scholarly journals Spontaneous breaking of U(1) symmetry in coupled complex SYK models

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Igor R. Klebanov ◽  
Alexey Milekhin ◽  
Grigory Tarnopolsky ◽  
Wenli Zhao
Keyword(s):  
Fixed Points ◽  
Low Temperatures ◽  
Coupled Model ◽  
Spontaneous Breaking ◽  
Expectation Value ◽  
Bilinear Operators ◽  
Complex Dimension ◽  
Quartic Term ◽  
Fixed Line

Abstract As shown in [1], two copies of the large N Majorana SYK model can produce spontaneous breaking of a Z2 symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the U(1) × U(1) symmetry. We also present a tensor counterpart of this coupled model. When the coefficient α of the quartic term lies in a certain range, the coupled large N theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of α. We show that the operator $$ {c}_{1i}^{\dagger }{c}_{2i} $$ c 1 i † c 2 i , which is charged under the axial U(1) symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large N Dyson-Schwinger equations and show that, outside the fixed line, this U(1) symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large N.

scholarly journals The Super-Stückelberg procedure and dS in pure supergravity

2020 ◽  
Vol 476 (2237) ◽  
pp. 20200035 ◽  
Author(s):  
Silvia Nagy ◽  
Antonio Padilla ◽  
Ivonne Zavala
Keyword(s):  
Cosmological Constant ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Accelerated Expansion ◽  
Spontaneous Breaking ◽  
De Sitter ◽  
Expectation Value ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Natural Way

Understanding de Sitter space in supergravity—and string theory—has led to an intense amount of work for more than two decades, largely motivated by the discovery of the accelerated expansion of the Universe in 1998. In this paper, we consider a non-trivial generalization of unimodular gravity to minimal N = 1 supergravity, which allows for de Sitter solutions without the need of introducing any matter. We formulate a superspace version of the Stückelberg procedure, which restores diffeomorphism and local supersymmetry invariance. This introduces the goldstino associated with spontaneous breaking of supersymmetry in a natural way. The cosmological constant and gravitino mass are related to the vacuum expectation value of the components of a Lagrange multiplier imposing a super-unimodularity condition.

scholarly journals Thermal order in large N conformal gauge theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Soumyadeep Chaudhuri ◽  
Changha Choi ◽  
Eliezer Rabinovici
Keyword(s):  
Symmetry Breaking ◽  
Fixed Points ◽  
Gauge Theories ◽  
Scalar Fields ◽  
The Other ◽  
Spontaneous Breaking ◽  
Global Symmetry ◽  
Gauge Groups ◽  
Large N ◽  
Work Done

Abstract In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in D = 4 space-time dimensions. We show that such a symmetry-breaking indeed occurs in certain families of non-supersymmetric large N gauge theories at a planar limit. We also show that this phenomenon is accompanied by the system remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature. These analyses are motivated by the work done in [1, 2] where symmetry-breaking was observed in all thermal states for certain CFTs in fractional dimensions.In our case, the theories demonstrating the above features have gauge groups which are specific products of SO(N) in one family and SU(N) in the other. Working in a perturbative regime at the N → ∞ limit, we show that the beta functions in these theories yield circles of fixed points in the space of couplings. We explicitly check this structure up to two loops and then present a proof of its survival under all loop corrections. We show that under certain conditions, an interval on this circle of fixed points demonstrates both the spontaneous breaking of a global symmetry as well as a persistent BEH phase at all nonzero temperatures. The broken global symmetry is ℤ2 in one family of theories and U(1) in the other. The corresponding order parameters are expectation values of the determinants of bifundamental scalar fields in these theories. We characterize these symmetries as baryon-like symmetries in the respective models.

scholarly journals Fixed points and the spontaneous breaking of scale invariance

2017 ◽  
Vol 95 (12) ◽  
Author(s):  
Daniel F. Litim ◽  
Edouard Marchais ◽  
Péter Mati
Keyword(s):  
Fixed Points ◽  
Scale Invariance ◽  
Spontaneous Breaking

Interpretation of irradiation-induced changes in electron diffractograms and images of extinction contours at low temperatures

1984 ◽  
Vol 42 ◽  
pp. 268-269
Author(s):  
E. Knapek ◽  
H. Formanek ◽  
G. Lefranc ◽  
I. Dietrich
Keyword(s):  
Low Temperatures ◽  
Carbon Films ◽  
Organic Crystals ◽  
Wide Spread ◽  
Lens System ◽  
Preparation Conditions ◽  
Thin Carbon ◽  
Electron Diffractograms ◽  
Diffraction Patterns ◽  
Induced Changes

A few years ago results on cryoprotection of L-valine were reported, where the values of the critical fluence De i.e, the electron exposure which decreases the intensity of the diffraction reflections by a factor e, amounted to the order of 2000 + 1000 e/nm2. In the meantime a discrepancy arose, since several groups published De values between 100 e/nm2 and 1200 e/nm2 /1 - 4/. This disagreement and particularly the wide spread of the results induced us to investigate more thoroughly the behaviour of organic crystals at very low temperatures during electron irradiation.For this purpose large L-valine crystals with homogenuous thickness were deposited on holey carbon films, thin carbon films or Au-coated holey carbon films. These specimens were cooled down to nearly liquid helium temperature in an electron microscope with a superconducting lens system and irradiated with 200 keU-electrons. The progress of radiation damage under different preparation conditions has been observed with series of electron diffraction patterns and direct images of extinction contours.

Radiation Damage of Support Films

1981 ◽  
Vol 39 ◽  
pp. 28-29
Author(s):  
H.A. Cohen ◽  
W. Chiu
Keyword(s):  
Transfer Function ◽  
Low Temperatures ◽  
Carbon Support ◽  
Contrast Transfer Function ◽  
Electron Dose ◽  
Imaging Parameters ◽  
Negative Stain ◽  
Phase Corrections ◽  
Two Parameters ◽  
Medium Dose

The goal of imaging the finest detail possible in biological specimens leads to contradictory requirements for the choice of an electron dose. The dose should be as low as possible to minimize object damage, yet as high as possible to optimize image statistics. For specimens that are protected by low temperatures or for which the low resolution associated with negative stain is acceptable, the first condition may be partially relaxed, allowing the use of (for example) 6 to 10 e/Å2. However, this medium dose is marginal for obtaining the contrast transfer function (CTF) of the microscope, which is necessary to allow phase corrections to the image. We have explored two parameters that affect the CTF under medium dose conditions.Figure 1 displays the CTF for carbon (C, row 1) and triafol plus carbon (T+C, row 2). For any column, the images to which the CTF correspond were from a carbon covered hole (C) and the adjacent triafol plus carbon support film (T+C), both recorded on the same micrograph; therefore the imaging parameters of defocus, illumination angle, and electron statistics were identical.

Correlation analysis of radiation damage

1978 ◽  
Vol 36 (1) ◽  
pp. 214-215
Author(s):  
R. Hegerl ◽  
A. Feltynowski ◽  
B. Grill
Keyword(s):  
Electron Microscopy ◽  
Independent Random Variables ◽  
Optical Parameters ◽  
Bright Field Image ◽  
Bright Field ◽  
Expectation Value ◽  
All Optical ◽  
Image Element ◽  
Stochastic Series ◽  
The Common

Till now correlation functions have been used in electron microscopy for two purposes: a) to find the common origin of two micrographs representing the same object, b) to check the optical parameters e. g. the focus. There is a third possibility of application, if all optical parameters are constant during a series of exposures. In this case all differences between the micrographs can only be caused by different noise distributions and by modifications of the object induced by radiation.Because of the electron noise, a discrete bright field image can be considered as a stochastic series Pm,where i denotes the number of the image and m (m = 1,.., M) the image element. Assuming a stable object, the expectation value of Pm would be Ηm for all images. The electron noise can be introduced by addition of stationary, mutual independent random variables nm with zero expectation and the variance. It is possible to treat the modifications of the object as a noise, too.

In situ Tensile Experiments at Low Temperatures on Niobium Single Crystals by H.V.E.M.

1975 ◽  
Vol 33 ◽  
pp. 58-59
Author(s):  
F. H. Louchet ◽  
L. P. Kubin
Keyword(s):  
Electron Microscope ◽  
Transition Temperature ◽  
Low Temperature ◽  
Slip System ◽  
Low Temperatures ◽  
Tensile Axis ◽  
Image Intensifier ◽  
Screw Dislocations ◽  
Source Operation

Experiments have been carried out on the 3 MeV electron microscope in Toulouse. The low temperature straining holder has been previously described Images given by an image intensifier are recorded on magnetic tape.The microtensile niobium samples are cut in a plane with the two operative slip directions [111] and lying in the foil plane. The tensile axis is near [011].Our results concern:- The transition temperature of niobium near 220 K: at this temperature and below an increasing difference appears between the mobilities of the screw and edge portions of dislocations loops. Source operation and interactions between screw dislocations of different slip system have been recorded.

Ultrastructure of the soil fungus, Geomyces pannorus

1984 ◽  
Vol 42 ◽  
pp. 738-739
Author(s):  
J. A. Traquair ◽  
E. G. Kokko
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Fine Structure ◽  
Low Temperatures ◽  
Soil Fungus ◽  
Organic Soils ◽  
Anatomical Studies ◽  
Transmission Electron ◽  
Electron Microscopical ◽  
Scanning Electron

With the advent of improved dehydration techniques, scanning electron microscopy has become routine in anatomical studies of fungi. Fine structure of hyphae and spore surfaces has been illustrated for many hyphomycetes, and yet, the ultrastructure of the ubiquitous soil fungus, Geomyces pannorus (Link) Sigler & Carmichael has been neglected. This presentation shows that scanning and transmission electron microscopical data must be correlated in resolving septal structure and conidial release in G. pannorus.Although it is reported to be cellulolytic but not keratinolytic, G. pannorus is found on human skin, animals, birds, mushrooms, dung, roots, and frozen meat in addition to various organic soils. In fact, it readily adapts to growth at low temperatures.

Structure and Orientation of As Precipitates in LT-MBE Grown GaAs

1991 ◽  
Vol 49 ◽  
pp. 900-901 ◽  
Author(s):  
Alain Claverie ◽  
Zuzanna Liliental-Weber
Keyword(s):  
Transport Properties ◽  
Layer Thickness ◽  
Growth Temperature ◽  
Low Temperatures ◽  
Lattice Parameter ◽  
Crystalline Quality ◽  
Insulating Properties ◽  
Lt Gaas

GaAs layers grown by MBE at low temperatures (in the 200°C range, LT-GaAs) have been reported to have very interesting electronic and transport properties. Previous studies have shown that, before annealing, the crystalline quality of the layers is related to the growth temperature. Lowering the temperature or increasing the layer thickness generally results in some columnar polycrystalline growth. For the best “temperature-thickness” combinations, the layers may be very As rich (up to 1.25%) resulting in an up to 0.15% increase of the lattice parameter, consistent with the excess As. Only after annealing are the technologically important semi-insulating properties of these layers observed. When annealed in As atmosphere at about 600°C a decrease of the lattice parameter to the substrate value is observed. TEM studies show formation of precipitates which are supposed to be As related since the average As concentration remains almost unchanged upon annealing.

Point and planar defects in the iron sulfide compounds Fe1-xS

1984 ◽  
Vol 42 ◽  
pp. 434-435
Author(s):  
Thao A. Nguyen
Keyword(s):  
Low Temperatures ◽  
Direct Evidence ◽  
Iron Sulfide ◽  
Planar Defects ◽  
Selective Area ◽  
Vacancy Ordering ◽  
Different Types ◽  
Lattice Images ◽  
The Subject ◽  
Beam Lattice

It is well known that the large deviations from stoichiometry in iron sulfide compounds, Fe1-xS (0≤x≤0.125), are accommodated by iron vacancies which order and form superstructures at low temperatures. Although the ordering of the iron vacancies has been well established, the modes of vacancy ordering, hence superstructures, as a function of composition and temperature are still the subject of much controversy. This investigation gives direct evidence from many-beam lattice images of Fe1-xS that the 4C superstructure transforms into the 3C superstructure (Fig. 1) rather than the MC phase as previously suggested. Also observed are an intrinsic stacking fault in the sulfur sublattice and two different types of vacancy-ordering antiphase boundaries. Evidence from selective area optical diffractograms suggests that these planar defects complicate the diffraction pattern greatly.

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