersection theory on the moduli space of flat connections on Riemann surfaces; (c) four-dimensional theories with critical behavior, which give some remarkable constraints on Seiberg-Witten invariants and new results on the geography of four-manifolds.Comment: 10 pages, LaTeX. Talk given at the 3rd ECM, Barcelona, July 2000; references adde

Preface

Preface - The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013

Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity

We explore the relation between positivity of the energy constraints in conformal field theories and causality in their dual gravity description. Our discussion involves CFTs with different central charges whose description, in the gravity side, requires the inclusion of quadratic curvature corrections. It is enough, indeed, to consider the Gauss-Bonnet term. We find that both sides of the AdS/CFT correspondence impose a restriction on the Gauss-Bonnet coupling. In the case of 6d supersymmetric CFTs, we show the full matching of these restrictions. We perform this computation in two ways. First by considering a thermal setup in a black hole background. Second by scrutinizing the scattering of gravitons with a shock wave in AdS. The different helicities provide the corresponding lower and upper bounds. We generalize these results to arbitrary higher dimensions and comment on some hints and puzzles they prompt regarding the possible existence of higher dimensional CFTs and the extent to which the AdS/CFT correspondence would be valid for them.Comment: 31 pages, 5 figures; v2: typos fixed, cosmetic amendments and references adde

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth

Counting Exceptional Instantons

We show how to obtain the instanton partition function of N=2 SYM with exceptional gauge group EFG using blow-up recursion relations derived by Nakajima and Yoshioka. We compute the two instanton contribution and match it with the recent proposal for the superconformal index of rank 2 SCFTs with E6, E7 global symmetry.Comment: 16 pages, references adde

The matrix model version of AGT conjecture and CIV-DV prepotential

Recently exact formulas were provided for partition function of conformal (multi-Penner) beta-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted as Dotsenko-Fateev correlator of screenings and analytically continued in the number of screening insertions, represents generic Virasoro conformal blocks. Actually these formulas describe the lowest terms of the q_a-expansion, where q_a parameterize the shape of the Penner potential, and are exact in the filling numbers N_a. At the same time, the older theory of CIV-DV prepotential, straightforwardly extended to arbitrary beta and to non-polynomial potentials, provides an alternative expansion: in powers of N_a and exact in q_a. We check that the two expansions coincide in the overlapping region, i.e. for the lowest terms of expansions in both q_a and N_a. This coincidence is somewhat non-trivial, since the two methods use different integration contours: integrals in one case are of the B-function (Euler-Selberg) type, while in the other case they are Gaussian integrals.Comment: 27 pages, 1 figur

Multi-scalar tachyon potential on non-BPS domain walls

We have considered the multi-scalar and multi-tachyon fields living on a 3d domain wall embedded in a 5d dimensional Minkowski spacetime. The effective action for such a domain wall can be found by integrating out the normal modes as vibrating modes around the domain wall solution of a truncated 5d supergravity action. The multi-scalar tachyon potential are good enough to modeling assisted inflation scenario with multi-tachyon fields. The tachyon condensation are also briefly addressed.Comment: version to appear in JHEP, 18 pages, 3 figure

Supersymmetry Breaking on Gauged Non-Abelian Vortices

There are a large number of systems characterized by a completely broken gauge symmetry, but with an unbroken global color-flavor diagonal symmetry, i.e., systems in the so-called color-flavor locked phase. If the gauge symmetry breaking supports vortices, the latter develop non-Abelian orientational zero-modes and become non-Abelian vortices, a subject of intense study in the last several years. In this paper we consider the effects of weakly gauging the full exact global flavor symmetry in such systems, deriving an effective description of the light excitations in the presence of a vortex. Surprising consequences are shown to follow. The fluctuations of the vortex orientational modes get diffused to bulk modes through tunneling processes. When our model is embedded in a supersymmetric theory, the vortex is still 1/2 BPS saturated, but the vortex effective action breaks supersymmetry spontaneously.Comment: Latex, 24 pages, 1 figur

Derivation of a Triple Mosaic Adenovirus for Cancer Gene Therapy

A safe and efficacious cancer medicine is necessary due to the increasing population of cancer patients whose particular diseases cannot be cured by the currently available treatment. Adenoviral (Ad) vectors represent a promising therapeutic medicine for human cancer therapy. However, several improvements are needed in order for Ad vectors to be effective cancer therapeutics, which include, but are not limited to, improvement of cellular uptake, enhanced cancer cell killing activity, and the capability of vector visualization and tracking once injected into the patients. To this end, we attempted to develop an Ad as a multifunctional platform incorporating targeting, imaging, and therapeutic motifs. In this study, we explored the utility of this proposed platform by generating an Ad vector containing the poly-lysine (pK), the herpes simplex virus type 1 (HSV-1) thymidine kinase (TK), and the monomeric red fluorescent protein (mRFP1) as targeting, tumor cell killing, and imaging motifs, respectively. Our study herein demonstrates the generation of the triple mosaic Ad vector with pK, HSV-1 TK, and mRFP1 at the carboxyl termini of Ad minor capsid protein IX (pIX). In addition, the functionalities of pK, HSV-1 TK, and mRFP1 proteins on the Ad vector were retained as confirmed by corresponding functional assays, indicating the potential multifunctional application of this new Ad vector for cancer gene therapy. The validation of the triple mosaic Ad vectors also argues for the ability of pIX modification as a base for the development of multifunctional Ad vectors

The VicGeneration study - a birth cohort to examine the environmental, behavioural and biological predictors of early childhood caries: background, aims and methods

Background Dental caries (decay) during childhood is largely preventable however it remains a significant and costly public health concern, identified as the most prevalent chronic disease of childhood. Caries in children aged less than five years (early childhood caries) is a rapid and progressive disease that can be painful and debilitating, and significantly increases the likelihood of poor child growth, development and social outcomes. Early childhood caries may also result in a substantial social burden on families and significant costs to the public health system. A disproportionate burden of disease is also experienced by disadvantaged populations. Methods/Design This study involves the establishment of a birth cohort in disadvantaged communities in Victoria, Australia. Children will be followed for at least 18 months and the data gathered will explore longitudinal relationships and generate new evidence on the natural history of early childhood caries, the prevalence of the disease and relative contributions of risk and protective biological, environmental and behavioural factors. Specifically, the study aims to: 1. Describe the natural history of early childhood caries (at ages 1, 6, 12 and 18 months), tracking pathways from early bacterial colonisation, through non-cavitated enamel white spot lesions to cavitated lesions extending into dentine. 2. Enumerate oral bacterial species in the saliva of infants and their primary care giver. 3. Identify the strength of concurrent associations between early childhood caries and putative risk and protective factors, including biological (eg microbiota, saliva), environmental (fluoride exposure) and socio-behavioural factors (proximal factors such as: feeding practices and oral hygiene; and distal factors such as parental health behaviours, physical health, coping and broader socio-economic conditions). 4. Quantify the longitudinal relationships between these factors and the development and progression of early childhood caries from age 1-18 months. Discussion There is currently a lack of research describing the natural history of early childhood caries in very young children, or exploring the interactions between risk and protective factors that extend to include contemporary measures of socio-behavioural factors. This study will generate knowledge about pathways, prevalence and preventive opportunities for early childhood caries, the most prevalent child health inequality