Related papers: Super Sum rules for Long-Range Models
Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to sum rules that suppress the double-twist sector of…
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…
Locality of bulk operators in AdS imposes stringent constraints on their description in terms of the boundary CFT. These constraints are encoded as sum rules on the bulk-to-boundary expansion coefficients. In this paper, we construct…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more…
We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering…
We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on…
For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional…
It is a long-standing conjecture that any CFT with a large central charge and a large gap $\Delta_{\text{gap}}$ in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp…
The bulk phase shift, related to a CFT four-point function, describes two-to-two scattering at fixed impact parameter in the dual AdS spacetime. We describe its properties for a generic CFT and then focus on large $N$ CFTs with classical…
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…
A sum rule which relates a stress-energy tensor correlator to thermodynamic functions is examined within the context of a simple non-conformal gravity dual. Such a sum rule was previously derived using AdS/CFT for conformal $\mathcal{N} =…
The problem of constructing local bulk observables from boundary CFT data is of paramount importance in holography. In this work, we begin addressing this question from a modern bootstrap perspective. Our main tool is the boundary operator…
We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the…
We develop the technology for Polyakov-Mellin (PM) bootstrap in one-dimensional conformal field theories (CFT$_1$). By adding appropriate contact terms, we bootstrap various effective field theories in AdS$_2$ and analytically compute the…
We consider the Regge limit of the CFT correlation functions $\langle {\cal J} {\cal J} {\cal O}{\cal O}\rangle$ and $\langle TT {\cal O}{\cal O}\rangle$, where ${\cal J}$ is a vector current, $T$ is the stress tensor and ${\cal O}$ is some…
We present a systematic exploration of conformal field theories (CFTs) constrained by duality-inspired fusion rules using the conformal bootstrap. We classify the operator spectrum into three sectors: $[\sigma]$, $[\epsilon]$, and $[1]$.…
We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j \pm 1| and…
We study the conformal field theory data (CFT-data) of planar 4D $\mathcal{N} = 4$ Super-Yang-Mills theory in the strong 't Hooft coupling limit. This regime explores the physics of massive short strings in the flat-space limit of the dual…
Sum rules connecting low-energy observables to high-energy physics are an interesting way to probe the mechanism of inflation and its ultraviolet origin. Unfortunately, such sum rules have proven difficult to study in a cosmological…