Table of Contents
What is a Chern Simons term?
Chern–Simons theory is a gauge theory, which means that a classical configuration in the Chern–Simons theory on M with gauge group G is described by a principal G-bundle on M. The connection of this bundle is characterized by a connection one-form A which is valued in the Lie algebra g of the Lie group G.
What Chern Simons theory assigns to a point?
We answer the questions, “What does Chern–Simons theory assign to a point?” and “What kind of mathematical object does Chern–Simons theory assign to a point?” Our answer to the first question is representations of the based loop group.
Is Chern Simons theory a CFT?
Abstract: We explore the connection between Chern Simons theory on a manifold and rational conformal field theories (CFTs) defined on the boundary of the manifold, by map- ping the degrees of freedom of the two theories and defining the Hilbert space of the bulk Chern Simons theory through this map.
What is a Chern number?
Chern number is an integer which determines the topological classification of different materials or structures.
What are topological phases?
In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.
Why is Chern an integer number?
Chern classes are integer cohomology classes. On an oriented manifold the numbers must be integers. The remarkable fact is that Chern classes can be expressed as differential forms derived from the curvature 2 form. These are real cohomology classes but the numbers they produce are always integers.
What is a Chern insulator?
A Chern insulator is 2-dimensional insulator with broken time-reversal symmetry. (If you have for example a 2-dimensional insulator with time-reversal symmetry it can exhibit a Quantum Spin Hall phase). The topological invariant of such a system is called the Chern number and this gives the number of edge states.
What is topological order physics?
What is Chern number?
Why is it called Chern-Simons theory?
The Chern–Simons theory, named after Shiing-Shen Chern and James Harris Simons, is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It is so named because its action is proportional to the integral of the Chern–Simons 3-form.
What is the action integral of the Chern–Simons form?
The action integral ( path integral) of the field theory in physics is viewed as the Lagrangian integral of the Chern–Simons form and Wilson loop, holonomy of vector bundle on M. These explain why the Chern–Simons theory is closely related to topological field theory .
What is the Chern-Simons TQFT?
The Chern-Simons TQFT was introduced in ( Witten 1989 ). The properties of the field configuration space of Chern-Simons theory depends on the properties of its gauge group G.
Is there a Chern–Simons gravity theory in three dimensions?
In addition the U ( N) and SO ( N) Chern–Simons theories at large N are well approximated by matrix models . In 1982, S. Deser, R. Jackiw and S. Templeton proposed the Chern–Simons gravity theory in three dimensions, in which the Einstein–Hilbert action in gravity theory is modified by adding the Chern–Simons term.