The bootstrap program for boundary CFTd

By P. Liendo, L. Rastelli, B. C. Rees. 2012

327 citations recorded by the source corpus.

A bstractWe study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible for free-field theory and at one loop in the epsilon expansion, but more generally one has to resort to numerical methods. Using the recently developed linear programming techniques we find several interesting bounds for operator dimensions and OPE coefficients and comment on their physical relevance. We also show that the “boundary bootstrap” can be easily applied to correlation functions of tensorial operators and study the stress tensor as an example. In the appendices we present conformal block decompositions of a variety of physically interesting correlation functions.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/337b9fe5379ababe68f397e73fe9015f8ada0c0a

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Citations in the corpus

From correlation functions to event shapes (2013, background): “9) is remarkably similar to the well-known expression for the two-point correlation function in a boundary CFT [29].”
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”
Defects in conformal field theory (2016, methodology): “onformal transformations on the defect and rotations around it. In the special case of a codimension one defect, i.e. a CFT with a boundary or an interface, the embedding formalism has been set up in [43]. Defect operators carry both SO(q) and SO(p) quantum numbers. We call them transverse and paral”
Carving out OPE space and precise O(2) model critical exponents (2019, result): “Other analysis can also be found in [75–81].”
Critical exponents of the 3d Ising and related models from conformal bootstrap (2014, background): “In recent years it has been shown that the conformal bootstrap approach can give accurate predictions for specific CFTs in any space-time dimension [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23].”
Boundary conformal field theory and a boundary central charge (2017, methodology): “ ; (3.77) (1) bry (v) = 1 2(d+ 1) (v 1 v)d(v 2 v2) ; (3.78) where now ˘d (1) bry ! 1 in the boundary limit while the other two vanish. For spin 9The results in the basis of A (v);B ;C ) are given in [14]. { 24 { two exchange with weight = d, we have 1(2) bry (d;v) = (v v)d(v 1 v)2 ; (3.79) 1(2) bry ”
Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, background): “[100] Pedro Liendo, Leonardo Rastelli, and Balt C.”
The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, methodology): “sing unitarity could also help in studies of boundary and defect crossing equations, which in some cases haven’t been formulated in a way that takes advantage of positivity (even in unitary theories) [91, 13,93]. 43We thank Douglas Stanford for this suggestion. 62 operators in the lowest twist-famil”
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, background): “This has been checked to a high level in [43], and we checked it to even higher levels.”
Conformal invariance in the long-range Ising model (2015, background): “25) (44)For a similar concept of bulk-to-boundary OPE in boundary CFTs, see for example [69, 70].”