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After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing the classical conformal blocks for the sphere topology to the tours topology. We give the explicit results for the classical blocks up to the third order in the nome included and compare them with the classical limit of the quantum conformal blocks. The extension to higher orders is straightforward.
We give a simple iterative procedure to compute the classical conformal blocks on the sphere to all order in the modulus.
We continue to develop the holographic interpretation of classical conformal blocks in terms of particles propagating in an asymptotically $AdS_3$ geometry. We study $n$-point block with two heavy and $n-2$ light fields. Using the worldline approach
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding spa
We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called `seed blocks in three dimensions.
We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group theoretic str