Carving out the space of 4D CFTs

By David Poland, David Simmons-Duffin, A. Vichi. 2011

334 citations recorded by the source corpus.

A bstractWe introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and $$ \mathcal{N} = 1 $$ superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In $$ \mathcal{N} = 1 $$ superconformal theories, we place strong bounds on dim(Φ†Φ), where Φ is a chiral operator. These bounds asymptote to the line dim(Φ†Φ) ≤ 2 dim(Φ) near dim(Φ) ≃ 1, forbidding positive anomalous dimensions in this region. We also place novel upper and lower bounds on OPE coefficients of protected operators in the Φ × Φ OPE. Finally, we find examples of lower bounds on central charges and flavor current two-point functions that scale with the size of global symmetry representations. In the case of $$ \mathcal{N} = 1 $$ theories with an SU(N) flavor symmetry, our bounds on current two-point functions lie within an O(1) factor of the values realized in supersymmetric QCD in the conformal window.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/44bfc73f2fe3655bffd0a518bb673a14ca0a7846

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Citations in the corpus

Walking, weak first-order transitions, and complex CFTs (2018, methodology): “ed to make conformal technicolor scenario phenomenologically viable can be constrained from rst principles using the conformal bootstrap techniques. The resulting constraints were fully worked out in [47], with rather pessimistic conclusions: the generic scenario was found inconsistent.22 There is h”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, methodology): “Note that a lower bound can only be found this way for OPE coefficients of protected multiplets, as shown in [20].”
Four-dimensional SCFTs from M5-branes (2012, background): “20) obey the bound on c studied in [34, 35].”
Bootstrapping SCFTs with four supercharges (2015, positive): “Some of the first papers on the modern incarnation of the bootstrap program studied N = 1 SCFTs in d = 4 [13, 26, 27].”
The (2, 0) superconformal bootstrap (2015, methodology): “To find functionals we use linear and semidefinite programming techniques, which were pioneered in [36] and [71], respectively.”
Analyticity and the holographic S-matrix (2011, methodology): “In any case, our work suggests that there is an intimate connection between the Bootstrap Program for large N CFTs [27, 21, 20, 22, 23, 24, 25, 26, 50] and the S-Matrix Program, and that solving general CFTs via the Bootstrap will be at least as difficult as finding consistent S-Matrices using the c”
The N=2$$ \mathcal{N}=2 $$ superconformal bootstrap (2014, methodology): “The semidefinite programming approach to the numerical bootstrap depends on our ability to approximate conformal blocks of fixed spin ` and varying conformal dimension ∆ by polynomials in ∆ [39, 44].”
The analytic bootstrap and AdS superhorizon locality (2012, methodology): “We can proceed to consider the OPE coefficients of the twist 2∆φ tower, which were bounded as a function of ∆φ in [7].”
Unitarity and the holographic S-Matrix (2011, methodology): “This means that one can obtain robust results about quantum gravity by modeling the correlators of low-dimension operators using bulk effective field theory, and then using the bootstrap approach [17, 19, 35, 36, 25, 20, 37, 38, 39, 26] to constrain correlators that involve operators of larger dimen”
A semidefinite program solver for the conformal bootstrap (2015, methodology): “Bootstrap optimization problems can be naturally approximated as PMPs [17, 9].”
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, background): “5 (the original bound is due to Rattazzi, Rychkov, Tonni, Vichi [30]; the shown plot is from a paper by Poland, Simmons-Duffin and Vichi [31])”
The bootstrap program for boundary CFTd (2012, background): “This approach has been refined and extended in a series of papers [5, 6, 7, 8, 9, 10, 11, 12, 13].”
Carving out OPE space and precise O(2) model critical exponents (2019, methodology): “In practice, this means we would like to study large systems of correlation functions involving multiple scalars [10–15], fermions [16–18], currents [19, 20], stress tensors [21], various global symmetry representations [22–42], etc.”
Bootstrapping 3D fermions (2015, background): “The bound has similar features to analogous bounds on CT coming from scalar 4-point functions in four dimensional CFTs [55–57].”