nLab
conformal bootstrap

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

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.

References

General

See also

Superconformal bootstrap

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:

In AdS/CFT

Discussion of superconformal bootstrap in view of AdS/CFT, hence as a precise and detailed construction of large-N and asymptotically AdS string theory/M-theory:

extra dimensions:

string scattering amplitudes ;

The D=6 N=(2,0) SCFT on the M5-brane:

  • Shai M. Chester, Eric Perlmutter, M-Theory Reconstruction from (2,0)(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:

  • Nathan B. Agmon, Shai M. Chester, Silviu S. Pufu, The M-theory Archipelago (arXiv:1907.13222)

Last revised on November 8, 2019 at 03:08:13. See the history of this page for a list of all contributions to it.