Built on

D. Ponomarev, E. Sezgin and E. Skvortsov, On one loop corrections in higher spin gravity , 1904.01042
Original
1904
Earlier work this paper cites.
L. F. Alday and E. Perlmutter, Growing Extra Dimensions in AdS/CFT , 1906.01477
Original
1906
Earlier work this paper cites.
L. F. Alday, J. Henriksson and M. van Loon, An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1 / N 2 1/N^{2} , 1907.02445
Original
1907
Earlier work this paper cites.
R. E. Cutkosky, Singularities and discontinuities of Feynman amplitudes , J. Math. Phys. 1
1960
Earlier work this paper cites.
R. J. Eden, P. V. Landshoff, O. D. I. and J. C. Polkinghorne, The Analytic S-Matrix . Cambridge University Press, 1966
1966
Earlier work this paper cites.
K. Symanzik, On Calculations in conformal invariant field theories , Lett. Nuovo Cim. 3
1972
Earlier work this paper cites.
C. Fronsdal, Elementary particles in a curved space. ii , Phys. Rev. D10
1974
Earlier work this paper cites.
G. Mack, Group Theoretical Approach to Conformal Invariant Quantum Field Theory , NATO Sci. Ser. B 5
1974
Earlier work this paper cites.
G. Mack, Osterwalder-Schrader Positivity in Conformal Invariant Quantum Field Theory , Lect. Notes Phys. 37
1975
Earlier work this paper cites.
V. K. Dobrev, G. Mack, I. T. Todorov, V. B. Petkova and S. G. Petrova, On the Clebsch-Gordan Expansion for the Lorentz Group in n Dimensions , Rept. Math. Phys. 9
1976
Earlier work this paper cites.
V. K. Dobrev, V. B. Petkova, S. G. Petrova and I. T. Todorov, Dynamical Derivation of Vacuum Operator Product Expansion in Euclidean Conformal Quantum Field Theory , Phys. Rev. D13
1976
Earlier work this paper cites.
V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov, Harmonic Analysis on the n-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory , Lect. Notes Phys. 63
1977
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory , Phys. Lett. B428
1998
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
V. K. Dobrev, Intertwining operator realization of the AdS / CFT correspondence , Nucl. Phys. B553
1999
Earlier work this paper cites.
D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d) / AdS(d+1) correspondence , Nucl. Phys. B546
1999
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B599
2001
Earlier work this paper cites.
T. Leonhardt, R. Manvelyan and W. Ruhl, The Group approach to AdS space propagators , Nucl. Phys. B667
2003
Earlier work this paper cites.
T. Leonhardt, W. Ruhl and R. Manvelyan, The Group approach to AdS space propagators: A Fast algorithm , J. Phys. A37
2004
Earlier work this paper cites.

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2019

From bulk loops to boundary large-N expansion

Ponomarev, Dmitry

Understand

We study the analytic structure of loop Witten diagrams in Euclidean AdS represented by their conformal partial wave expansions.

We show that, as in flat space, amplitude's singularities are associated with non-trivial cuts of the diagram and factorize into products of the coefficient functions for the subdiagrams resulting from these cuts.
We consider an example of a one-loop four-point diagram in detail and then briefly discuss how the procedure can be extended to more general diagrams.
Finally, we show that this analysis reproduces simple relations that follow from the large-N considerations on the boundary.

Built on

D. Ponomarev, E. Sezgin and E. Skvortsov, On one loop corrections in higher spin gravity , 1904.01042
Original
1904
Earlier work this paper cites.
L. F. Alday and E. Perlmutter, Growing Extra Dimensions in AdS/CFT , 1906.01477
Original
1906
Earlier work this paper cites.
L. F. Alday, J. Henriksson and M. van Loon, An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1 / N 2 1/N^{2} , 1907.02445
Original
1907
Earlier work this paper cites.
R. E. Cutkosky, Singularities and discontinuities of Feynman amplitudes , J. Math. Phys. 1
1960
Earlier work this paper cites.
R. J. Eden, P. V. Landshoff, O. D. I. and J. C. Polkinghorne, The Analytic S-Matrix . Cambridge University Press, 1966
1966
Earlier work this paper cites.
K. Symanzik, On Calculations in conformal invariant field theories , Lett. Nuovo Cim. 3
1972
Earlier work this paper cites.
C. Fronsdal, Elementary particles in a curved space. ii , Phys. Rev. D10
1974
Earlier work this paper cites.
G. Mack, Group Theoretical Approach to Conformal Invariant Quantum Field Theory , NATO Sci. Ser. B 5
1974
Earlier work this paper cites.
G. Mack, Osterwalder-Schrader Positivity in Conformal Invariant Quantum Field Theory , Lect. Notes Phys. 37
1975
Earlier work this paper cites.
V. K. Dobrev, G. Mack, I. T. Todorov, V. B. Petkova and S. G. Petrova, On the Clebsch-Gordan Expansion for the Lorentz Group in n Dimensions , Rept. Math. Phys. 9
1976
Earlier work this paper cites.
V. K. Dobrev, V. B. Petkova, S. G. Petrova and I. T. Todorov, Dynamical Derivation of Vacuum Operator Product Expansion in Euclidean Conformal Quantum Field Theory , Phys. Rev. D13
1976
Earlier work this paper cites.
V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov, Harmonic Analysis on the n-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory , Lect. Notes Phys. 63
1977
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory , Phys. Lett. B428
1998
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
V. K. Dobrev, Intertwining operator realization of the AdS / CFT correspondence , Nucl. Phys. B553
1999
Earlier work this paper cites.
D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d) / AdS(d+1) correspondence , Nucl. Phys. B546
1999
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B599
2001
Earlier work this paper cites.
T. Leonhardt, R. Manvelyan and W. Ruhl, The Group approach to AdS space propagators , Nucl. Phys. B667
2003
Earlier work this paper cites.
T. Leonhardt, W. Ruhl and R. Manvelyan, The Group approach to AdS space propagators: A Fast algorithm , J. Phys. A37
2004
Earlier work this paper cites.