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New answers tagged conformal-field-theory

0

I think I can help. Pick up the expression you started with. Convert to coordinates $\tau$ and $\sigma$ as you did. Use the Green's theorem in these coordinates and then convert back to the complex coordinates again. I am not good with word by this transliterates in the following expression $$2∫∫dσ dτ (∂_{σ}v^{σ} + ∂_{τ}v^{τ})$$ = (now use Green’s theorem ...

3

Given the four point function $\langle \phi(x_1)\phi(x_2)\phi(x_3)\phi(x_4)\rangle$, the conformal block expansion depends on what operators you replace by the OPE. So if you insert the OPE for $\phi(x_1)\phi(x_2)$ and the OPE for $\phi(x_3)\phi(x_4)$ then this corresponds to the s channel---one can also call this the (12)(34) channel---.. The t channel is ...

1

It is an unfortunate choice of $z, z'$, nevertheless it is correct. Let $g\colon z \mapsto z'$ be a conformal transformation: a field $\phi$ is said to be primary of dimension $h$ if, under such transformation, it transforms as $$\phi'(z') = \left(\frac{\partial g(z)}{\partial z}\right)^{-h}\,\phi(z)$$ where we look at just one coordinate at a time ...

0

For the transformation of field \begin{align} \phi_{ R \times S^{D-1}}(t, \Phi) \rightarrow \phi_{R^D}(r, \Phi) = r^{-\Delta}\phi_{ R \times S^{D-1}}(t, \Phi) \end{align} where $\Delta$ is scaling dimension.

1

This is not a state-operator correspondence map. The 2D state-operator correspondence is given by a map between the Hilbert space of states $\mathcal{H}$ with a $\mathrm{PSL}(2,\mathbb{C})$-invariant vacuum $\Omega$ and fields $\phi: \mathbb{C}\to\mathrm{U}(\mathcal{H})$ explicitly given by  \{\text{fields}\}\to\mathcal{H},\ \phi \mapsto \lim_{z\to ...

1

Under conformal mapping z=>w(z) and $\bar{z}$=>$\bar{w}(\bar{z})$ a field of conformal dimension(h,$\bar{h}$) transforms as $\tilde{\phi}(w,\bar{w})=(\frac{\partial w}{\partial{z}})^{-h}(\frac{\partial \bar{w}}{\partial\bar{z}})^{-\bar{h}}\phi(z,\bar{z})$..

1

What came to be called "discrete torsion" is simply the data that makes the B-field gerbe be equivariant over the orbifold. This was clarified by Eric Sharpe, see the references here: Eric Sharpe, Discrete Torsion and Gerbes I (arXiv:hep-th/9909108) Discrete Torsion and Gerbes II (arXiv:hep-th/9909120) Discrete Torsion, Quotient Stacks, and String ...

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