scholarly journals A note on one-loop cluster adjacency in $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jorge Mago ◽  
Anders Schreiber ◽  
Marcus Spradlin ◽  
Anastasia Volovich
Keyword(s):  
Yang Mills ◽  
Plücker Coordinates ◽  
The One ◽  
Weak Separation

Abstract We study cluster adjacency conjectures for amplitudes in maximally supersymmetric Yang-Mills theory. We show that the n-point one-loop NMHV ratio function satisfies Steinmann cluster adjacency. We also show that the one-loop BDS-like normalized NMHV amplitude satisfies cluster adjacency between Yangian invariants and final symbol entries up to 9-points. We present conjectures for cluster adjacency properties of Plücker coordinates, quadratic cluster variables, and NMHV Yangian invariants that generalize the notion of weak separation.

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 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 NONCOMMUTATIVE U(1) SUPER-YANG–MILLS THEORY: PERTURBATIVE SELF-ENERGY CORRECTIONS

2004 ◽  
Vol 19 (25) ◽  
pp. 4231-4249 ◽  
Author(s):  
A. A. BICHL ◽  
M. ERTL ◽  
A. GERHOLD ◽  
J. M. GRIMSTRUP ◽  
L. POPP ◽  
...  
Keyword(s):  
Power Counting ◽  
The Self ◽  
Field Theories ◽  
Yang Mills ◽  
Self Energy ◽  
Supersymmetric Field Theories ◽  
Crucial Feature ◽  
The One ◽  
Infrared Divergences ◽  
Super Yang Mills Theory

The quantization of the noncommutative [Formula: see text], U(1) super-Yang–Mills action is performed in the superfield formalism. We calculate the one-loop corrections to the self-energy of the vector superfield. Although the power-counting theorem predicts quadratic ultraviolet and infrared divergences, there are actually only logarithmic UV and IR divergences, which is a crucial feature of noncommutative supersymmetric field theories.

scholarly journals Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1237
Author(s):  
Dmitry Antonov
Keyword(s):  
Gauge Boson ◽  
Effective Action ◽  
Dimensional Reduction ◽  
Higgs Model ◽  
Analytic Calculation ◽  
Standard Result ◽  
Correlation Lengths ◽  
Yang Mills ◽  
Diamagnetic Contribution ◽  
The One

We present an analytic calculation of the paramagnetic and diamagnetic contributions to the one-loop effective action in the SU(2) Higgs model. The paramagnetic contribution is produced by the gauge boson, while the diamagnetic contribution is produced by the gauge boson and the ghost. In the limit, where these particles are massless, the standard result of - 12 for the ratio of the paramagnetic to the diamagnetic contribution is reproduced. If the mass of the gauge boson and the ghost become much larger than the inverse vacuum correlation lengths of the Yang–Mills vacuum, the value of the ratio goes to - 8 . We also find that the same values of the ratio are achieved in the deconfinement phase of the model, up to the temperatures at which the dimensional reduction occurs.

scholarly journals 4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

2018 ◽  
Vol 175 ◽  
pp. 11014
Author(s):  
Kenji Hieda ◽  
Aya Kasai ◽  
Hiroki Makino ◽  
Hiroshi Suzuki
Keyword(s):  
Gradient Flow ◽  
Independent Manner ◽  
Yang Mills ◽  
Loop Level ◽  
Lattice Regularization ◽  
The One ◽  
Noether Current ◽  
Super Yang Mills Theory

The gradient flow [1–5] gives rise to a versatile method to construct renor-malized composite operators in a regularization-independent manner. By adopting this method, the authors of Refs. [6–9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D N = 1 super Yang–Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess–Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields [10].

DIVERGENT SURFACE TERMS IN NON-COVARIANT GAUGES

1991 ◽  
Vol 06 (24) ◽  
pp. 2217-2227
Author(s):  
R. B. MANN ◽  
T. RUDY
Keyword(s):  
Divergent Part ◽  
Surface Term ◽  
Yang Mills ◽  
Self Energy ◽  
Covariant Gauge ◽  
The Difference ◽  
The One

Using Leibbrandt's general prescription for regularizing (n · q)−1 poles in momentum intergrals in axial-type non-covariant gauges we show that the difference between two linearly divergent integrals which arise in such gauges yield a surface term which is logarithmically divergent. The form of divergence of this term is shown to be independent of the choice of non-covariant gauge. We show that such a term modifies the expression for the one-loop Yang–Mills self-energy evaluated using a cutoff scheme of adding to it a divergent part.

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 SUPERSYMMETRIC YANG–MILLS THEORIES WITH EXACT SUPERSYMMETRY ON THE LATTICE

2011 ◽  
Vol 26 (30n31) ◽  
pp. 5057-5132 ◽  
Author(s):  
ANOSH JOSEPH
Keyword(s):  
Field Theory ◽  
Euclidean Space ◽  
Topological Field Theory ◽  
Strongly Coupled ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Gravitational Theories ◽  
Topological Field ◽  
Perturbative Renormalization ◽  
The One

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang–Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean space–time lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice [Formula: see text] SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.

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.

MAGNETIC FIELDS AND VACUUM POLARIZATION AT THE PLANCK ERA

2003 ◽  
Vol 12 (07) ◽  
pp. 1289-1298 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vacuum State ◽  
Background Field ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Maxwell Theory ◽  
Yang Mills ◽  
Electron Positron ◽  
The One

The one-loop effective action describing polarization of the vacuum due to virtual electron-positron pairs in the Maxwell theory of electromagnetism was obtained by Heisenberg and Euler, in the limit of a background field that is constant on the scale of the electron Compton-wavelength. The case of vanishing electric field and constant, ultra-strong magnetic field B≫Bc, where [Formula: see text], yields a configuration whose energy density is less than that of the equivalent radiation field, suggesting why a magnetic field may be present in the early Universe back to the Planck era. For there is a similar but larger effect, allowing a "ferromagnetic" Yang–Mills vacuum state, in the grand-unified theory at temperatures [Formula: see text], analyzed by Skalozub. Some further aspects of ultra-strong magnetic fields are discussed vis-à-vis the origin of the Galactic field B g .

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