Boundary and interface CFTs from the conformal bootstrap

By F. Gliozzi, P. Liendo, M. Meineri, Antonio Rago. Journal of High Energy Physics, 2015

199 citations recorded by the source corpus.

We explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N ) models through numerical solutions to the crossing equations with the method of determinants. In the extraordinary transition, where the low-lying spectrum of the surface operators is known, we use the bootstrap equations to obtain information on the bulk spectrum of the theory. In the ordinary transition the knowledge of the low-lying bulk spectrum allows to calculate the scale dimension of the relevant surface operator, which compares well with known results of two-loop calculations in 3d. Estimates of various OPE coefficients are also obtained. We also analyze in 4-ϵ dimensions the renormalization group interface between the O(N ) model and the free theory and check numerically the results in 3d.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0b94ba0ad588f539b38d04d56a60f7774178e695

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

Defects in conformal field theory (2016, background): “Moreover, in the specific case of a codimension two defect, and for equal external operators, we map the bulk Casimir (4)Interfaces make a small exception, for they require the set of data to be slightly enlarged [8].”
Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, background): “[103] Ferdinando Gliozzi, Pedro Liendo, Marco Meineri, and Antonio Rago, “Boundary and interface CFTs from the conformal bootstrap,” Journal of High Energy Physics 2015 (2015), 10.”
A general proof of the quantum null energy condition (2017, methodology): “dOPE coecients i 6In a more familiar setting, if the later channel had been allowed, the equality between these two expansions would be akin to a bootstrap constraint on the defect CFT spectrum. See [63,64,67] for recent work on this bootstrap problem. { 19 { for this full replacement O BO A ! P i i”
Bootstrapping the O(N) archipelago (2015, unknown): “In recent years great progress has been made in the conformal bootstrap in d > 2, including rigorous bounds on operator dimensions and operator product expansion (OPE) coefficients [3–32], analytical constraints [33–45], and methods for approximate direct solutions to the bootstrap [46–49], includin”
Conformal invariance in the long-range Ising model (2015, methodology): “An alternative technique has been developed in [20–22].”
A scaling theory for the long-range to short-range crossover and an infrared duality (2017, background): “e trick [6], reviewed in section4.3. It follows from the bulk equations of motion together with the assumptions of conformal invariance and bulk-to-defect OPE. See the discussion around Eq. (4.34) in [42]. We are grateful to Pedro Liendo and Marco Meineri for emphasizing this connection to us. 35 ! ”
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 conformal field theory and a boundary central charge (2017, background): “What then happens for interacting theories? A canonical example of an interacting bCFT is the Wilson-Fisher fixed point, analyzed in either the [2, 15] or large N [3] expansion or more recently using boot strap ideas [14, 16].”