Introduction The notes give a survey of the basics of the following topological field theories: • The Chern-Simons gauge theory on 3-manifolds, its renormalization, geometric quantization, computation of partition functions by surgery, and relation with Jones Polynomials • Twisted N = 2 supersymmetric Yang-Mills theory on 4-manifolds, its reduction to N = 1 theory with a mass gap, and computati...

We consider recently-constructed solutions of three dimensional SL(N,R)×SL(N,R) Chern-Simons theories with non-relativistic symmetries. Solutions of the Chern-Simons theories can generically be mapped to solutions of a gravitational theory with a higherspin gauge symmetry. However, we will show that some of the non-relativistic solutions are not equivalent to metric solutions, as this mapping f...

We define an extended Bloch group and show it is naturally isomorphic to H3(PSL(2,C) δ ;Z). Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger–Chern–Simons class on this homology group. It also leads to an independent proof of the analytic relationship between volume and Chern–Simons invariant of hyperbolic 3–manifolds conjectured in [16] a...

Sperm morphometry is a part of the semen analysis based on CASA technology and has shown a big role in the prediction of male fertility. This analysis implies the use of stain techniques, although it has been shown that staining can make dramatic changes in the cell morphometry in different species. The aim of the present work was to evaluate the differences in sperm morphometry in Alpaca, intr...

We make a number of observations about matter-ghost string phase, which may eventually lead to a formal connection between matroid theory and string theory. In particular, in order to take advantage of the already established connection between matroid theory and Chern-Simons theory, we propose a generalization of string theory in terms of some kind of Kahler metric. We show that this generaliz...

In this paper we study supersymmetric Chern-Simons-matter (CSM) theories with several Higgs branches. Two such theories at small Chern-Simons level are conjectured to describe the superconformal field theory at the infrared fixed point of N = 4 QED with Nf = 2, 3. In particular, the mirror symmetry which exchanges the Coulomb and Higgs branches of N = 4 QED with Nf = 2 is manifest in the Chern-...

Three-dimensional Euclidean pure gravity with a negative cosmological constant can be formulated in terms of the Chern-Simons theory, classically. This theory can be written in a supersymmetric way by introducing auxiliary gauginos and scalars. We calculate the exact partition function of this Chern-Simons theory by using the localization technique. Thus, we obtain the quantum gravity partition...

A class of two dimensional conformal field theories is known to correspond to three dimensional Chern-Simons theory. Here we claim that there is an analogous class of four dimensional field theories corresponding to five dimensional Chern-Simons theory. The four dimensional theories give a coupling between a scalar field and an external divergenceless vector field and they may have some applica...

One of the possible low-energy consequences of string theory is the addition of a Chern-Simons term to the standard Einstein-Hilbert action of general relativity. It can be argued that the quintessence field should couple to this Chern-Simons term, and if so, it drives in the linearized theory a parity-violating interaction between the gravito-electric and gravitomagnetic fields. In this paper,...