Causality constraints in conformal field theory

By Thomas Hartman, Sachin Jain, Sandipan Kundu. Journal of High Energy Physics, 2015

258 citations recorded by the source corpus.

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4523c44654ee33cb55594160083395d7efbb2109

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Citations in the corpus

Analyticity in spin in conformal theories (2017, background): “The argument here (similar to [26, 27]), valid in conformal field theories, relied only on the usual positivity of Euclidean (t-channel) OPE coefficients.”
Loops in AdS from conformal field theory (2016, background): “Knowing loop amplitudes in a given bulk theory would open the door to nonplanar extensions of dynamical aspects of holography and the conformal bootstrap [34–50].”
An algebraic approach to the analytic bootstrap (2015, unknown): “This together with [26] may be useful for deriving [27] directly from bootstrap.”
Averaged null energy condition from causality (2016, methodology): “For comparison to previous work, we note that the arguments in [15, 16, 18] were phrased in terms of conformal cross ratios, and it was important that the correlator was evaluated on the ‘2nd sheet’, i.”
Light-ray operators in conformal field theory (2018, background): “1) is analytic in the following region [65, 107] (see [11] for a nice review):68 ζ1 > ζ2 > · · · > ζn.”
Recovering the QNEC from the ANEC (2018, background): “This same phenomenon happens in the light-cone limit of the (Rindler) thermal OTO correlator [28] and also in CFTs with a holographic gravitational dual as one sends = GN → 0 where in these cases the “spectral weight” is governed by the double discontinuity defined in [52].”
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, methodology): “In particular, using analytic bootstrap methods the HM bounds were proven for a class of three-point functions in [42], building on the work of [43, 44].”
Looking for a bulk point (2015, background): “This constraint was obtained in [49] for field theories in flat space, and more recently in [50] for AdS.”
Softness and amplitudes’ positivity for spinning particles (2016, background): “from the a-theorem [3] to the theory of pions [4–6], from WW-scattering [1, 7, 8] to composite Higgs models [8–11], from quantum gravity [12] to inflation [13, 14], from Galileons [15] to massive gravity [16], from the weak gravity conjecture [17, 18] to the OPE coefficients [19], from the conformal”
Bounding the space of holographic CFTs with chaos (2016, methodology): “Our work has a similar flavor to [56, 57], which uses the Lorentzian bootstrap to enforce causality in shock wave backgrounds.”