scholarly journals Applications of dispersive sum rules: $ε$-expansion and holography

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Dean Carmi ◽  
Joao Penedones ◽  
Joao A. Silva ◽  
Alexander Zhiboedov
Keyword(s):  
Sum Rules ◽  
Dispersion Relations ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Fisher Model ◽  
Twist Operators ◽  
Space Dispersion

We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in d=4-\epsilond=4−ϵ dimensions. We re-derive many of the known results to order \epsilon^4ϵ4 and we make new predictions. No assumption of analyticity down to spin 00 was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

scholarly journals Two-photon processes in conformal QCD: resummation of the descendants of leading-twist operators

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
V.M. Braun ◽  
Yao Ji ◽  
A.N. Manashov
Keyword(s):  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Field Theories ◽  
Tree Level ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Closed Expression ◽  
Conformal Field ◽  
Two Photon ◽  
Twist Operators

Abstract Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD β-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., γγ∗ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.

scholarly journals Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Johan Henriksson ◽  
Stefanos R. Kousvos ◽  
Andreas Stergiou
Keyword(s):  
Power Series ◽  
Fixed Points ◽  
Parameter Space ◽  
Field Theories ◽  
Global Symmetry ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Bootstrap Techniques ◽  
Perturbative Methods ◽  
Anomalous Dimensions

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n)O(m)×O(n) global symmetry in d=3d=3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-dε=4−d and in 1/n1/n, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n)O(2)×O(n) theories for various values of nn. Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilonε and large-nn expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

scholarly journals Boundary conformal field theory at large charge

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Gabriel Cuomo ◽  
Márk Mezei ◽  
Avia Raviv-Moshe
Keyword(s):  
Field Theory ◽  
Background Field ◽  
Effective Field ◽  
Three Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Four Dimensions ◽  
Conformal Field ◽  
Fisher Model ◽  
Large Charge

Abstract We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a |ϕ|6 interaction in three dimensions and the O(2) Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether’s theorem in perturbative theories.

scholarly journals Double copy structure of parity-violating CFT correlators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Flat Space ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin ◽  
Space Limit ◽  
Double Copy ◽  
Conserved Currents ◽  
Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

scholarly journals Exclusion inside or at the border of conformal bootstrap continent

2020 ◽  
Vol 35 (06) ◽  
pp. 2050036
Author(s):  
Yu Nakayama
Keyword(s):  
Bound States ◽  
Pauli Exclusion Principle ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Field Theories ◽  
Exclusion Principle ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Anomalous Dimensions

How large can anomalous dimensions be in conformal field theories? What can we do to attain larger values? One attempt to obtain large anomalous dimensions efficiently is to use the Pauli exclusion principle. Certain operators constructed out of constituent fermions cannot form bound states without introducing nontrivial excitations. To assess the efficiency of this mechanism, we compare them with the numerical conformal bootstrap bound as well as with other interacting field theory examples. In two dimensions, it turns out to be the most efficient: it saturates the bound and is located at the (second) kink. In higher dimensions, it more or less saturates the bound but it may be slightly inside.

scholarly journals Dispersive CFT sum rules

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Simon Caron-Huot ◽  
Dalimil Mazáč ◽  
Leonardo Rastelli ◽  
David Simmons-Duffin
Keyword(s):  
Field Theory ◽  
Sum Rules ◽  
Mean Field Theory ◽  
Mean Field ◽  
Dispersion Relations ◽  
Position Space ◽  
Central Idea ◽  
Conformal Field ◽  
Regge Behavior ◽  
Twist Operators

Abstract 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.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

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