A multipoint conformal block chain in d dimensions
- Creators
- Parikh, Sarthak
Abstract
Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group. In this paper, we systematically work out the d-dimensional n-point global conformal blocks (for arbitrary d and n) for external and exchanged scalar operators in the so-called comb channel. We use kinematic aspects of holography and previously worked out higher-point AdS propagator identities to first obtain the geodesic diagram representation for the (n + 2)-point block. Subsequently, upon taking a particular double-OPE limit, we obtain an explicit power series expansion for the n-point block expressed in terms of powers of conformal cross-ratios. Interestingly, the expansion coefficient is written entirely in terms of Pochhammer symbols and (n â 4) factors of the generalized hypergeometric function âFâ, for which we provide a holographic explanation. This generalizes the results previously obtained in the literature for n = 4, 5. We verify the results explicitly in embedding space using conformal Casimir equations.
Additional Information
© 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: December 17, 2019; Accepted: May 5, 2020; Published: May 25, 2020. I thank Robert Clemenson for valuable discussions and collaboration in the early stages, and Christian B. Jepsen for useful discussions. I would also like to thank Steve Gubser, my Ph.D. advisor. Our joint work from about two years ago [48] served as an important stepping stone and a springboard for many subsequent ideas, including the present work. Steve was an inspiring mentor, an extraordinary physicist and an exceptional human being. I am deeply grateful to Steve Gubser for everything, and would like to dedicate this paper to his fond memory.Attached Files
Published - Parikh2020_Article_AMultipointConformalBlockChain.pdf
Submitted - 1911.09190.pdf
Supplemental Material - 13130_2020_13058_MOESM1_ESM.tar
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Additional details
- Eprint ID
- 103495
- Resolver ID
- CaltechAUTHORS:20200527-131226276
- SCOAP3
- Created
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2020-05-27Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field