Universal constraints on conformal operator dimensions

By V. Rychkov, A. Vichi. 2009

245 citations recorded by the source corpus.

We continue the study of model-independent constraints on the unitary conformal field theories (CFTs) in four dimensions, initiated in [R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, J. High Energy Phys. 12 (2008) 031]. Our main result is an improved upper bound on the dimension Delta of the leading scalar operator appearing in the operator product expansion (OPE) of two identical scalars of dimension d: phi(d)x phi(d)=1+O-Delta+.... In the interval 1 < d < 1.7 this universal bound takes the form Delta < 2+0.7(d-1)(1/2)+2.1(d-1)+0.43(d-1)(3/2). The proof is based on prime principles of CFT: unitarity, crossing symmetry, OPE, and conformal block decomposition. We also discuss possible applications to particle phenomenology and, via a 2D analogue, to string theory.

Subfields: Applied Mathematics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/963a62f5282370672fe33b2a8cfdd3110aaa3c60

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Citations in the corpus

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”
Spinning conformal correlators (2011, methodology): “The efficiency of this method has been demonstrated in several recent applications [3–11].”
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].”
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).”
Improved bounds for CFT’s with global symmetries (2011, methodology): “As extensively discussed in [7, 8, 10, 12] crossing symmetry constraint are not compatible with arbitrary spectra of operators nor with arbitrary large OPE coefficients.”
A semidefinite program solver for the conformal bootstrap (2015, background): “Shockingly, the resulting bounds are sometimes saturated by actual CFTs, allowing high-precision computations of nonperturbative quantities [2–9].”
Bootstrapping SCFTs with four supercharges (2015, background): “[9, 30]) at precisely this point for all 2 ≤ d < 4.”
Bounds on 4D conformal and superconformal field theories (2010, methodology): “Since the φ 2 operator appearing in the φ× φ OPE is chiral, it always has dimension 2d and automatically satisfies the bounds derived in [33, 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.”
Minimal conformal technicolor and precision electroweak tests (2010, methodology): “The techniques used do not distinguish operators that dier only by internal symmetries, so they are not able to bound . The limits on min are quite restrictive [50, 51 ], but it is important to keep in mind that these bounds do not apply to the quantity of interest for these models.”
The bootstrap program for boundary CFTd (2012, background): “We discuss how the analogous bulk four-point function helps to explain a few features of the “kinks” observed in the bulk results of [5, 12, 13].”
Holography from Conformal Field Theory (2009, background): “Thus (15)We should note the recent papers [25, 26], which derive useful constraints on operator dimensions from general CFT properties.”
Bootstrapping the 3d Ising twist defect (2013, result): “Analysis of the first leads to an operator dimension bound in one dimension, similar to those derived between 2 and 4 dimensions in references [2, 11, 18, 19].”