scholarly journals POTENTIAL ENERGY OF YANG–MILLS VORTICES IN THREE AND FOUR DIMENSIONS

1999 ◽  
Vol 14 (25) ◽  
pp. 1725-1732 ◽  
Author(s):  
DMITRI DIAKONOV
Keyword(s):  
Magnetic Flux ◽  
Potential Energy ◽  
Wilson Loop ◽  
Parallel Line ◽  
Vortex Center ◽  
Four Dimensions ◽  
Yang Mills ◽  
Loop Approximation ◽  
The One

We calculate the energy of a Yang–Mills vortex as function of its magnetic flux or as the Wilson loop surrounding the vortex center. The calculation is performed in the one-loop approximation. A parallel line with a potential as function of the Polyakov at nonzero temperatures is drawn. We find that quantized Z(2) vortices are dynamically preferred though vortices with arbitrary fluxes cannot be ruled out.

NULL ZIG-ZAG WILSON LOOPS IN $\mathcal{N}=4$ SYM

2010 ◽  
Vol 25 (08) ◽  
pp. 627-639
Author(s):  
ZHIFENG XIE
Keyword(s):  
Perturbation Theory ◽  
Wilson Loop ◽  
Wilson Loops ◽  
Finite Part ◽  
Expectation Value ◽  
Line Segments ◽  
Yang Mills ◽  
Circular Shape ◽  
The One ◽  
Arbitrary Shapes

In planar [Formula: see text] supersymmetric Yang–Mills theory we have studied one kind of (locally) BPS Wilson loops composed of a large number of light-like segments, i.e. null zig-zags. These contours oscillate around smooth underlying spacelike paths. At one-loop in perturbation theory, we have compared the finite part of the expectation value of null zig-zags to the finite part of the expectation value of non-scalar-coupled Wilson loops whose contours are the underlying smooth spacelike paths. In arXiv:0710.1060 [hep-th] it was argued that these quantities are equal for the case of a rectangular Wilson loop. Here we present a modest extension of this result to zig-zags of circular shape and zig-zags following non-parallel, disconnected line segments and show analytically that the one-loop finite part is indeed that given by the smooth spacelike Wilson loop without coupling to scalars which the zig-zag contour approximates. We make some comments regarding the generalization to arbitrary shapes.

scholarly journals QUARKS AS TOPOLOGICAL DEFECTS — OR, WHAT IS CONFINED INSIDE A HADRON?

1993 ◽  
Vol 08 (31) ◽  
pp. 5575-5604 ◽  
Author(s):  
A. KOVNER ◽  
B. ROSENSTEIN
Keyword(s):  
Magnetic Flux ◽  
Topological Charge ◽  
Domain Walls ◽  
Topological Defects ◽  
Complex Scalar ◽  
Yang Mills ◽  
Effective Lagrangian ◽  
Local Complex ◽  
Complex Scalar Field ◽  
The One

We present a picture of confinement based on representation of constituent quarks as pointlike topological defects. The topological charge carried by quarks and confined in hadrons is explicitly constructed in terms of Yang-Mills variables. In 2+1 dimensions we are able to construct a local complex scalar field V(x), in terms of which the topological charge is [Formula: see text]. The VEV of the field V in the confining phase is nonzero and the charge is the winding number corresponding to homotopy group π1(S1). Quarks carry the charge Q and therefore are topological solitons. The phase rotation of V is generated by the operator of magnetic flux. Unlike in QED, the U(1) magnetic flux is explicitly broken by the monopoles. This results in formation of a string between a quark and an antiquark. The effective Lagrangian for V is derived in models with adjoint and fundamental quarks. This topological mechanism of confinement is basically different from the one proposed by ’t Hooft in which the elementary objects are linelike domain walls. A baryon is described as a Y-shaped configuration of strings. In 3+1 dimensions the explicit expression for V, and therefore a detailed picture, is not available. However, assuming the validity of the same mechanism we point out several interesting qualitative consequences.

scholarly journals Twistor Parametrization of Locally BPS Super-Wilson Loops

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Cristian Vergu
Keyword(s):  
Correlation Function ◽  
Wilson Loop ◽  
Point Of View ◽  
Scalar Coupling ◽  
Wilson Loops ◽  
Yang Mills ◽  
The One

We consider the kinematics of the locally BPS super-Wilson loop in N=4 super-Yang-Mills with scalar coupling from a twistorial point of view. We find that the kinematics can be described either as supersymmetrized pure spinors or as a point in the product of two super-Grassmannian manifolds G2∣2(4∣4)×G2∣2(4∣4). In this description of the kinematics the scalar–scalar correlation function appearing in the one-loop evaluation of the super-Wilson loop can be neatly written as a sum of four superdeterminants.

scholarly journals One-Loop Renormalization of General Noncommutative Yang–Mills Field Model Coupled to Scalar and Spinor Fields

2003 ◽  
Vol 18 (17) ◽  
pp. 3057-3088 ◽  
Author(s):  
I. L. Buchbinder ◽  
V. A. Krykhtin
Keyword(s):  
Field Model ◽  
Coupling Constants ◽  
Noncommutative Field Theory ◽  
Yang Mills ◽  
Interaction Terms ◽  
Spinor Fields ◽  
Loop Approximation ◽  
The One ◽  
Mills Field ◽  
Matter Fields

We study the theory of noncommutative U (N) Yang–Mills field interacting with scalar and spinor fields in the fundamental and the adjoint representations. We include in the action both the terms describing interaction between the gauge and the matter fields and the terms which describe interaction among the matter fields only. Some of these interaction terms have not been considered previously in the context of noncommutative field theory. We find all counterterms for the theory to be finite in the one-loop approximation. It is shown that these counterterms allow to absorb all the divergencies by renormalization of the fields and the coupling constants, so the theory turns out to be multiplicatively renormalizable. In case of 1PI gauge field functions the result may easily be generalized on an arbitrary number of the matter fields. To generalize the results for the other 1PI functions it is necessary for the matter coupling constants to be adapted in the proper way. In some simple cases this generalization for a part of these 1PI functions is considered.

scholarly journals QUANTUM DILATONIC GRAVITY IN d=2,4 AND 5 DIMENSIONS

2001 ◽  
Vol 16 (06) ◽  
pp. 1015-1108 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Black Hole ◽  
Effective Action ◽  
Gauge Coupling ◽  
Conformal Anomaly ◽  
De Sitter ◽  
Nonzero Temperature ◽  
Four Dimensions ◽  
Yang Mills ◽  
Renormalization Group Equations ◽  
The One

We review (mainly) quantum effects in the theories where the gravity sector is described by metric and dilaton. The one-loop effective action for dilatonic gravity in two and four dimensions is evaluated. Renormalization group equations are constructed. The conformal anomaly and induced effective action for 2d and 4d dilaton coupled theories are found. It is applied to the study of quantum aspects of black hole thermodynamics, like calculation of Hawking radiation and quantum corrections to black hole parameters and investigation of quantum instability for such objects with multiple horizons. The use of the above effective action in the construction of nonsingular cosmological models in Einstein or Brans–Dicke (super)gravity and investigation of induced wormholes in supersymmetric Yang–Mills theory are given.5d dilatonic gravity (bosonic sector of compactified IIB supergravity) is discussed in connection with bulk/boundary (or AdS/CFT) correspondence. Running gauge coupling and quark–antiquark potential for boundary gauge theory at zero or nonzero temperature are calculated from d=5 dilatonic anti-de Sitter-like background solution which represents anti-de Sitter black hole for periodic time.

Operator regularization and massive Yang–Mills theory

1990 ◽  
Vol 68 (10) ◽  
pp. 1149-1156 ◽  
Author(s):  
L. Culumovic ◽  
D. G. C. McKeon ◽  
T. N. Sherry
Keyword(s):  
Arbitrary Order ◽  
Practical Method ◽  
Log P ◽  
Arbitrary Parameter ◽  
Vector Particle ◽  
Four Dimensions ◽  
Yang Mills ◽  
Pole Structure ◽  
The One ◽  
Higgs Scalar

Operator regularization has proved to be a practical method for computing finite, symmetry preserving Green's functions to arbitrary order in perturbation theory. This finiteness has been shown to persist in such nonrenormalizable theories as [Formula: see text] and quantum gravity; in this paper we apply the technique to massive gauge theories. The mass for the vector particle is inserted by hand using the Stueckleberg–Kunimasa–Goto mechanism; no degree of freedom associated with the Higgs scalar is present in the initial Lagrangian. Several one-loop calculations serve to illustrate that no divergences ever arise in this theory if one uses operator regularization. The one-loop effective action is examined in both 4 and n = (4 − ε) dimensions. The result is finite in 4 dimensions and in (4 − ε) dimensions has the pole structure at ε = 0 found by Kafiev. In four dimensions, we find that, in contrast to the case of renormalizable theories, radiatively induced interactions occur with coefficients depending on log (p2/μ2). Consequently μ2 is no longer an arbitrary parameter but must be fixed experimentally.

scholarly journals The integrable (hyper)eclectic spin chain

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changrim Ahn ◽  
Matthias Staudacher
Keyword(s):  
Spin Chain ◽  
Nearest Neighbor ◽  
Inverse Scattering Method ◽  
Spin Chains ◽  
Scattering Method ◽  
Yang Mills ◽  
Deformation Parameters ◽  
Dilatation Operator ◽  
The One ◽  
State Spin

Abstract We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills Theory.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

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