Built on

N. Afkhami-Jeddi, T. Hartman, and A. Tajdini, Fast Conformal Bootstrap and Constraints on 3d Gravity
Original
1903
Earlier work this paper cites.
W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB
Original
1909
Earlier work this paper cites.
K. Levenberg, A method for the solution of certain non-linear problems in least squares
1944
Earlier work this paper cites.
D. W. Marquardt, An Algorithm for Least-Squares Estimation of Nonlinear Parameters
1963
Earlier work this paper cites.
A. B. Zamolodchikov, Two-dimensional conformal symmetry and critical four-spin correlation functions in the Ashkin-Teller model
1986
Earlier work this paper cites.
L. J. Dixon, D. Friedan, E. J. Martinec, and S. H. Shenker, The Conformal Field Theory of Orbifolds
1987
Earlier work this paper cites.
hep-th/9108028
P. H. Ginsparg, APPLIED CONFORMAL FIELD THEORY · 1988
Earlier work this paper cites.
Graduate texts in contemporary physics. Springer, New York, NY, 1997
P. Di Francesco, Mathieu, Pierre, and Sénéchal, David, Conformal field theory · 1997
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion
2004
Earlier work this paper cites.
Cambridge University Press, 3rd ed ed., 2007
B. P. Flannery, Saul A. Teukolsky, William H. Press, and William T. Vetterling, Numerical recipes: the art of scientific computing · 2007
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, Bounding scalar operator dimensions in 4D CFT
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions
Original
2009
Earlier work this paper cites.

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2022

A Monte Carlo approach to the conformal bootstrap

Laio, Alessandro, Valenzuela, Uriel Luviano, Serone, Marco

Understand

We introduce an approach to find approximate numerical solutions of truncated bootstrap equations for Conformal Field Theories (CFTs) in arbitrary dimensions.

The method is based on a stochastic search via a Metropolis algorithm guided by an action $S$ which is the logarithm of the truncated bootstrap equations for a single scalar field correlator.
While numerical conformal bootstrap methods based on semi-definite programming put rigorous exclusion bounds on CFTs, this method looks for approximate solutions, which correspond to local minima of $S$, when present, and can be even far from the extremality region.
By this protocol we find that if no constraint on the operator scaling dimensions is imposed, $S$ has a single minimum, corresponding to the Free Theory.

Built on

N. Afkhami-Jeddi, T. Hartman, and A. Tajdini, Fast Conformal Bootstrap and Constraints on 3d Gravity
Original
1903
Earlier work this paper cites.
W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB
Original
1909
Earlier work this paper cites.
K. Levenberg, A method for the solution of certain non-linear problems in least squares
1944
Earlier work this paper cites.
D. W. Marquardt, An Algorithm for Least-Squares Estimation of Nonlinear Parameters
1963
Earlier work this paper cites.
A. B. Zamolodchikov, Two-dimensional conformal symmetry and critical four-spin correlation functions in the Ashkin-Teller model
1986
Earlier work this paper cites.
L. J. Dixon, D. Friedan, E. J. Martinec, and S. H. Shenker, The Conformal Field Theory of Orbifolds
1987
Earlier work this paper cites.
hep-th/9108028
P. H. Ginsparg, APPLIED CONFORMAL FIELD THEORY · 1988
Earlier work this paper cites.
Graduate texts in contemporary physics. Springer, New York, NY, 1997
P. Di Francesco, Mathieu, Pierre, and Sénéchal, David, Conformal field theory · 1997
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion
2004
Earlier work this paper cites.
Cambridge University Press, 3rd ed ed., 2007
B. P. Flannery, Saul A. Teukolsky, William H. Press, and William T. Vetterling, Numerical recipes: the art of scientific computing · 2007
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, Bounding scalar operator dimensions in 4D CFT
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions
Original
2009
Earlier work this paper cites.