On Some Recent Developments in Yang—Mills Theory

1995 ◽  
pp. 1-14 ◽  
Author(s):  
Raoul Bott
Keyword(s):  
Yang Mills ◽  
Recent Developments

QFT, STRINGS AND LOW-DIMENSIONAL TOPOLOGY

2002 ◽  
Vol 17 (35) ◽  
pp. 2289-2295
Author(s):  
HU SEN
Keyword(s):  
Mirror Symmetry ◽  
Theoretical Physics ◽  
Yang Mills ◽  
Low Dimensional Topology ◽  
Witten Theory ◽  
Close Relationship ◽  
Jones Polynomials ◽  
Recent Developments ◽  
Low Dimensional ◽  
Chern Simons

In between the 80's and 90's we witnessed deep interactions between mathematics and theoretical physics, especially in the understanding of low-dimensional topology in terms of quantum field theory. For example, Jones polynomials (Chern–Simons–Witten theory), Donaldson and Seiberg–Witten invariants (SUSY Yang–Mills theory) and mirror symmetry (T duality in strings) are all naturally understood in terms of QFT and strings. Recent developments indicate a close relationship between gauge theory and gravity theory both in physics and in low-dimensional topology. We shall survey these developments and report some of our work. We shall also find that the keys to connect geometric and physical objects are through symmetry and quantization.

scholarly journals DYSON–SCHWINGER APPROACH TO STRONGLY COUPLED THEORIES

2013 ◽  
Vol 28 (09) ◽  
pp. 1330006 ◽  
Author(s):  
CARINA POPOVICI
Keyword(s):  
High Temperature Superconductivity ◽  
Landau Gauge ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Theoretical Predictions ◽  
Recent Developments ◽  
Heavy Quark Limit ◽  
Many Body Systems ◽  
Energy Quantum ◽  
Experimental Findings

Although non-perturbative functional methods are often associated with low energy Quantum Chromodynamics, contemporary studies indicate that they provide reliable tools to characterize a much wider spectrum of strongly interacting many-body systems. In this paper, we aim to provide a modest overview on a few notable applications of Dyson–Schwinger equations to QCD and condensed matter physics. After a short introduction, we lay out some formal considerations and proceed by addressing the confinement problem. We discuss in some detail the heavy quark limit of Coulomb gauge QCD, in particular the simple connection between the non-perturbative Green's functions of Yang–Mills theory and the confinement potential. Landau gauge results on the infrared Yang–Mills propagators are also briefly reviewed. We then focus on less common applications, in graphene and high-temperature superconductivity. We discuss recent developments, and present theoretical predictions that are supported by experimental findings.

TWISTORS, YANG-MILLS AMPLITUDES AND LANDAU LEVELS

2005 ◽  
Vol 20 (27) ◽  
pp. 6107-6121
Author(s):  
V. P. NAIR
Keyword(s):  
Twistor Space ◽  
Point Of View ◽  
Wave Functions ◽  
Landau Levels ◽  
Holomorphic Curves ◽  
Short Discussion ◽  
Yang Mills ◽  
Lowest Landau Level ◽  
Recent Developments ◽  
Discussion Review

We give a short discussion/review of the recent developments expressing the perturbative scattering amplitudes in Yang-Mills theory, specifically for the [Formula: see text] theory, in terms of holomorphic curves in a supersymmetric twistor space. Holomorphic curves, which are maps of CP1 to the supertwistor space, can also be interpreted as the lowest Landau level wave functions; this point of view is also briefly explained.

scholarly journals The Gribov phenomenon in flat and curved spaces

2014 ◽  
Vol 11 (03) ◽  
pp. 1450018
Author(s):  
Marco de Cesare
Keyword(s):  
Integral Formula ◽  
Functional Integral ◽  
Green Functions ◽  
Ghost Propagator ◽  
Yang Mills ◽  
Color Confinement ◽  
Spacetime Curvature ◽  
Gauge Fixing ◽  
Recent Developments ◽  
Gribov Ambiguity

The quantization of Yang–Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well-known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider, in particular, the SU (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass gap problem and on color confinement. We discuss some recent developments on the subject in the case of a curved background. We argue that the concurrent presence of a spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared.

scholarly journals AN INTRODUCTION TO QUANTUM GRAVITY

2008 ◽  
Vol 05 (01) ◽  
pp. 101-156 ◽  
Author(s):  
BRYCE S. DEWITT ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Quantum Gravity ◽  
Functional Integral ◽  
Formal Structure ◽  
Kind Permission ◽  
Covariant Formalism ◽  
Yang Mills ◽  
Recent Developments ◽  
Basic Concepts ◽  
Short Time ◽  
Business Media

After an overview of the physical motivations for studying quantum gravity, we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargèse Lectures in Levy & Deser (1979): Recent Developments in Gravitation pp. 275–322 by Professor B. S. DeWitt, with kind permission of Springer Science and Business Media. The reader is therefore introduced, in a pedagogical way, to the functional integral quantization of gravitation and Yang–Mills theory. It is hoped that such a paper will remain useful for all lecturers or Ph.D. students who face the task of introducing (resp. learning) some basic concepts in quantum gravity in a relatively short time. In the second part, we outline selected topics such as the braneworld picture with the same covariant formalism of the first part, and spectral asymptotics of Euclidean quantum gravity with diffeomorphism-invariant boundary conditions. The latter might have implications for singularity avoidance in quantum cosmology.

COMMENTS ON GLUON SCATTERING AMPLITUDES IN $\mathcal{N} = 4$ SUPER YANG-MILLS THEORY AT STRONG COUPLING

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2135-2142 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Scattering Amplitudes ◽  
Strong Coupling ◽  
Yang Mills ◽  
Recent Developments ◽  
Point Amplitude ◽  
Super Yang Mills Theory

We review recent developments in calculation of the gluon scattering amplitudes in [Formula: see text] super Yang-Mills theory at strong coupling via AdS/CFT correspondence. We discuss certain class of 6 and 8 point amplitudes at strong coupling, which can be obtained by cutting and gluing the 4-point amplitude.

scholarly journals Exact properties of an integrated correlator in $$ \mathcal{N} $$ = 4 SU(N) SYM

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Daniele Dorigoni ◽  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Asymptotic Series ◽  
Perturbative Expansion ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Recent Developments ◽  
Rational Multiple ◽  
Zeta Values ◽  
The Subject ◽  
Perturbative Corrections

Abstract We present a novel expression for an integrated correlation function of four superconformal primaries in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills ($$ \mathcal{N} $$ N = 4 SYM) theory. This integrated correlator, which is based on supersymmetric localisation, has been the subject of several recent developments. In this paper the correlator is re-expressed as a sum over a two dimensional lattice that is valid for all N and all values of the complex Yang-Mills coupling $$ \tau =\theta /2\pi +4\pi i/{g}_{\mathrm{YM}}^2 $$ τ = θ / 2 π + 4 πi / g YM 2 . In this form it is manifestly invariant under SL(2, ℤ) Montonen-Olive duality. Furthermore, it satisfies a remarkable Laplace-difference equation that relates the SU(N) correlator to the SU(N + 1) and SU(N − 1) correlators. For any fixed value of N the correlator can be expressed as an infinite series of non-holomorphic Eisenstein series, $$ E\left(s;\tau, \overline{\tau}\right) $$ E s τ τ ¯ with s ∈ ℤ, and rational coefficients that depend on the values of N and s. The perturbative expansion of the integrated correlator is an asymptotic but Borel summable series, in which the n-loop coefficient of order (gYM/π)2n is a rational multiple of ζ(2n + 1). The n = 1 and n = 2 terms agree precisely with results determined directly by integrating the expressions in one-loop and two-loop perturbative $$ \mathcal{N} $$ N = 4 SYM field theory. Likewise, the charge-k instanton contributions (|k| = 1, 2, . . .) have an asymptotic, but Borel summable, series of perturbative corrections. The large-N expansion of the correlator with fixed τ is a series in powers of $$ {N}^{\frac{1}{2}-\mathrm{\ell}} $$ N 1 2 − ℓ (ℓ ∈ ℤ) with coefficients that are rational sums of $$ E\left(s;\tau, \overline{\tau}\right) $$ E s τ τ ¯ with s ∈ ℤ + 1/2. This gives an all orders derivation of the form of the recently conjectured expansion. We further consider the ’t Hooft topological expansion of large-N Yang-Mills theory in which $$ \lambda ={g}_{\mathrm{YM}}^2N $$ λ = g YM 2 N is fixed. The coefficient of each order in the 1/N expansion can be expanded as a series of powers of λ that converges for |λ| < π2. For large λ this becomes an asymptotic series when expanded in powers of $$ 1/\sqrt{\lambda } $$ 1 / λ with coefficients that are again rational multiples of odd zeta values, in agreement with earlier results and providing new ones. We demonstrate that the large-λ series is not Borel summable, and determine its resurgent non-perturbative completion, which is $$ O\left(\exp \left(-2\sqrt{\lambda}\right)\right) $$ O exp − 2 λ .

scholarly journals Two Applications of the Analytic Conformal Bootstrap: A Quick Tour Guide

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 247
Author(s):  
Agnese Bissi ◽  
Parijat Dey ◽  
Giulia Fardelli
Keyword(s):  
Operator Product ◽  
Analytic Structure ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Large N ◽  
Fisher Model ◽  
Recent Developments ◽  
Analytic Aspect

We reviewed the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are solely based on symmetries, particularly on the analytic structure and in the associativity of the operator product expansion. We focused on two applications of the analytic conformal bootstrap: the study of the ϵ expansion of the Wilson–Fisher model via the introduction of a dispersion relation and the large N expansion of the maximally supersymmetric Super Yang–Mills theory in four dimensions.

Trends in Electron Energy Loss Spectroscopy

1977 ◽  
Vol 35 ◽  
pp. 228-229
Author(s):  
C. Colliex ◽  
P. Trebbia
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Materials Science ◽  
Analytical Technique ◽  
Recent Developments ◽  
Quantitative Results ◽  
Electron Microscopes ◽  
Electron Energy Loss ◽  
Primary Electrons

The physical foundations for the use of electron energy loss spectroscopy towards analytical purposes, seem now rather well established and have been extensively discussed through recent publications. In this brief review we intend only to mention most recent developments in this field, which became available to our knowledge. We derive also some lines of discussion to define more clearly the limits of this analytical technique in materials science problems.The spectral information carried in both low ( 0<ΔE<100eV ) and high ( >100eV ) energy regions of the loss spectrum, is capable to provide quantitative results. Spectrometers have therefore been designed to work with all kinds of electron microscopes and to cover large energy ranges for the detection of inelastically scattered electrons (for instance the L-edge of molybdenum at 2500eV has been measured by van Zuylen with primary electrons of 80 kV). It is rather easy to fix a post-specimen magnetic optics on a STEM, but Crewe has recently underlined that great care should be devoted to optimize the collecting power and the energy resolution of the whole system.

Filaments and membranes in the mitotic apparatus

1983 ◽  
Vol 41 ◽  
pp. 544-547
Author(s):  
Kent McDonald
Keyword(s):  
Intermediate Filaments ◽  
Mitotic Spindle ◽  
Mitotic Apparatus ◽  
Light Microscope Level ◽  
Microtubule Associated Proteins ◽  
Recent Developments ◽  
Associated Proteins ◽  
Force Generator ◽  
Spindle Function ◽  
Antibody Technology

At the light microscope level the recent developments and interest in antibody technology have permitted the localization of certain non-microtubule proteins within the mitotic spindle, e.g., calmodulin, actin, intermediate filaments, protein kinases and various microtubule associated proteins. Also, the use of fluorescent probes like chlorotetracycline suggest the presence of membranes in the spindle. Localization of non-microtubule structures in the spindle at the EM level has been less rewarding. Some mitosis researchers, e.g., Rarer, have maintained that actin is involved in mitosis movements though the bulk of evidence argues against this interpretation. Others suggest that a microtrabecular network such as found in chromatophore granule movement might be a possible force generator but there is little evidence for or against this view. At the level of regulation of spindle function, Harris and more recently Hepler have argued for the importance of studying spindle membranes. Hepler also believes that membranes might play a structural or mechanical role in moving chromosomes.

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