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Instantons in QCD
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We review the theory and phenomenology of instantons in QCD. After a general overview, we provide a pedagogical introduction to semi-classical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. We also discuss properties of instantons at finite temperature and the chiral phase transition. We give an overview over the importance of instantons in some other models, in particular two dimensional sigma models, electroweak theory and supersymmetric QCD.
Forward citations
Cited by 27 Pith papers
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Polarized Nucleon as a Topological Dipole
A polarized nucleon generically hosts a topological charge dipole q_top ∝ S · r̂ whose moment equals −ΔΣ/N_f in the chiral limit.
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Fermions and the Renormalisation Group at Large N
At large N, fermionic quantum field theories have exact effective actions depending only on flavour-singlet fermion bilinears, making the local potential approximation exact and yielding new conformal fixed points.
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Search for soft unclustered energy patterns in proton-proton collisions at $\sqrt{s}$ = 13 TeV using data scouting
No SUEP signal is observed in CMS scouting data; the search sets the most stringent limits to date on gluon-fusion production of heavy scalars decaying to SUEP-like final states.
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Experimental access to the gluonic origin of the proton mass
The scalar gluonic trace form factor of the proton can be reconstructed from DVCS quark GFFs, near-threshold J/ψ gluon GFFs, and the nucleon sigma-term form factor.
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Heavy mesons from the QCD instanton vacuum beyond the static limit
Computes f_B, residual mass Λ, kinetic matrix element λ1, and Isgur-Wise slope in instanton vacuum with finite-mass heavy-light vertex calibrated to B data.
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Instanton condensation and a new phase of BPS black holes
Instanton condensation in the matrix model for the BPS index reveals a new instability and dominant phase for small black holes, connected to partial deconfinement.
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Weak Scale Triggers in the SMEFT
No weak scale triggers exist in the SMEFT up to dimension six (and likely eight) that can solve the hierarchy problem far above the weak scale.
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The One-Loop QCD $\beta$-Function as an Index
The one-loop QCD beta-function coefficient b and the Weyl anomaly difference a-c are computed as the first Chern class of a determinant line bundle via Grothendieck-Riemann-Roch on twistor space.
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Self-dual monopole loops, instantons and confinement
Interactions among self-dual monopole-like constituents of instantons remove the infrared divergence and, the authors conjecture, drive confinement in 4d Yang-Mills.
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Perception in Plan: Coupled Perception and Planning for End-to-End Autonomous Driving
The supplied body text is an unrelated physics preprint (arXiv:2508.11491), so the advertised autonomous-driving results cannot be verified from this submission.
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Pentaquarks made of light quarks and their admixture to baryons
Light pentaquark wavefunctions are constructed from permutation symmetry, and a nucleon-pentaquark mixing model yields a five-quark Fock probability P5q of order 0.4.
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Chiral-odd generalized parton distributions in the large-$N_{c}$ limit of QCD: Next-to-leading-order contributions
Derives the NLO (1/Nc) chiral-odd GPDs in the pion mean-field picture, proves polynomiality and sum rules, and gives gradient-expansion estimates partially matching lattice QCD.
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Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures
Using Möbius domain-wall fermions in two-flavor QCD, the authors find that vector/axial-vector and tensor/axial-tensor screening masses become degenerate above Tc, while the chiral-spin A-X splitting stays around 40 M...
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Nucleon tensor form factors at large $N_{c}$
In the pion mean-field picture at large Nc, the nucleon tensor charge and anomalous tensor magnetic moment are valence dominated, while the tensor quadrupole moment is sea dominated and strongly enhanced near the chir...
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Electromagnetic form factors of the nucleon from the instanton vacuum
Nucleon EM form factors computed in instanton vacuum model with parameters fixed by saddle-point equation yield proton charge radius 0.841 fm matching muonic hydrogen and good agreement on Q2 dependence of ratios.
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Quark orbital angular momentum as a chiral magnetic effect
The calculation yields a large negative orbital angular momentum L_{u-d} from chiral magnetic effects that partially cancels the positive spin contribution and reduces total J_{u-d} to match lattice QCD.
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The color force acting on a quark in the pion and nucleon
In the instanton liquid model, the color force on a struck quark in the pion and nucleon is derived from twist-3 operators, related to gravitational and transversity form factors, and mapped in the transverse plane wi...
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Nucleon and singly heavy baryons from the QCD instanton vacuum
A chiral soliton model with a momentum-dependent quark mass from the instanton vacuum predicts Delta-N and Sigma_Q-Lambda_Q mass splittings of 214 and 206 MeV.
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Holographic correlation functions of fermions in anisotropic plasma
Generalizes the holographic prescription for fermionic retarded Green's functions to anisotropic geometries and numerically evaluates direction-dependent features, instabilities, Landau levels, and a pseudogap in thre...
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Multipole structure of the nucleon tensor form factors
In the chiral quark-soliton model with 1/N_c corrections, the isoscalar tensor charge is 0.81, the isovector anomalous tensor magnetic moment is 1.97, and the isoscalar tensor quadrupole moment is 5.98, completing the...
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The imaginary-$\theta$ dependence of the SU($N$) spectrum
The theta-squared curvature of the SU(3) glueball mass and string tension is measured in the continuum, and the N=3 and N=6 data support the expected large-N 1/N^2 scaling.
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Anomalies, Topology, and Hadron Structure in QCD
A review unifying the QCD axial and trace anomalies with vacuum topology, arguing that the proton spin puzzle and the U(1)_A problem are both controlled by topological screening encoded in the susceptibility slope χ′(0).
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Hunting for QCD Instantons
Outlines signatures and backgrounds for searching QCD instantons in diffractive LHC events and via hyperon spin correlations at NICA.
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Experimental Search for the Chiral Magnetic Effect in Relativistic Heavy-Ion Collisions: A Perspective
The chiral magnetic effect in heavy-ion collisions remains unconfirmed, with current data giving a 2.9-sigma hint in Au+Au and an upper limit near 10% in isobar collisions.
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CP conservation in the strong interactions
CP conservation in QCD follows from taking the infinite volume limit prior to summing over topological sectors, shown consistent with steepest-descent contours and chiral EFT.
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What is the Quark-Gluon Plasma made of?
The quark-gluon plasma is best described as a strongly coupled liquid of massive, very short-lived quark and gluon quasiparticles, with sound (phonon) modes becoming the most well-defined collective excitation at low momenta.
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Generic framework for non-perturbative QCD in light hadrons
The instanton liquid model, with instanton size, density, and quark mass as its main inputs, is presented as a generic framework for light-hadron vacuum condensates, matrix elements, and form factors.
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