An official website of the United States government
A bstract It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆ gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆ gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆ gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS 4 naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.
more »
« less
Dispersive CFT sum rules
A bstract We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule “dispersive” if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity). They have been discussed using three seemingly different methods: analytic functionals dual to double-twist operators, dispersion relations in position space, and dispersion relations in Mellin space. We show that these three approaches can be mapped into one another and lead to completely equivalent sum rules. A central idea of our discussion is a fully nonperturbative expansion of the correlator as a sum over Polyakov-Regge blocks . Unlike the usual OPE sum, the Polyakov-Regge expansion utilizes the data of two separate channels, while having (term by term) good Regge behavior in the third channel. We construct sum rules which are non-negative above the double-twist gap; they have the physical interpretation of a subtracted version of “superconvergence” sum rules. We expect dispersive sum rules to be a very useful tool to study expansions around mean-field theory, and to constrain the low-energy description of holographic CFTs with a large gap. We give examples of the first kind of applications, notably we exhibit a candidate extremal functional for the spin-two gap problem.
more »
« less
- Award ID(s):
- 1915093
- PAR ID:
- 10249286
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 5
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A bstract Dispersion relations for S-matrices and CFT correlators translate UV consistency into bounds on IR observables. In this note, we construct dispersive sum rules for 1D CFTs. We use them to prove bounds on higher-derivative couplings in weakly-coupled non-gravitational EFTs in AdS 2 . At the leading order in the bulk-point limit, the bounds agree with the flat-space result. We compute the leading universal effect of finite AdS radius on the bounds. Along the way, we give an explicit formula for anomalous dimensions in general higher-derivative contact Witten diagrams in AdS 2 .more » « less
-
A bstract We initiate a study of asymptotic detector operators in weakly-coupled field theories. These operators describe measurements that can be performed at future null infinity in a collider experiment. In a conformal theory they can be identified with light-ray operators, and thus have a direct relation to the spectrum of the theory. After a general discussion of the underlying physical picture, we show how infrared divergences of general detector operators can be renormalized in perturbation theory, and how they give rise to detector anomalous dimensions. We discuss in detail how this renormalization can be performed at the intersections of the Regge trajectories where non-trivial mixing occurs, which is related to the poles in anomalous dimensions at special values of spin. Finally, we discuss novel horizontal trajectories in scalar theories and show how they contribute to correlation functions. Our calculations are done in the example of ϕ 4 theory in d = 4 − ϵ dimensions, but the methods are applicable more broadly. At the Wilson-Fisher fixed point our results include an explicit expression for the Pomeron light-ray operator at two loops, as well as a prediction for the value of the Regge intercept at five loops.more » « less
-
A bstract We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s - and t -channel expansions) can be thought of as a vector equation in an infinite-dimensional space of complex analytic functions in two variables, which satisfy a boundedness condition at infinity. We identify a useful basis for this space of functions, consisting of the set of s- and t-channel conformal blocks of double-twist operators in mean field theory. We describe two independent algorithms to construct the dual basis of linear functionals, and work out explicitly many examples. Our basis of functionals appears to be closely related to the CFT dispersion relation recently derived by Carmi and Caron-Huot.more » « less
-
null (Ed.)A bstract Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this aim we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP05(2021)243
