2 questions. 1 on Field theory, the other on Ads/CFT.

In summary, the interactions in QFT on curved spacetime are different from those in flat space due to the use of covariant derivatives. The concept of positive curvature in our universe is not directly related to the use of AdS/CFT correspondence, which is a theoretical tool used to explore the possibility of a 4d gauge group and a 3d CFT at the boundary of AdS space. This research avenue is still being explored and could potentially provide insights into our universe.
  • #1
sox
5
0
My first question:

QED has U(1) symmetry. The transformation is a function of x (psi -> psi*theta(x)). How does this depend on the spacetime? Do interactions therefore differ between curved space and flat space? Is this what leads on to QFT on curved spacetime research?

My second question:

If we believe that the curvature of spacetime in our universe is positive, why do string theorists like to play around with the Ads/CFT correspondance? Ads is a space with negative curvature is it not? If so, then surely any correspondance between string theory and gauge theory, whilst interesting, is ultimatley incorrect based on the fact that the string theory has been set up in an unphysical space?

Any illumination here would be appreciated.

Sox
 
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  • #2
sox said:
Do interactions therefore differ between curved space and flat space? Is this what leads on to QFT on curved spacetime research?
Yes and yes. The interactions are obtained by replacing ordinary derivatives by covariant derivatives, which are nontrivial in curved spacetime.
 
  • #3
Oh yeah! I had forgotten that the derivative changes in curved spacetime.
Thanks.

Anyone got an answer for the second one?
 
  • #4
We don't actually believe that spacetime has positive curvature, at least as I understand it; currently, the measurements are consistent with a flat spacetime (no curvature). What you may be confusing this with is the statement that our universe is expanding. That means that it's inflating faster and faster with respect to time, or the second derivative of the size of the universe with respect to time is positive. This is uncorrelated with the curvature of the universe. The cosmological constant does indeed contribute to the expansion rate of the universe, but so do matter and energy.

One could imagine a 4d gauge group that appeared to be (at least approximately) conformal above, say, 10 TeV, but confined below that. That would be dual to AdS space with boundaries (D3-branes or something of the sort). That's one situation in which one could imagine using AdS/CFT in our universe. Also, you could pretend that our universe was in fact AdS, but with a damn big radius of curvature, meaning a 3d CFT would exist at the boundary. This avenue of research is less popular since it's a little less clear what to do to make progress. However, it's certainly an interesting possibility.
 

1. What is field theory?

Field theory is a theoretical framework used in physics to describe the interactions between particles and fields. It is based on the concept of fields, which are physical quantities that vary in space and time, and can be used to explain various phenomena such as electromagnetism, gravity, and nuclear interactions.

2. What is the Ads/CFT correspondence?

The Ads/CFT correspondence, or Anti-de Sitter/Conformal Field Theory correspondence, is a theoretical framework that relates two seemingly different theories: anti-de Sitter space (Ads) and conformal field theory (CFT). It suggests that certain quantum theories in Ads can be described by classical theories in CFT, providing a powerful tool for understanding the properties of strongly interacting quantum systems.

3. How is field theory used in particle physics?

Field theory is used in particle physics to describe the behavior and interactions of subatomic particles. It is a crucial tool for understanding the fundamental forces and particles that make up the universe, and has been successful in predicting and explaining experimental results in particle accelerators such as the Large Hadron Collider.

4. What is the significance of the Ads/CFT correspondence in theoretical physics?

The Ads/CFT correspondence is significant in theoretical physics because it provides a new way of understanding the fundamental nature of quantum gravity and its connection to other quantum theories. It has also been used to solve long-standing problems in theoretical physics, such as the black hole information paradox and the nature of quantum entanglement.

5. Are there any practical applications of field theory and the Ads/CFT correspondence?

While field theory and the Ads/CFT correspondence are primarily used in theoretical physics, there are some potential practical applications that are currently being explored. For example, field theory techniques have been used in condensed matter physics to study the behavior of materials at the atomic level, and the Ads/CFT correspondence has been used in computer science to develop new algorithms for solving complex problems. However, further research and development is needed for these potential applications to become more practical and widely used.

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