Central charge bounds in 4D conformal field theory

By R. Rattazzi, S. Rychkov, A. Vichi. 2010

191 citations recorded by the source corpus.

We derive model-independent lower bounds on the stress tensor central charge C-T in terms of the operator content of a 4-dimensional conformal field theory. More precisely, C-T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the conformal field theory. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a6ed89c69470f75caa0fbac7c32ebf5f9f37ebc0

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Citations in the corpus

Bootstrapping the O(N ) vector models (2013, background): “Our primary goal, following previous numerical studies of the bootstrap [3–15], will be to place general upper bounds on the scaling dimensions of the first nontrivial scalar operators (both O(N) singlets S and O(N) symmetric tensors Tij) in the φi × φj operator product expansion (OPE).”
Carving out OPE space and precise O(2) model critical exponents (2019, result): “Other analysis can also be found in [75–81].”
A scaling theory for the long-range to short-range crossover and an infrared duality (2017, background): “The 2pt function normalization customary for d dimensional CFT is [33] (see also [34])”
Emergent spacetime and holographic CFTs (2011, methodology): “See [68], [69], [70], [71], [72], [73] for recent work were the unitarity of the CFT in d > 2 was used to derive certain constraints for the data ∆i, Cijk, in special cases.”
Four-dimensional SCFTs from M5-branes (2012, background): “20) obey the bound on c studied in [34, 35].”
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].”
The bootstrap program for boundary CFTd (2012, methodology): “This approach has been refined and extended in a series of papers [5, 6, 7, 8, 9, 10, 11, 12, 13].”
Bootstrapping mixed correlators in the 3D Ising model (2014, background): “The conformal bootstrap [1, 2] in D > 2 dimensions has produced remarkable results, including numerical bounds on operator dimensions and OPE coefficients [3–29], analytical constraints [30–36], and recently a precise conjecture for the Z2-even spectrum of the 3D Ising model [23].”
Universality of long-distance AdS physics from the CFT bootstrap (2014, methodology): “The bootstrap was originally developed in the case of CFT2 [1, 2], and has recently seen extensive analytic [7, 9, 14, 40–43] and numerical [3, 7, 44–61] application in CFT≥3.”
Bootstrapping the 3d Ising twist defect (2013, methodology): “More recently, interesting constraints on the Ising model [2] and other CFTs have been derived using the methods of the conformal bootstrap [3–21].”
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”
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, methodology): “8 This would imply a small but noticeable discrepancy (7)The prefactor is different from [20] due to the different conformal block normalization, see Eq.”
The Swampland: Introduction and Review (2019, unknown): “For early work on the Weak Gravity Conjecture and AdS/CFT see [65,66].”