1 vote
227 views

### Is Weyl transformation part of diffeomorphism? Does a gravitational anomaly capture also the anomaly due to Weyl transformation? [duplicate]

Weyl transformation is a local rescaling of the metric tensor $$g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}$$ Diffeomorphism maps to a theory under arbitrary differentiable coordinate transformations (...
• 4,346
1 vote
218 views

### Confused about the definition of conformal transformation [duplicate]

Recently, I read some books and articles about conformal field theory and I find there exists two completely different views about conformal transformation... The first is that: Conformal ...
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54 views

### Conformal Transformations [duplicate]

I am getting confused if the conformal transformations are transformations of charts on the manifold, or something else. Basically, I can imagine a Euclidean plane, and two observers one with chart $x$...
3k views

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### Simple conceptual question conformal field theory

I come up with this conclusion after reading some books and review articles on conformal field theory (CFT). CFT is a subset of FT such that the action is invariant under conformal transformation ...
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### Relation of conformal symmetry and traceless energy momentum tensor

In usual string theory, or conformal field theory textbook, they states traceless energy momentum tensor $T_{a}^{\phantom{a}a}=0$ implies (Here energy momentum tensor is usual one which is symmetric ...
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### Is conformal transformation a coordinate transformation or not?

I have been looking through several questions and answers on conformal transformation in the stack exchange community. While they have helped me gain a better understanding of the basic issues, I am ...
2k views

### Noether's theorem for arbitrary conformal coordinate transformations

I have been reading Introduction to Conformal Field Theory by Blumenhagen and Plauschinn. Equation (2.19) on page 19 states that if our theory is invariant under a general conformal transformation \$x^\...
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### conformal, Weyl transformations, apparent discrepancies and confusions

Because of the apparent discrepancy of how some CFT and GR books define conformal transformation unlike in string theory area, I wanted to get rid of all the confusion from McGreevy's lecture notes: ...
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### Conformal group in 2D being a subgroup of Diff x Weyl - Polchinksi's 'String Theory'

I am trying to understand how the conformal group in two dimensions is a subgroup of the direct product of the diffeomorphism group and the group of Weyl transformations, as explained by Polchinski in ...
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### What is the significance of the conformal invariance of electrodynamics in a covariant formulation?

I am a confused about the role of symmetry transformations in a covariant formulation. Maxwell's equations can be shown to be invariant under conformal transformations. See e.g. here: https://arxiv....
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### Weyl transformation vs diffeomorphism; conformal invariant vs general in/covariant

Background info: My understanding: 1. Weyl transformation is a local rescaling of the metric tensor $$g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}$$ A theory invariant under this Weyl transformation is ...
• 4,346
1 vote
326 views

### Why does the Weyl transformation preserve angles in string theory?

The Weyl invariance symmetry of the Polyakov action is said to be considered as the invariance of the theory under a local change of scale which preserves the angles between all lines. However, why ...
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