# Tag Info

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 ...

2

Please note that the light-cone coordinate transformation is not an element of the Poincaré group, nor of the full Conformal group. The easiest way to see this for the conformal group is to consider the transformation properties of the metric tensor. For the Poincaré group note that the proper distance $x_0^2-x_1^2 \rightarrow t\bar{t}$ which is not of the ...

1

I can only answer the mathematical part of your question (or make a stab at it). We could say that by describing a space as an orbifold, the singularities are taken care of by somehow declaring them to be under control. Where a manifold is a topological space that may be very complicated, but locally looks very nice, namely like $\mathbb R^n$, an orbifold ...

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 ...

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

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 $$\{\text{fields}\}\to\mathcal{H},\ \phi \mapsto \lim_{z\to ... 1 It is an unfortunate choice of z, z', nevertheless it is correct. Let g\colon z \mapsto z' be a conformal transformation: a field \phi is said to be primary of dimension h if, under such transformation, it transforms as$$ \phi'(z') = \left(\frac{\partial g(z)}{\partial z}\right)^{-h}\,\phi(z)  where we look at just one coordinate at a time ...

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