Fetching the paper…

Reading the bibliography…

Conformal Basis, Optical Theorem, and the Bulk Point Singularity · Around

2017

Conformal Basis, Optical Theorem, and the Bulk Point Singularity

Lam, Ho Tat, Shao, Shu-Heng

Original
PDF
Post on X

Understand

We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$.

Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators.
We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis.
In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis.

Built on

P. A. M. Dirac, “Wave equations in conformal space,” Annals Math
1936
Earlier work this paper cites.
G. Mack and A. Salam, “Finite component field representations of the conformal group,” Annals Phys
1969
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi, and R. Gatto, “The shadow operator formalism for conformal algebra. vacuum expectation values and operator products,” Lett. Nuovo Cim
1972
Earlier work this paper cites.
S. Ferrara, R. Gatto, and A. F. Grillo, “Properties of Partial Wave Amplitudes in Conformal Invariant Field Theories,” Nuovo Cim
1975
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys
1998
Earlier work this paper cites.
L. Susskind, “Holography in the flat space limit,” hep-th/9901079 . [AIP Conf. Proc.493,98(1999)]
1999
Earlier work this paper cites.
S. B. Giddings, “Flat space scattering and bulk locality in the AdS / CFT correspondence,” Phys. Rev
2000
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys
2001
Earlier work this paper cites.
J. de Boer and S. N. Solodukhin, “A Holographic reduction of Minkowski space-time,” Nucl. Phys
2003
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal partial waves and the operator product expansion,” Nucl. Phys
2004
Earlier work this paper cites.
R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl. Phys
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys. Rev. Lett
2005
Earlier work this paper cites.
M. Gary, S. B. Giddings, and J. Penedones, “Local bulk S-matrix elements and CFT singularities,” Phys. Rev
Original
2009
Earlier work this paper cites.
I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully, “Holography from Conformal Field Theory,” JHEP
Original
2009
Earlier work this paper cites.
G. Barnich and C. Troessaert, “Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited,” Phys. Rev. Lett
Original
2010
Earlier work this paper cites.

Similar

G. Barnich and C. Troessaert, “Aspects of the BMS/CFT correspondence,” JHEP
Original
2010
Cited alongside, same era.
L. Cornalba, M. S. Costa, and J. Penedones, “Deep Inelastic Scattering in Conformal QCD,” JHEP
Original
2010
Cited alongside, same era.
S. Weinberg, “Six-dimensional Methods for Four-dimensional Conformal Field Theories,” Phys. Rev
Original
2010
Cited alongside, same era.
G. Barnich and C. Troessaert, “Supertranslations call for superrotations,” PoS
Original
2011
Cited alongside, same era.
J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP
Original

Then

M. S. Costa, V. Gonçalves, and J. Penedones, “Spinning AdS Propagators,” JHEP
Original
2014
Later among the works it cites.
A. E. Lipstein, “Soft Theorems from Conformal Field Theory,” JHEP
Original
2015
Later among the works it cites.
M. Campiglia, “Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime,” JHEP
Original
2015
Later among the works it cites.
T. He, P. Mitra, and A. Strominger, “2D Kac-Moody Symmetry of 4D Yang-Mills Theory,” JHEP
Original
2016
Later among the works it cites.
J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2011

Cited alongside, same era.

T. Okuda and J. Penedones, “String scattering in flat space and a scaling limit of Yang-Mills correlators,” Phys. Rev

2011

Cited alongside, same era.

A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, and B. C. van Rees, “A Natural Language for AdS/CFT Correlators,” JHEP

2011

Cited alongside, same era.

M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinning Conformal Correlators,” JHEP

2011

Cited alongside, same era.

M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinning Conformal Blocks,” JHEP

2011

Cited alongside, same era.

M. S. Costa, V. Goncalves, and J. Penedones, “Conformal Regge theory,” JHEP

2012

Cited alongside, same era.

A. L. Fitzpatrick and J. Kaplan, “Analyticity and the Holographic S-Matrix,” JHEP

2012

Cited alongside, same era.

A. L. Fitzpatrick and J. Kaplan, “Unitarity and the Holographic S-Matrix,” JHEP

2012

Cited alongside, same era.

2016

Later among the works it cites.

E. Hijano, P. Kraus, E. Perlmutter, and R. Snively, “Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks,” JHEP

2016

Later among the works it cites.

T. Hartman, S. Jain, and S. Kundu, “Causality Constraints in Conformal Field Theory,” JHEP

2016

Later among the works it cites.

C. Cheung, A. de la Fuente, and R. Sundrum, “4D scattering amplitudes and asymptotic symmetries from 2D CFT,” JHEP

2017

Closest in time.

S. Pasterski, S.-H. Shao, and A. Strominger, “Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere,” Phys. Rev

2017

Closest in time.

S. Pasterski and S.-H. Shao, “A Conformal Basis for Flat Space Amplitudes,” Phys. Rev

2017

Closest in time.

S. Caron-Huot, “Analyticity in Spin in Conformal Theories,” JHEP

2017

Closest in time.

S. Pasterski, S.-H. Shao, and A. Strominger, “Gluon Amplitudes as 2d Conformal Correlators,” Phys. Rev

2017

Closest in time.

C. Cardona and Y.-t. Huang, “S-matrix singularities and CFT correlation functions,” JHEP

2017

Closest in time.

J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, “Looking for a bulk point,” JHEP

2017

Closest in time.