Spinning conformal correlators

By M. Costa, J. Penedones, David Poland, S. Rychkov. 2011

574 citations recorded by the source corpus.

A bstractWe develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an indexfree 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.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/407e902a2a37b44dcf72e16ef62e96d868975aef

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In Atomic and Molecular Physics, and Optics

In Geometry and Topology

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Citations in the corpus

Causality constraints on corrections to the graviton three-point coupling (2014, background): “We have three type of contractions (see also [79])”
Bootstrapping the O(N ) vector models (2013, background): “Although much progress has been made computing conformal blocks for these types of operators using series manipulations [12, 39–42], derivative relations [43, 44], and conformal integrals [45], we believe the residues ci are the most convenient and directly useful data for numerical bootstrap applic”
Analyticity and the holographic S-matrix (2011, methodology): “In any case, our work suggests that there is an intimate connection between the Bootstrap Program for large N CFTs [27, 21, 20, 22, 23, 24, 25, 26, 50] and the S-Matrix Program, and that solving general CFTs via the Bootstrap will be at least as difficult as finding consistent S-Matrices using the c”
Operator bases, S-matrices, and their partition functions (2017, methodology): “In a similar vein, when an n-point conformal correlator involves spinning objects, the correlator is first decomposed into tensor structures which then multiply functions of the conformal-cross ratios [29].”
Bootstrapping 3D fermions (2015, background): “In particular, the number of conformal invariants grows with the spin of the insertions (see, for instance, [18, 19]).”
Averaged null energy condition from causality (2016, background): “The most general 3-point function 〈JXJ〉 consistent with conformal symmetry is written in appendix B, following [47].”
Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory (2012, background): “There are two basic structures [25, 26] that may appear inside correlation functions.”
The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, methodology): “ng symmetry (3.11) and the transversality of the operators. More general spinning correlators are obtained in the same way and can be written in terms of a simple basis of tensor structures (see e.g. [62,67]), although this will not be needed in this paper. For specic weights, the operators become c”
The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “In a future publication [65], we will show how to obtain them in a more systematic way, using tools from conformal field theory [66–68].”
The conformal bootstrap: Theory, numerical techniques, and applications (2018, methodology): “(56) 52 The limit is worked out carefully in e.g. Dolan and Osborn (2001b) or Costa et al. (2011a).”
Recursion relations for conformal blocks (2015, background): “When the external operators are tensor we have many of such functions, each one of them multiplied by a different tensor structure [44]”
Defects in conformal field theory (2016, methodology): “The machinery to do this was elucidated in [3] (see also [4]), where an algorithmic way of constructing conformally covariant correlators of symmetric traceless tensors (STT) was set up.”
Shape dependence of entanglement entropy in conformal field theories (2015, unknown): “This can be done efficiently using the embedding space formalism developed in [42].”
TASI Lectures on the Conformal Bootstrap (2016, background): “The embedding space formalism provides a transparent and practical way to derive all of these results [24], so it’s not worth dwelling on them here.”
Conformal Regge theory (2012, background): “Conformal symmetry imposes constrains on the form of two and three point functions between scalar and symmetric traceless operators [59].”