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Conformal four point functions and the operator product expansion
Open accessAbstract
Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This is solved explicitly in two and four dimensions in terms of ordinary hypergeometric functions of variables z,x which are simply related to u,v. The operator product expansion analysis is applied to the explicit expressions for the four point function found for free scalar, fermion and vector field theories in four dimensions. The results for four point functions obtained by using the AdS/CFT correspondence are also analysed in terms of functions related to those appearing in the operator product discussion.
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Cites
Anti de Sitter space and holography
Witten, E. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n2.a2 · Cited by 13,070
Cited by
Holography from conformal field theory
Heemskerk, I., Penedones, J., Polchinski, J., & Sully, J. (2009) · Journal of High Energy Physics · doi:10.1088/1126-6708/2009/10/079 · Cited by 787
The conformal bootstrap: Theory, numerical techniques, and applications
Poland, D., Rychkov, S., & Vichi, A. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015002 · Cited by 760
Magic identities for conformal four-point integrals
Drummond, J. M., Henn, J., Smirnov, V. A., & Sokatchev, E. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/01/064 · Cited by 481
Convexity and liberation at large spin
Komargodski, Z., & Zhiboedov, A. (2013) · Journal of High Energy Physics · doi:10.1007/jhep11(2013)140 · Cited by 420
Bootstrapping mixed correlators in the 3D Ising model
Kos, F., Poland, D., & Simmons-Duffin, D. (2014) · Journal of High Energy Physics · doi:10.1007/jhep11(2014)109 · Cited by 299
Metadata
- Authors
- Dolan, F. A., & Osborn, H.
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 2001-04
- Volume
- 599
- Issue
- 1-2
- Pages
- 459-496
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W1985777033
- Cited by
- 673
- References
- 1
- FWCI
- 4.77
- Type
- journal article
- Language
- en
- Open access
- green
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