Near conformal perturbation theory in SYK type models

Abstract We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbative scheme of arXiv:1608.07567 based on a specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-N saddle point. While this breaking term formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of O(1) corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large q limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced O(J) and the subleading O(1) contributions originate from the Schwarzian dynamics of the soft mode and its interaction with h = 2 (bi-local) matter.

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EQUIVALENCE OF LIOUVILLE THEORY AND 2-D QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732391000774 ◽

1991 ◽

Vol 06 (09) ◽

pp. 745-767 ◽

Cited By ~ 32

Author(s):

ERIC D’HOKER

Keyword(s):

Perturbation Theory ◽

Invariant Measure ◽

Quantum Gravity ◽

Effective Potential ◽

Effective Action ◽

Liouville Theory ◽

Ward Identities ◽

Explicit Equation ◽

Translation Invariant

The equivalence of 2-dimensional quantum gravity and Liouville theory quantized with the standard translation invariant measure, is shown to hold to all orders in perturbation theory. Also, an explicit equation for the Liouville effective action as a function of the effective potential is derived from Weyl Ward identities. We speculate on some of the non-perturbative aspects of the theory.

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From correlation functions to event shapes in QCD

Journal of High Energy Physics ◽

10.1007/jhep02(2021)053 ◽

2021 ◽

Vol 2021 (2) ◽

Cited By ~ 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.

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Spurious poles in the scattering of electric and magnetic charges

Journal of High Energy Physics ◽

10.1007/jhep12(2020)153 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

John Terning ◽

Christopher B. Verhaaren

Keyword(s):

Perturbation Theory ◽

Scattering Amplitudes ◽

Pair Production ◽

Magnetic Particles ◽

Single Photon ◽

Low Energy ◽

Magnetic Interactions ◽

Parity Conservation ◽

Non Local ◽

The Way

Abstract Theories with both electric and magnetic charges (“mutually non-local” theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one of the U(1)’s being broken. Here we show how the constraints of confinement and parity conservation on observable processes manages to cancel the spurious poles in scattering and pair production amplitudes, paving the way for systematic studies of the experimental signatures of “dark” electric-magnetic processes. Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes.

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Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

Journal of High Energy Physics ◽

10.1007/jhep12(2020)019 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Yifei He ◽

Jesper Lykke Jacobsen ◽

Hubert Saleur

Keyword(s):

Potts Model ◽

Correlation Functions ◽

Liouville Theory ◽

Analytical Determination ◽

Conformal Weight ◽

Two Dimensional ◽

Conformal Blocks ◽

Conformal Bootstrap ◽

Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

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On the low-energy effective action of N = 2 supersymmetric Yang-Mills theory

Nuclear Physics B ◽

10.1016/s0550-3213(98)00660-9 ◽

1999 ◽

Vol 537 (1-3) ◽

pp. 161-183 ◽

Cited By ~ 1

Author(s):

M. Chaichian ◽

W.F. Chen ◽

C. Montonen

Keyword(s):

Effective Action ◽

Low Energy ◽

Yang Mills

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On the three-dimensional spatial correlations of curved dislocation systems

Materials Theory ◽

10.1186/s41313-020-00026-w ◽

2021 ◽

Vol 5 (1) ◽

Author(s):

Joseph Pierre Anderson ◽

Anter El-Azab

Keyword(s):

Correlation Function ◽

Slip System ◽

Correlation Functions ◽

Mean Field ◽

Coarse Graining ◽

Dislocation Dynamics ◽

Coarse Grained ◽

Spatial Correlation Function ◽

Line System ◽

Dislocation Densities

AbstractCoarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

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GRAVITY ON NONCOMMUTATIVE D-BRANES

International Journal of Modern Physics A ◽

10.1142/s0217751x03010991 ◽

2003 ◽

Vol 18 (07) ◽

pp. 1051-1066 ◽

Cited By ~ 20

Author(s):

F. ARDALAN ◽

H. ARFAEI ◽

M. R. GAROUSI ◽

A. GHODSI

Keyword(s):

String Theory ◽

Effective Action ◽

Low Energy ◽

Bosonic String ◽

First Order ◽

Energy Scattering ◽

Bosonic String Theory ◽

Brane Action

The effective action for the low energy scattering of two gravitons with a D-brane in the presence of a constant antisymmetric B field in bosonic string theory is calculated and the modification to the standard D-brane action to first order in α′ is obtained.

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Low-energy scale of the periodic Anderson model

Physical Review B ◽

10.1103/physrevb.61.12799 ◽

2000 ◽

Vol 61 (19) ◽

pp. 12799-12809 ◽

Cited By ~ 96

Author(s):

Th. Pruschke ◽

R. Bulla ◽

M. Jarrell

Keyword(s):

Anderson Model ◽

Energy Scale ◽

Low Energy ◽

Periodic Anderson Model

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A Side-Peak Cancellation Scheme for Unambiguous BOC Signal Tracking

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.764-765.462 ◽

2015 ◽

Vol 764-765 ◽

pp. 462-465

Author(s):

Keun Hong Chae ◽

Hua Ping Liu ◽

Seok Ho Yoon

Keyword(s):

Correlation Function ◽

Correlation Functions ◽

Numerical Results ◽

Tracking Performance ◽

Side Peak ◽

Signal Tracking ◽

Partial Correlations

In this paper, we propose a side-peak cancellation scheme for unambiguous BOC signal tracking. We obtain partial correlations using a pulse model of a BOC signal, and then, we finally obtain an unambiguous correlation function based on the partial correlations. The proposed correlation function is confirmed from numerical results to provide an improved tracking performance over the conventional correlation functions.

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