algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
The conformal bootstrap program (Belavin-Polyakov-Zamolofchikov 84) is an attempt to construct and classify conformal field theories non-perturbatively by axiomatizing the properties of their operator product expansion/correlation functions.
The conformal bootstrap was proposed in the 1970s as a strategy for calculating the properties of second-order phase transitions. After spectacular success elucidating two-dimensional systems, little progress was made on systems in higher dimensions until a recent renaissance beginning in 2008 (Poland-Simmons-Duffin 16).
The generalization of the conformal bootstrap to superconformal field theories has the potential to provide, via AdS/CFT, a precise and detailed construction of large-N and asymptotically AdS string/M-theory.
Alexander Belavin, Alexander Polyakov, Alexander Zamolodchikov, (1984). Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B. 241 (2): 333–380 (1984)
David Poland, David Simmons-Duffin, The conformal bootstrap, Nature Physics 535–539 (2016) doi:10.1038/nphys3761
David Simmons-Duffin, TASI Lectures on the Conformal Bootstrap (arXiv:1602.07982)
David Poland, Slava Rychkov, Alessandro Vichi, The Conformal Bootstrap: Numerical Techniques and Applications (arXiv:1805.04405)
Shai M. Chester, Weizmann Lectures on the Numerical Conformal Bootstrap (arXiv:1907.05147)
See also
For superconformal field theory, such as D=4 N=1 SYM, D=4 N=2 SYM, D=4 N=4 SYM, D=6 N=(1,0) SCFT, D=6 N=(2,0) SCFT:
Christopher Beem, Madalena Lemos, Pedro Liendo, Leonardo Rastelli, Balt C. van Rees, The $N=2$ superconformal bootstrap (arXiv:1412.7541)
Christopher Beem, Madalena Lemos, Leonardo Rastelli, Balt C. van Rees, The $(2,0)$ superconformal bootstrap (arXiv:1507.05637)
Christopher Beem, Leonardo Rastelli, Balt C. van Rees, More $N=4$ superconformal bootstrap (arXiv:1612.02363)
Discussion of superconformal bootstrap in view of AdS/CFT, hence as a precise and detailed construction of large-N but also small N and asymptotically AdS string theory/M-theory:
string scattering amplitudes :
Discussion of small N effects in M-theory AdS4/CFT3? using the conformal bootstrap:
The D=6 N=(2,0) SCFT on the M5-brane:
Shai M. Chester, Eric Perlmutter, M-Theory Reconstruction from $(2,0)$ CFT and the Chiral Algebra Conjecture, J. High Energ. Phys. (2018) 2018: 116 (arXiv:1805.00892)
from p. 2:
On the other hand, given our utter lack of a complete description of M-theory, the bulk is not terribly useful for determining finite aspects of the dual CFT. However, we can turn this problem around using the modern perspective of the conformal bootstrap, which gives an a priori independent formulation of the (local sector of the) CFT. This provides an independent tool for constructing M-theory at the non-perturbative level, a philosophy that we will substantiate in this work.
The D=3 SCFT (BLG-model, ABJM model) on the M2-brane:
Last revised on January 24, 2020 at 07:47:54. See the history of this page for a list of all contributions to it.