More constraining conformal bootstrap

By F. Gliozzi. 2013

157 citations recorded by the source corpus.

Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories (CFT) in diverse space-time dimensions. It appears that the calculations can be done only for theories lying at the boundary of the allowed parameter space. Here it is pointed out that a similar method can be applied to a larger class of CFT’s, whether unitary or not, and no free parameter remains, provided we know the fusion algebra of the low lying primary operators. As an example we calculate using first principles, with no phenomenological input, the lowest scaling dimensions of the local operators associated with the Yang-Lee edge singularity in three and four space dimensions. The edge exponents compare favorably with the latest numerical estimates. A consistency check of this approach on the 3d critical Ising model is also made.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a9404a71a3ba6c8111614ea313a06d217a400e60

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

Critical exponents of the 3d Ising and related models from conformal bootstrap (2014, methodology): “Most of them correspond to non-unitary CFTs.”
Defects in conformal field theory (2016, methodology): “Besides specific examples, one more motivation for our work is provided by the recent progress in exploring the space of CFTs using the conformal bootstrap [36, 37, 38, 39, 40, 41, 42].”
TASI Lectures on the Conformal Bootstrap (2016, background): “• Can the requirement of unitarity be relaxed? Gliozzi’s method of determinants [95] has shown success analyzing the crossing equation in nonunitary theories and other situations where positivity is not obviously present [96–98].”
The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, methodology): “On the other hand, the possibility of working with fewer derivatives, at lower precision, with larger systems of correlators, and perhaps without imposing unitarity (using the methods of [15, 90, 91])(42) makes this hybrid approach worth exploring.”
Boundary and interface CFTs from the conformal bootstrap (2015, methodology): “Here we shall employ a different technique, introduced in [17], which we review in section 2.”