Triangle Seminars

Abstract:
Standard nonperturbative covariant gauge fixing procedure leaves the theory with Gribov copies and on lattice even Neuberger zero-zero problem. Due to this Neuberger problem, BRST and SUSY on lattice are still open and urgent questions to be addressed. I will introduce the problems using Landau gauge
for a simple toy model, compact QED on a one dimensional lattice, and propose a modification which completely resolves Gribov-Neuberger problems on this simple toy model
and even the higher dimensional generalization. This gauge-fixing term for compact QED on lattice is the classical XY-model Hamiltonian, and in condensed matter terms the problem is to get ALL extrema of this Hamiltonian exactly. To
give a full analytical proof for the higher dimensional generalization, I will need to introduce a tailor-made terminology of Algebraic Geometry. I will also go on proposing two algorithms for gauge-fixing on lattice that use
sophisticated applied mathematics and give efficient results derived from Numerical Algebraic Geometry.

Abstract:
D-branes in Calabi-Yau manifolds are interesting objects from the point of view of string phenomenology and of pure mathematics, and they have been studied using a conformal field theory as well as geometric methods. In the past few years, a new tool has emerged in the form of matrix factorisations of Landau-Ginzburg potentials, which gives a rather efficient computational handle on the properties of topological Calabi-Yau branes. I will try to give an overview of some of these developments.

Abstract:
Given two conformal field theories, one of which is defined on the upper half plane and the other on the lower half plane, one can ask for conformally invariant ways to join them along the real line. The resulting interface is called a defect line. These defects contain interesting information about the CFT, such as its symmetries, order-disorder dualities and T-dualities. They also provide relations between string theories on different target spaces.

Abstract:
The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this talk we present an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one-loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. This settles the previously open question of a potential regularization scheme dependence of the one-loop beta-function traditionally computed in the background field approach. Furthermore, we show that the remaining logarithmic divergencies give rise to an effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six.