Built on

J. L. Cardy, “Conformal Invariance and Surface Critical Behavior,” Nucl.Phys
1984
Earlier work this paper cites.
A. B. Zamolodchikov, “CONFORMAL SYMMETRY IN TWO-DIMENSIONS: AN EXPLICIT RECURRENCE FORMULA FOR THE CONFORMAL PARTIAL WAVE AMPLITUDE,” Commun. Math. Phys
1984
Earlier work this paper cites.
D. M. McAvity and H. Osborn, “Conformal field theories near a boundary in general dimensions,” Nucl. Phys
1995
Earlier work this paper cites.
D. E. Berenstein, R. Corrado, W. Fischler, and J. M. Maldacena, “The Operator product expansion for Wilson loops and surfaces in the large N limit,” Phys. Rev
1999
Earlier work this paper cites.
A. M. Polyakov and V. S. Rychkov, “Gauge field strings duality and the loop equation,” Nucl. Phys
2000
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P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech
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R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
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M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinning Conformal Correlators,” JHEP
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D. Pappadopulo, S. Rychkov, J. Espin, and R. Rattazzi, “OPE Convergence in Conformal Field Theory,” Phys. Rev
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M. Billò, M. Caselle, D. Gaiotto, F. Gliozzi, M. Meineri, and R. Pellegrini, “Line defects in the 3d Ising model,” JHEP
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2013
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P. Liendo, L. Rastelli, and B. C. van Rees, “The Bootstrap Program for Boundary CFT d
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M. Hogervorst and S. Rychkov, “Radial Coordinates for Conformal Blocks,” Phys. Rev
Original
2013
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2017

Radial coordinates for defect CFTs

Lauria, Edoardo, Meineri, Marco, Trevisani, Emilio

Understand

We study the two-point function of local operators in the presence of a defect in a generic conformal field theory.

We define two pairs of cross ratios, which are convenient in the analysis of the OPE in the bulk and defect channel respectively.
The new coordinates have a simple geometric interpretation, which can be exploited to efficiently compute conformal blocks in a power expansion.
We illustrate this fact in the case of scalar external operators.

Built on

J. L. Cardy, “Conformal Invariance and Surface Critical Behavior,” Nucl.Phys
1984
Earlier work this paper cites.
A. B. Zamolodchikov, “CONFORMAL SYMMETRY IN TWO-DIMENSIONS: AN EXPLICIT RECURRENCE FORMULA FOR THE CONFORMAL PARTIAL WAVE AMPLITUDE,” Commun. Math. Phys
1984
Earlier work this paper cites.
D. M. McAvity and H. Osborn, “Conformal field theories near a boundary in general dimensions,” Nucl. Phys
1995
Earlier work this paper cites.
D. E. Berenstein, R. Corrado, W. Fischler, and J. M. Maldacena, “The Operator product expansion for Wilson loops and surfaces in the large N limit,” Phys. Rev
1999
Earlier work this paper cites.
A. M. Polyakov and V. S. Rychkov, “Gauge field strings duality and the loop equation,” Nucl. Phys
2000
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech
2004
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinning Conformal Correlators,” JHEP
Original
2011
Earlier work this paper cites.
D. Pappadopulo, S. Rychkov, J. Espin, and R. Rattazzi, “OPE Convergence in Conformal Field Theory,” Phys. Rev
Original
2012
Earlier work this paper cites.
M. Billò, M. Caselle, D. Gaiotto, F. Gliozzi, M. Meineri, and R. Pellegrini, “Line defects in the 3d Ising model,” JHEP
Original
2013
Earlier work this paper cites.
P. Liendo, L. Rastelli, and B. C. van Rees, “The Bootstrap Program for Boundary CFT d
Original
2013
Earlier work this paper cites.
M. Hogervorst and S. Rychkov, “Radial Coordinates for Conformal Blocks,” Phys. Rev
Original
2013
Earlier work this paper cites.