scholarly journals Boundary conformal field theory at the extraordinary transition: The layer susceptibility to O(ε)

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. A. Shpot
Keyword(s):  
General Structure ◽  
Mean Field ◽  
Integral Transforms ◽  
Nucl Phys ◽  
Space Representation ◽  
Coordinate Space ◽  
Operator Product ◽  
Conformal Field ◽  
Starting Point ◽  
Loop Approximation

Abstract We present an analytic calculation of the layer (parallel) susceptibility at the extraordinary transition in a semi-infinite system with a flat boundary. Using the method of integral transforms put forward by McAvity and Osborn [Nucl. Phys. B455 (1995) 522] in the boundary CFT, we derive the coordinate-space representation of the mean-field propagator at the transition point. The simple algebraic structure of this function provides a practical possibility of higher-order calculations. Thus we calculate the explicit expression for the layer susceptibility at the extraordinary transition in the one-loop approximation. Our result is correct up to order O(ε) of the ε = 4 − d expansion and holds for arbitrary width of the layer and its position in the half-space. We discuss the general structure of our result and consider the limiting cases related to the boundary operator expansion and (bulk) operator product expansion. We compare our findings with previously known results and less complicated formulas in the case of the ordinary transition. We believe that analytic results for layer susceptibilities could be a good starting point for efficient calculations of two-point correlation functions. This possibility would be of great importance given the recent breakthrough in bulk and boundary conformal field theories in general dimensions.

scholarly journals Searching for elusive dark sectors with terrestrial and celestial observations

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Roberto Contino ◽  
Kevin Max ◽  
Rashmish K. Mishra
Keyword(s):  
Field Theory ◽  
Broad Class ◽  
High Energy ◽  
Effective Field ◽  
Dark Sector ◽  
Minimum Requirement ◽  
Conformal Field ◽  
Starting Point ◽  
The Standard Model ◽  
Visible Sector

Abstract We consider the possible existence of a SM-neutral and light dark sector coupled to the visible sector through irrelevant portal interactions. Scenarios of this kind are motivated by dark matter and arise in various extensions of the Standard Model. We characterize the dark dynamics in terms of one ultraviolet scale Λuv, at which the exchange of heavy mediator fields generates the portal operators, and by one infrared scale ΛIR, setting the mass gap. At energies ΛIR « E « Λuv the dark sector behaves like a conformal field theory and its phenomenology can be studied model independently. We derive the constraints set on this scenario by high- and low-energy laboratory experiments and by astrophysical observations. Our results are conservative and serve as a minimum requirement that must be fulfilled by the broad class of models satisfying our assumptions, of which we give several examples. The experimental constraints are derived in a manner consistent with the validity of the effective field theory used to define the portal interactions. We find that high-energy colliders give the strongest bounds and exclude UV scales up to a few TeV, but only in specific ranges of the IR scale. The picture emerging from current searches can be taken as a starting point to design a future experimental strategy with broader sensitivity.

scholarly journals Conformal Regge theory at finite boost

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Simon Caron-Huot ◽  
Joshua Sandor
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Exact Results ◽  
Double Integral ◽  
Regge Theory ◽  
Conformal Field ◽  
Regge Trajectories ◽  
Continuous Spins ◽  
Regge Limit

Abstract The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid even away from Regge limit. The representation extends convergence of the OPE by rewriting it as a double integral over continuous spins and dimensions, and features a novel “Regge block”. We test the formula in the conformal fishnet theory, where exact results involving nontrivial Regge trajectories are available.

scholarly journals Monodromy defects in free field theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenzo Bianchi ◽  
Adam Chalabi ◽  
Vladimír Procházka ◽  
Brandon Robinson ◽  
Jacopo Sisti
Keyword(s):  
Entanglement Entropy ◽  
Free Field ◽  
Operator Product ◽  
Dirac Fermions ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Defect Operator ◽  
Crucial Information ◽  
The One ◽  
Group Flow

Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

scholarly journals Spontaneously broken boosts in CFTs

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Zohar Komargodski ◽  
Márk Mezei ◽  
Sridip Pal ◽  
Avia Raviv-Moshe
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Surface States ◽  
Field Theories ◽  
Conformal Anomaly ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Scaling Dimension ◽  
Large Charge

Abstract Conformal Field Theories (CFTs) have rich dynamics in heavy states. We describe the constraints due to spontaneously broken boost and dilatation symmetries in such states. The spontaneously broken boost symmetries require the existence of new low-lying primaries whose scaling dimension gap, we argue, scales as O(1). We demonstrate these ideas in various states, including fluid, superfluid, mean field theory, and Fermi surface states. We end with some remarks about the large charge limit in 2d and discuss a theory of a single compact boson with an arbitrary conformal anomaly.

scholarly journals Operator product expansion convergence in conformal field theory

2012 ◽  
Vol 86 (10) ◽  
Author(s):  
Duccio Pappadopulo ◽  
Slava Rychkov ◽  
Johnny Espin ◽  
Riccardo Rattazzi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Conformal Field

Nature of Non-magnetic Strongly-Correlated State in Plutonium

2006 ◽  
Vol 986 ◽  
Author(s):  
Leniod Purovskii ◽  
Alexander Shick ◽  
Ladislav Havela ◽  
Mikhail Katsnelson ◽  
Alexander Lichtenstein
Keyword(s):  
Field Theory ◽  
Density Functional ◽  
Local Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Dynamical Mean Field Theory ◽  
Cubic Phase ◽  
Face Centered Cubic ◽  
Strongly Correlated ◽  
Starting Point

AbstractLocal density approximation for the electronic structure calculations has been highly successful for non-correlated systems. The LDA scheme quite often failed for strongly correlated materials containing transition metals and rare-earth elements with complicated charge, spin and orbital ordering. Dynamical mean field theory in combination with the first-principle scheme (LDA+DMFT) can be a starting point to go beyond static density functional approximation and include effects of charge, spin and orbital fluctuations. Ab-initio relativistic dynamical mean-field theory is applied to resolve the long-standing controversy between theory and experiment in the “simple” face-centered cubic phase of plutonium called δ-Pu. In agreement with experiment, neither static nor dynamical magnetic moments are predicted. In addition, the quasiparticle density of states reproduces not only the peak close to the Fermi level, which explains the large coefficient of electronic specific heat, but also main 5f features observed in photoelectron spectroscopy.

NLO EVOLUTION OF STRUCTURE FUNCTIONS AT SMALL x

2011 ◽  
Vol 04 ◽  
pp. 46-55
Author(s):  
GIOVANNI ANTONIO CHIRILLI
Keyword(s):  
Impact Factor ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Coordinate Space ◽  
Operator Product ◽  
Leading Order ◽  
Small X ◽  
Evolution Of Structure ◽  
First Time

Using the high-energy Operator Product Expansion of the T-product of two electromagnetic currents, we calculate the Photon Impact Factor for Deep Inelastic Scattering at small value of the Bjorken variable x B at the next-to-leading order (NLO) accuracy in αs. We provide for the first time an analytic expression in coordinate space and in Mellin space of the NLO impact factor for the forward unpolarized structure functions.

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