Distributions in CFT II. Minkowski Space

Kravchuk, Petr; Qiao, Jiaxin; Rychkov, Slava

doi:10.48550/arxiv.2104.02090

Cited by 5 publications

(6 citation statements)

References 111 publications

(335 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result relies on the technical assumption that (G − 1) vanishes in the u-channel collinear limit even on the second sheet, which has never been rigorously proven[44,58]. However, we do not expect this assumption to affect the results of the present paper, as long as the right-hand-side can be computed from the EFT correlator 10.…”

mentioning

confidence: 85%

“…A distinct advantage of the CFT approach to AdS theories is that it is fully rigorous. The requisite analyticity and causality properties of the four-point correlator are direct consequences of the bootstrap axioms (see [44] for a recent discussion of how Lorentzian CFT axioms follow from the standard Euclidean axioms), while boundedness in the Regge limit (with Regge intercept ≤ 1) is a consequence of unitarity and the OPE at the non-perturbative level [16].…”

Section: Application To Holographic Cftsmentioning

confidence: 99%

See 1 more Smart Citation

AdS Bulk Locality from Sharp CFT Bounds

Caron-Huot,

Mazac,

Rastelli

et al. 2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

mentioning

confidence: 85%

Section: Application To Holographic Cftsmentioning

confidence: 99%

AdS Bulk Locality from Sharp CFT Bounds

Caron-Huot,

Mazac,

Rastelli

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Many implicit assumptions made in QFTs are on firmer footing in CFTs (eg. [45]) and as such lessons from CFTs will be useful guiding beacons for QFTs. Since the crossing symmetric dispersion relation was set up for CFT Mellin amplitudes in [46], a reasonably straightforward extension of the methods set up in this paper should be possible.…”

Section: It Remains An Important Open Problem To Show What Role Typic...mentioning

confidence: 97%

QFT, EFT and GFT

Raman,

Sinha

2021

Preprint

View full text Add to dashboard Cite

We explore the correspondence between geometric function theory (GFT) and quantum field theory (QFT). The crossing symmetric dispersion relation provides the necessary tool to examine the connection between GFT, QFT, and effective field theories (EFTs), enabling us to connect with the crossing-symmetric EFT-hedron. Several existing mathematical bounds on the Taylor coefficients of Typically Real functions are summarized and shown to be of enormous use in bounding Wilson coefficients in the context of 2-2 scattering. We prove that two-sided bounds on Wilson coefficients are guaranteed to exist quite generally for the fully crossing symmetric situation. Numerical implementation of the GFT constraints (Bieberbach-Rogosinski inequalities) is straightforward and allows a systematic exploration. A comparison of our findings obtained using GFT techniques and other results in the literature is made. We study both the three-channel as well as the two-channel crossing-symmetric cases, the latter having some crucial differences.We also consider bound state poles as well as massless poles in EFTs. Finally, we consider nonlinear constraints arising from the positivity of certain Toeplitz determinants, which occur in the trigonometric moment problem.

show abstract

“…Although the case of non-unitary CFTs has not been rigorously established, it is reasonable to assume that they share some similarities based on the 2d examples. See [75,76] for recent discussions of the OPE convergence in the distributional sense and in Minkowski space. 18 Introducing more conformal blocks can cancel out some part of the small difference in a subregion.…”

Section: Numerical Implementation Of η Minimizationmentioning

confidence: 99%

Ising model close to $d=2$

2021

Preprint

View full text Add to dashboard Cite

We study the Ising model in d = 2 + dimensions using the conformal bootstrap. As a minimal-model Conformal Field Theory (CFT), the critical Ising model is exactly solvable at d = 2. The deformation to d = 2 + with 1 furnishes a relatively simple system at strong coupling outside of even dimensions. At d = 2 + , the scaling dimensions and correlation function coefficients receive -dependent corrections. Using numerical and analytical conformal bootstrap methods in Lorentzian signature, we rule out the possibility that the leading corrections are of order 1 . The essential conflict comes from the d-dependence of conformal symmetry, which implies the presence of new states. A resolution is that there exist corrections of order 1/k where k > 1 is an integer. The linear independence of conformal blocks plays a central role in our analyses. Since our results are not derived from positivity constraints, this bootstrap approach can be extended to the rigorous studies of non-positive systems, such as non-unitary, defect/boundary and thermal CFTs.

show abstract

Distributions in CFT II. Minkowski Space

Abstract: I wanted to learn about elementary particles by studying boiling water.

Cited by 5 publications

References 111 publications

AdS Bulk Locality from Sharp CFT Bounds

AdS Bulk Locality from Sharp CFT Bounds

QFT, EFT and GFT

Ising model close to $d=2$

Contact Info

Product

Resources

About