Related papers: Quantum Cohomology And All That

We discuss the isometry group structure of three-dimensional black holes and Chern-Simons invariants. Aspects of the holographic principle relevant to black hole geometry are analyzed.

In this paper we elaborate on the correspondence between the quantum Hall system with filling factor equal to one and the N=4 SYM theory in the 1/2 BPS sector, previously mentioned in the [hep-th/0409174, hep-th/0409115]. We show the…

The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. Instead of local order parameters, topological phases are described by global topological invariants and are…

We study a three-dimensional symmetric Chern-Simons field theory with a general covariance and it turns out that the original Chern-Simons theory is just a gauge fixed action of the symmetric Chern-Simons theory whose constraint algebra…

Chern-Simons theories, which are topological quantum field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of quantum field theories which can be exactly and…

It is well known that Chern-Simons Theories are in the constrained systems and their total Hamiltonians become identically zero, because of their gauge invariance. While treating the constraints quantum mechanially, it will be expected taht…

We introduce the concept of super universality in quantum Hall and spin liquids which has emerged from previous studies. It states that all the fundamental features of the quantum Hall effect are generically displayed as general topological…

In cohomological formulations of the calculus of variations obstructions to the existence of (global) solutions of the Euler-Lagrange equations can arise in principle. It seems, however, quite common to assume that such obstructions always…

We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been…

We propose a relation between the operator of S-duality (of N=4 super Yang-Mills theory in 3+1D) and a topological theory in one dimension lower. We construct the topological theory by compactifying N=4 super Yang-Mills on a circle with an…

This article reviews the development of photonic analogues of quantum Hall effects, which have given rise to broad interest in topological phenomena in photonic systems over the past decade. We cover early investigations of geometric…

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical…

For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants…

A cohomological study is made of an equivariant map betwen the configuration space of n points in space and the flag manifold of U(n).

Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time…

We develop a theory for the pseudorelativistic fractional quantum Hall effect in graphene, which is based on a multicomponent abelian Chern-Simons theory in the fermionic functional integral approach. Calculations are performed in the…

Fundamental duality is a concept which refers to two irreducible, heterogeneous principles which are in opposite and complementary of each other. The complementary principle in quantum mechanics is also praised by Bohr. This important…

Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasiparticles finds applications in many different contexts, including quantum…

Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…

This is the third of a series of papers on a new equivariant cohomology that takes values in a vertex algebra, and contains and generalizes the classical equivariant cohomology of a manifold with a Lie group action a la H. Cartan. In this…