scholarly journals On the UV completion of the O(N) model in 6 − ϵ dimensions: a stable large-charge sector

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
G. Arias-Tamargo ◽  
D. Rodriguez-Gomez ◽  
J. G. Russo
Keyword(s):  
Fixed Point ◽  
Perturbation Theory ◽  
Correlation Function ◽  
Scaling Limit ◽  
Stable Fixed Point ◽  
Higher Spin ◽  
Point Correlation ◽  
Charge Sector ◽  
Double Scaling Limit ◽  
Large Charge

Abstract We study large charge sectors in the O(N) model in 6 − ϵ dimensions. For 4 < d < 6, in perturbation theory, the quartic O(N) theory has a UV stable fixed point at large N . It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic O(N) model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2N) ⊃ U(1) × SU(N) theory, as a first step towards tests of (higher spin) AdS/CFT.

scholarly journals Resurgence of the large-charge expansion

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Nicola Dondi ◽  
Ioannis Kalogerakis ◽  
Domenico Orlando ◽  
Susanne Reffert
Keyword(s):  
Asymptotic Series ◽  
Scaling Limit ◽  
Three Dimensions ◽  
Lattice Data ◽  
Perturbative Corrections ◽  
Double Scaling Limit ◽  
Large Charge ◽  
Good Agreement

Abstract We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the non-perturbative corrections and to extend the validity of the eft to any value of the charge. We conjecture the general form of the non-perturbative behavior of the conformal dimensions for any value of N and find very good agreement with previous lattice data.

scholarly journals Complex Sachdev-Ye-Kitaev model in the double scaling limit

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Micha Berkooz ◽  
Vladimir Narovlansky ◽  
Himanshu Raj
Keyword(s):  
Chemical Potential ◽  
Scaling Limit ◽  
Chord Diagram ◽  
Global Symmetry ◽  
Simple Description ◽  
Spectral Asymmetry ◽  
Kitaev Model ◽  
Asymmetry Measure ◽  
Charge Sector ◽  
Double Scaling Limit

Abstract We solve for the exact energy spectrum, 2-point and 4-point functions of the complex SYK model, in the double scaling limit at all energy scales. This model has a U(1) global symmetry. The analysis shows how to incorporate a chemical potential in the chord diagram picture, and we present results for the various observables also at a given fixed charge sector. In addition to matching to the spectral asymmetry, we consider an analogous asymmetry measure of the 2-point function obeying a non-trivial dependence on the operator’s dimension. We also provide the chord diagram structure for an SYK-like model that has a U(M) global symmetry at any disorder realization. We then show how to exactly compute the effect of inserting very heavy operators, with formally infinite conformal dimension. The latter separate the gravitational spacetime into several parts connected by an interface, whose properties are exactly computable at all scales. In particular, light enough states can still go between the spaces. This behavior has a simple description in the chord diagram picture.

Estimation of the Stable Fixed Point of Passive Dynamic Walking with BP Neural Network

ROBOT ◽  
2010 ◽  
Vol 32 (4) ◽  
pp. 478-483 ◽  
Author(s):  
Xiuhua NI ◽  
Weishan CHEN ◽  
Junkao LIU ◽  
Shengjun SHI
Keyword(s):  
Neural Network ◽  
Fixed Point ◽  
Bp Neural Network ◽  
Stable Fixed Point ◽  
Dynamic Walking ◽  
Passive Dynamic Walking

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals Characters of irrelevant deformations

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Shouvik Datta ◽  
Yunfeng Jiang
Keyword(s):  
Deformation Parameter ◽  
Central Charge ◽  
Scaling Limit ◽  
Small Deformation ◽  
State Dependent ◽  
Dependent Change ◽  
Left And Right ◽  
Double Scaling Limit

Abstract We analyse the $$ T\overline{T} $$ T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $$ T\overline{T} $$ T T ¯ , $$ J\overline{T} $$ J T ¯ and $$ T\overline{J} $$ T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

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