Critical Ising model in varying dimension by conformal bootstrap

Abstract

The single-correlator conformal bootstrap is solved numerically for several values of dimension 4 > d > 2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained over the entire range of dimensions with up to four-decimal precision and then compared with several existing results. The conformal dimensions of leading-twist fields are also determined up to high spin, and their d-dependence shows how the conformal states rearrange themselves around d = 2.2 for matching the Virasoro conformal blocks in the d = 2 limit. The decoupling of states at the Ising point is studied for 3 > d > 2 and the vanishing of one structure constant at d = 3 is found to persist till d = 2 where it corresponds to a Virasoro null-vector condition. arXiv:1811.07751v2 [hep-th]

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

“…operators in N = 1 [14]. Furthermore, in [51] the operator spectrum was numerically traced along the N = 1 line from d = 3 towards d = 2, where it was shown how the spectrum reorganizes into appropriate Virasoro primaries as one approaches the 2d Ising model. In table 2 we compare our large N result for the central charge C J with some numeric values in the unitary theories in three dimensions at finite N and can see that the inclusion of the new N −2 term significantly improves the truncated expansion results when comparing with the numeric results in the literature.…”

Carving out OPE space and precise O(2) model critical exponents

“…See for instance[43][44][45][46][47][48][49][50][51] or for supersymmetric studies. Other analysis can also be found in[75][76][77][78][79][80][81].…”

Bootstrapping boundary-localized interactions

“…with our best estimate for the allowed region shaded in blue. The curves have n max = 5, 6, 7, 8 in the notation of [49,50]. As for the number of derivative components being kept in each crossing equation, these correspond to 21, 28, 36, 45 respectively.…”