Showing papers by "Miguel S. Costa published in 2011"
TL;DR: The embedding formalism for conformal field theories is developed, aimed at doing computations with symmetric traceless operators of arbitrary spin, using an indexfree notation where tensors are encoded by polynomials in auxiliary polarization vectors.
Abstract: We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.
624 citations
TL;DR: For conformal field theories in arbitrary dimensions, this paper introduced 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.
Abstract: 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 space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.
375 citations
TL;DR: In this article, the embedding formalism for conformal field theories was developed, aimed at doing computations with symmetric traceless operators of arbitrary spin operators, where tensors are encoded by polynomials in auxiliary polarization vectors.
Abstract: We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.
96 citations
TL;DR: This paper introduces 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 space formalism.
Abstract: 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 space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.
60 citations
02 Jun 2011
TL;DR: In this paper, a simple AdS black disk model is proposed to describe saturation in DIS, where the structure functions have the same power-law scaling, F(T) similar to F(L) and F(X) similar with respect to x −1 −1−1−ε, where is related to the expansion rate of the black disk with energy.
Abstract: Using the approximate conformal invariance of QCD at high energies we consider a simple AdS black disk model to describe saturation in DIS. Deep inside saturation the structure functions have the same power law scaling, F(T) similar to F(L) similar to x(-omega), where. is related to the expansion rate of the black disk with energy. Furthermore, the ratio F(L)/F(T) is given by the universal value 1+omega/3+omega, independently of the target.
18 citations