Built on

K. G. Wilson, Nonlagrangian models of current algebra
1969
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory
1974
Earlier work this paper cites.
R. Hettich and K. O. Kortanek, Semi-infinite programming: theory, methods, and applications
1993
Earlier work this paper cites.
Springer Science & Business Media, 1998
R. Reemtsen and J.-J. Rückmann, Semi-infinite programming · 1998
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal four point functions and the operator product expansion
2001
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal partial waves and the operator product expansion
2004
Earlier work this paper cites.
M. López and G. Still, Semi-infinite programming
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.

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Then

S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin, and A. Vichi, Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
Original
2014
Later among the works it cites.
F. Kos, D. Poland, and D. Simmons-Duffin, Bootstrapping Mixed Correlators in the 3D Ising Model
Original
2014
Later among the works it cites.
D. Gaiotto, D. Mazac, and M. F. Paulos, Bootstrapping the 3d Ising twist defect
Original
2014
Later among the works it cites.
F. Gliozzi and A. Rago, Critical exponents of the 3d Ising and related models from Conformal Bootstrap
Original
2014
Later among the works it cites.
F. Gliozzi, P. Liendo, M. Meineri, and A. Rago, Boundary and Interface CFTs from the Conformal Bootstrap

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2016

Extremal bootstrapping: go with the flow

El-Showk, Sheer, Paulos, Miguel F.

Understand

The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs.

We show that such solutions are characterized by extremality conditions, which may be used to flow continuously along the boundaries of parameter space.
Along the flow there is generically no further need for optimization, which dramatically reduces computational requirements, bringing calculations from the realm of computing clusters to laptops.
Conceptually, extremality sheds light on possible ways to bootstrap without positivity, extending the method to non-unitary theories, and implies that theories saturating bounds, and especially those sitting at kinks, have unusually sparse spectra.

Built on

K. G. Wilson, Nonlagrangian models of current algebra
1969
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory
1974
Earlier work this paper cites.
R. Hettich and K. O. Kortanek, Semi-infinite programming: theory, methods, and applications
1993
Earlier work this paper cites.
Springer Science & Business Media, 1998
R. Reemtsen and J.-J. Rückmann, Semi-infinite programming · 1998
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal four point functions and the operator product expansion
2001
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal partial waves and the operator product expansion
2004
Earlier work this paper cites.
M. López and G. Still, Semi-infinite programming
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.