# 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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### What does it mean by "minimally coupled action" and "Weyl invariant"?

The scalar field action, minimally coupled to the background field looks like $$S= \int d^Dx \sqrt{-g} [\partial_{\mu} \phi \partial_{\nu} \phi g^{\mu\nu} - \lambda \phi^{\beta}]$$ Now in general the ...
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### Derivation of the Conformal Ward Identity in Di Francesco et al

I am reading section 5.2.2. (titled The Conformal Ward Identity) from Conformal Field Theory by Di Francesco et al. The authors write \begin{align} \partial_\mu(\epsilon_\nu T^{\mu\nu}) &= \...
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### Scale transformation of scalars in curved backgrounds

I am puzzled by the concept of scalar fields that arise in conformal field theory in curved backgrounds. In general relativity, so far as I understand it, a scalar field is basically a function ...
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### WZW primary fields / correlations in terms of current algebra?

Cross-posted from a Mathoverflow thread! Answer there for a bounty ;) Given the $\mathfrak{u}_N$ algebra with generators $L^a$ and commutation relations $[L^a,L^b] = \sum_c f^{a,b}_{c} L^c$ , the ...
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$\text{AdS}_{n}/\text{CFT}_{n-1}$ correspondence provides a dictionary for one-to-one mapping observables in bulk gravity to boundary conformal field theories. However, does the reverse correspondence ...
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### Faddeev-Popov Method for Gauge Fixing in CFT (Light-ray Operators)

I was attempting to go through the paper by Petr Kravchuk and David Simmons-Duffin: https://arxiv.org/abs/1805.00098 where I encountered the following Just below E.4, it is mentioned that for the ...
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### Derivation of Hofman-Maldacena Bounds

I am trying to study the section where the author of the article - https://gitlab.com/davidsd/lorentzian-cft-notes tries to outline the derivation of the Hofman-Maldacena bounds in Section 6.2. I have ...
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### Gauge Fixing in Derivation of Lorentzian OPE Inversion Formula in 2D CFT

I have been looking through the following article: https://arxiv.org/abs/1711.03816 and wish to understand the derivation from scratch. The definition of conformal partial waves and the object of ...
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### Polchinski's doubling trick for extending open string theory to the whole complex plane

Open string theory can be described on the upper-half complex plane. To simplify the description of open string theory, Polchinski asserts (eq. 2.6.28 in his Vol. I String Theory book) that it is ...
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### How to understand non-invertible symmetries from stacking TQFTs?

I'm reading section 3.3.3 of https://arxiv.org/abs/2305.18296. The idea is to stack a 1d TQFT with G symmetry on a quantum field theory T with symmetry G, then gauge the diagonal G symmetry, the 1d ...
In the paper I am reading, there is a statement that seems to use the fact that the scaling dimension of stress tensor is $\Delta=d$, and I would like to show that this is correct. I found a similar ...