Rigorous limits on the interaction strength in quantum field theory

By Francesco Caracciolo, S. Rychkov. 2009

171 citations recorded by the source corpus.

We derive model-independent, universal upper bounds on the operator product expansion coefficients in unitary 4-dimensional conformal field theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the operator product expansion coefficient of three identical dimension d scalar primaries is found to be bounded by {approx_equal}10(d-1) for 1<d<1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d6f463ac2950071188a0112e851e3415ae2ad38c

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In Nuclear and High Energy Physics

Citations in the corpus

Carving out OPE space and precise O(2) model critical exponents (2019, result): “Other analysis can also be found in [75–81].”
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, background): “This important know-how was developed in a series of recent papers [16–23].”
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.”
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).”
A universal inequality for CFT and quantum gravity (2009, unknown): “(Also see [16, 17, 18, 19, 20, 21, 22].)”
Bounds on 4D conformal and superconformal field theories (2010, background): “In [35] bounds were also derived on the size of the three-point function coefficients of scalar operators appearing in φ × φ.”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, background): “In most examples, crossing symmetry is combined with unitarity and is implemented numerically on various four-point functions (see, for example, [12–43]).”
Bounds in 4D conformal field theories with global symmetry (2010, methodology): “These studies are made possible by the existence of O(1) universal bounds on the coefficients p ,l in the conformal block decomposition [3], and that the coefficients p4,2 and p3,1 can be related to the inverse central charges by the Ward identities [11].”
Effective conformal theory and the flat-space limit of AdS (2010, background): “When this happens, the description of the CFT must be modified to maintain unitarity, and if this is to occur before the n where perturbation theory fails then one must (8)We note that the above bound is not as general as those derived in [25, 26, 27], which are valid also when both n and N are smal”
The ϵ ?> -expansion from conformal field theory (2015, methodology): “The conformal bootstrap—using conformal symmetry to constrain the dynamics of various physically interesting critical theories—is an old idea [1–3] which in the last few years has been shown to be much more powerful than previously thought [4–11].”
Improved bounds for CFT’s with global symmetries (2011, methodology): “In order to constrain the size of the OPE coefficients p∆,l, we proceed as in [9].”
Modular bootstrap revisited (2016, background): “The degeneracy d∆,s of a primary of dimension ∆ and spin s is then subject to the following upper bound (this mirrors the upper bound on the squared OPE coefficients derived in the context of the four-point function bootstrap in [24])”
Spinning conformal correlators (2011, methodology): “The efficiency of this method has been demonstrated in several recent applications [3–11].”
Spinning conformal blocks (2011, background): “In [3–10] it was for example demonstrated that crossing symmetry of four point functions of scalars combined with unitarity leads to completely general bounds on CFT operator dimensions and OPE coefficients.”
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].”
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].”
A semidefinite program solver for the conformal bootstrap (2015, methodology): “This modern incarnation of the conformal bootstrap [10, 11] has been applied to numerous theories, and the list is growing [12–33].”