A diff-invariant 1+1d QFT with divergent central charge?

In summary, a free scalar field on a diff-invariant 1+1 dimensional background contributes to the central charge of the Virasoro algebra with a constant term in bosonic string theory. There are examples of 1+1d QFTs that have a central charge contribution that diverges when the regularization cut off is removed in the canonical quantization approach, which may be more suitable for discussion in the Quantum Physics forum.
  • #1
quelarion
9
0
We know that a free scalar field on a diff-invariant 1+1 dimensional background (i.e. bosonic string theory on the worldsheet) contributes to the central charge of the Virasoro algebra with a constant term.

Is there any examples of a 1+1d QFT that has instead a central charge contribution that diverges when the regularization cut off is removed in the canonical quantization approach?
 
Physics news on Phys.org
  • #3
PeterDonis said:
Shoudn't this be in the Quantum Physics forum?

Well, I thought that since we are talking of a quantum gravity related problem this was the best section, but maybe you are right.
Admins, please move if you think it's better.
 

1. What is a diff-invariant 1+1d QFT?

A diff-invariant 1+1d QFT, or diff-invariant two-dimensional quantum field theory, is a theoretical framework used to study the behavior of quantum fields in two-dimensional spacetime. It is diff-invariant, meaning that it is invariant under diffeomorphisms, which are transformations that preserve the local structure of spacetime.

2. What does a divergent central charge mean?

A central charge in a quantum field theory is a number that characterizes the behavior of the theory at critical points, or points where the system undergoes a phase transition. A divergent central charge means that this number becomes infinite, indicating that the theory does not behave as expected at these critical points.

3. Why is a diff-invariant 1+1d QFT with divergent central charge important?

This type of quantum field theory is important because it can provide insights into the behavior of physical systems at critical points, where traditional methods may fail. It also has applications in fields such as condensed matter physics and string theory.

4. How is this type of QFT studied?

A diff-invariant 1+1d QFT with divergent central charge is typically studied using mathematical and computational techniques. These may include renormalization, which is a method for dealing with divergences in quantum field theories, and numerical simulations using supercomputers.

5. What are some current research topics related to this type of QFT?

Current research in this area includes studying the properties of topological quantum field theories, which are diff-invariant and have important applications in condensed matter physics. Other topics include the study of holographic dualities, which are connections between quantum field theories and higher-dimensional theories, and the use of conformal field theories to describe critical behavior in condensed matter systems.

Similar threads

  • Advanced Physics Homework Help
Replies
3
Views
2K
  • Quantum Physics
Replies
2
Views
1K
  • Beyond the Standard Models
Replies
14
Views
3K
  • Other Physics Topics
3
Replies
85
Views
29K
  • Special and General Relativity
Replies
21
Views
6K
  • Quantum Physics
Replies
2
Views
3K
  • Beyond the Standard Models
Replies
10
Views
2K
Replies
2
Views
3K
  • Quantum Physics
Replies
11
Views
2K
  • Beyond the Standard Models
11
Replies
350
Views
47K
Back
Top