It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS
3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.

/pdf/quantum-field-theory-and-the-jones-polynomial-5897tp4ud9.pdf

Quantum field theory and the Jones polynomial

http://risa.stanford.edu/teaching/362/particledarkmatter.pdf

Particle dark matter: Evidence, candidates and constraints

We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (\phi) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.

/pdf/planck-2015-results-xx-constraints-on-inflation-4lq02ohyyn.pdf

Planck 2015 results. XX. Constraints on inflation

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

Noncommutative field theory

There is almost universal agreement among astronomers that most of the mass in the Universe and most of the mass in the Galactic halo is dark. Many lines of reasoning suggest that the dark matter consists of some new, as yet undiscovered, weakly-interacting massive particle (WIMP). There is now a vast experimental effort being surmounted to detect WIMPS in the halo. The most promising techniques involve direct detection in low-background laboratory detectors and indirect detection through observation of energetic neutrinos from annihilation of WIMPs that have accumulated in the Sun and/or the Earth. Of the many WIMP candidates, perhaps the best motivated and certainly the most theoretically developed is the neutralino, the lightest superpartner in many supersymmetric theories. We review the minimal supersymmetric extension of the Standard Model and discuss prospects for detection of neutralino dark matter. We review in detail how to calculate the cosmological abundance of the neutralino and the event rates for both direct- and indirect-detection schemes, and we discuss astrophysical and laboratory constraints on supersymmetric models. We isolate and clarify the uncertainties from particle physics, nuclear physics, and astrophysics that enter at each step in the calculation. We briefly review other related dark-matter candidates and detection techniques.

Supersymmetric Dark Matter

Minimal Low-Energy Supergravity

Low-Energy Supersymmetry

The Structure of Gauge and Gravitational Anomalies

We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure dependence of the chiral Dirac determinant on a Riemann surface is given by Riemann's theta function. We use this result to investigate the modular invariance of multiloop heterotic string amplitudes.

https://projecteuclid.org/download/pdf_1/euclid.cmp/1104115581

Theta functions, modular invariance, and strings

In these lectures a general introduction to T-duality is given. In the abelian case the approaches of Buscher, and Roucek and Verlinde are reviewed. Buscher’s prescription for the dilaton transformation is recovered from a careful definition of the gauge integration measure. It is also shown how duality can be understood as a quite simple canonical transformation. Some aspects of non-abelian duality are also discussed, in particular what is known on relation to canonical transformations. Some implications of the existence of duality on the cosmological constant and the definition of distance in String Theory are also suggested.

Luis Alvarez-Gaume

Papers

Minimal Low-Energy Supergravity

Low-Energy Supersymmetry

The Structure of Gauge and Gravitational Anomalies

Theta functions, modular invariance, and strings

An Introduction to T-Duality in String Theory