# Questions tagged [conformal-field-theory]

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In 2D, the infinite-dimensional algebra of local conformal transformations normally permits exact solution or classification of such theories. Further use for CFT applications to string theory, statistical mechanics, and condensed matter physics.

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### Splitting Scalar into Holomorphic and Anti-Holomorphic Parts

I am reading Tong’s string theory lecture notes. On page 78, he splits the 2d free scalar into left- and right-moving parts, seemingly using the classical equation of motion as justification. Why is ...
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### Weyl transformation of induced metric

Consider the Weyl/conformal transformation in four dimenions $$\tilde{g} \enspace = \enspace \Omega^2 g \quad \Longrightarrow \quad \sqrt{-|\tilde{g}|} \enspace = \enspace \Omega^4 \sqrt{-|g|}$$ The ...
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### How to deal with the numerical stability of the dimension and polynomial order in the SDPB? [closed]

This might be a far shot question, but any comment are welcome. I'm using David Simmons-Duffin, Walter Landry, and Vasiliy Dommes's SDPB (Semi-Definite Programming Bootstrap) package to find the ...
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### Ward identity for special conformal transformation in d dimensions

I am reading CFT from the yellow book ( "Conformal Field Theory" by Francesco, Mathieu, Sénéchal ). In section 4.3.2, they calculate three Ward identities corresponding to (i) translation ...
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### Cyclic Universe Problems

In Penroses's hypothesis, at the end of each iteration the universe undergoes a conformal transformation, meaning distances are rescaled. If I am right, it implies that a planet from the previous ...
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### Why Is There No Oscillator Representation for Operators in Planar ${\cal N}=4$ SYM Theory?

I'm studying the planar ${\cal N}=4$ Super Yang-Mills (SYM) theory and I'm curious about the representations of its operators, specifically the Hamiltonian and the dilatation operator. In many quantum ...
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### OPE limit of four-point function in de Sitter space

I have been trying to read the paper 'Cosmological Collider Physics'. This paper studies several things, of which the most interesting to me was studying the correlation function in de Sitter space by ...
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### Conformal symmetry and group in arbitrary dimensions [duplicate]

As far as i understand, the full symmetry of relativity is conformal symmetry. This is represented by the conformal group $\operatorname{Conf}(1, 3)$ Of Minkowski spacetime which is \$ \mathbb{R}^{1, ...
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