# 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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### Metric under conformal transformation

I have a question regarding the conformal factor $\Omega(x)$ when dealing with a conformal transformation. We know that under a change of coordinates $x\rightarrow x^{'}=x^{'}(x)$ our metric changes ...
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### Statement clarification: When do we have $\Delta = \frac{d-1}{2} q_R$?

This statement is for SCFT, where $\Delta$ is the conformal weight, $q_R$ is the R-charge. How many supersymmetries do we need? Do we need chiral primary scalar, or just chiral scalar? How to derive ...
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### Super Hilbert space of SYM

I hope this message finds you well. I am currently try to understand explicitly, at least in some sense, $d=4$, ${\cal N}=4$ super Yang-Mills theory. What is the explicit construction of the super ...
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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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### 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 ...