Wilson Loops Research Articles

Amplitudes at Strong Coupling as Hyper-Kähler Scalars.

Alday and Maldacena conjectured an equivalence between string amplitudes in AdS_{5}×S^{5} and null polygonal Wilson loops in planar N=4 super-Yang-Mills (SYM) theory. At strong coupling this identifies SYM amplitudes with areas of minimal surfaces in anti-de Sitter space. For minimal surfaces in AdS_{3}, we find that the nontrivial part of these amplitudes, the remainder function, satisfies an integrable system of nonlinear differential equations, and we give its Lax form. The result follows from a new perspective on "Y systems," which defines a new psuedo-hyper-Kähler structure directly on the space of kinematic data, via a natural twistor space defined by the Y-system equations. The remainder function is the (pseudo-)Kähler scalar for this geometry. This connection to pseudo-hyper-Kähler geometry and its twistor theory provides a new ingredient for extending recent conjectures for nonperturbative amplitudes using structures arising at strong coupling.

Four-dimensional \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 superconformal long circular quivers

We study four-dimensional \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 superconformal circular, cyclic symmetric quiver theories which are planar equivalent to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 4 super Yang-Mills. We use localization to compute nonplanar corrections to the free energy and the circular half-BPS Wilson loop in these theories for an arbitrary number of nodes, and examine their behaviour in the limit of long quivers. Exploiting the relationship between the localization quiver matrix integrals and an integrable Bessel operator, we find a closed-form expression for the leading nonplanar correction to both observables in the limit when the number of nodes and ’t Hooft coupling become large. We demonstrate that it has different asymptotic behaviour depending on how the two parameters are compared, and interpret this behaviour in terms of properties of a lattice model defined on the quiver diagram.

Unscreened forces in the quark-gluon plasma?

We study the correlator of temporal Wilson lines at nonzero temperature in 2+1 flavor lattice QCD with the aim to define the heavy quark-antiquark potential at nonzero temperature. For temperatures 153 MeV≤T≤352 MeV the spectral representation of this correlator is consistent with a broadened peak in the spectral function, position, or width of which then defines the real or imaginary parts of the heavy quark-antiquark potential at nonzero temperature, respectively. We find that the potential’s real part is not screened contrary to the widely held expectations. We comment on how this fact may modify the picture of quarkonium melting in the quark-gluon plasma. Published by the American Physical Society 2024

Directional Prediction of Financial Time Series Using SVM and Wilson Loop Perceptron

Directional Prediction of Financial Time Series Using SVM and Wilson Loop Perceptron

Nonperturbative Collins-Soper kernel from chiral quarks with physical masses

We present a lattice QCD calculation of the rapidity anomalous dimension of quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS) kernel, up to transverse separations of about 1 fm. This unitary lattice calculation is conducted, for the first time, employing the chiral-symmetry-preserving domain wall fermion discretization and physical values of light and strange quark masses. The CS kernel is extracted from the ratios of pion quasi-transverse-momentum-dependent wave functions (quasi-TMDWFs) at next-to-leading logarithmic perturbative accuracy. Also for the first time, we utilize the recently proposed Coulomb-gauge-fixed quasi-TMDWF correlator without a Wilson line. We observe significantly slower signal decay with increasing quark separations compared to the established gauge-invariant method with a staple-shaped Wilson line. This enables us to determine the CS kernel at large nonperturbative transverse separations and find its near-linear dependence on the latter. Our result is consistent with the recent lattice calculation using gauge-invariant quasi-TMDWFs, and agrees with various recent phenomenological parametrizations of experimental data.

Wilson loops and wormholes

We analyse the properties of Wilson loop observables for holographic gauge theories, when the dual bulk geometries have a single and/or multiple boundaries (Euclidean spacetime wormholes). Such observables lead to a generalisation and refinement of the characterisation in [1] based on the compressibility of cycles and the pinching limit of higher genus Riemann surfaces, since they carry information about the dynamics and phase structure of the dual gauge theory of an arbitrary dimensionality. Finally, we describe how backreacting correlated observables such as Wilson loops can lead to wormhole saddles in the dual gravitational path integral, by taking advantage of a representation theoretic entanglement structure proposed in [13, 15].

Photoinduced Electronic and Spin Topological Phase Transitions in Monolayer Bismuth.

Ultrathin bismuth exhibits rich physics including strong spin-orbit coupling, ferroelectricity, nontrivial topology, and light-induced structural dynamics. We use abinitio calculations to show that light can induce structural transitions to four transient phases in bismuth monolayers. These light-induced phases exhibit nontrivial topological character, which we illustrate using the recently introduced concept of spin bands and spin-resolved Wilson loops. Specifically, we find that the topology changes via the closing of the electron and spin band gaps during photoinduced structural phase transitions, leading to distinct edge states. Our study provides strategies to tailor electronic and spin topology via ultrafast control of photoexcited carriers and associated structural dynamics.

Entanglement and confinement in lattice gauge theory tensor networks

We develop a transfer operator approach for the calculation of Rényi entanglement entropies in arbitrary (i.e. Abelian and non-Abelian) pure lattice gauge theory projected entangled pair states in 2+1 dimensions. It is explicitly shown how the long-range behavior of these quantities gives rise to an entanglement area law in both the thermodynamic limit and in the continuum. We numerically demonstrate the applicability of our method to the ℤ2 lattice gauge theory and relate some entanglement properties to the confinement-deconfinement transition therein. We provide evidence that Rényi entanglement entropies in certain cases do not provide a complete probe of (de)confinement properties compared to Wilson loop expectation values as other genuine (nonlocal) observables.

Mixed boundary conditions in AdS2/CFT1 from the coupling with a Kalb-Ramond field

The open string dual to a 1/6 BPS Wilson line in the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 6 super Chern-Simons-matter theory is coupled to a flat Kalb-Ramond field. We show that the resulting boundary term imposes mixed boundary conditions on the fields that describe the fluctuations on the world-sheet. These boundary conditions fix a combination of the derivatives of the fluctuations, parallel and transverse to the boundary. We holographically compute the correlation functions of insertions on the Wilson line in terms of world-sheet Witten diagrams. We observe that their functional dependence is consistent with the conformal symmetry on the line.

The planar limit of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 E-theory: numerical calculations and the large λ expansion

We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal SU(N) YM theory with hypermultiplets in the symmetric and antisymmetric representations of the gauge group. This so called E theory is closely related to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM and has a holographic description in terms of a ℤ2 orientifold of AdS5 × S5. Using recent matrix model results based on supersymmetric localization we develop efficient numerical methods to calculate two- and three-point functions of certain single trace operators as well as 1/2-BPS Wilson loop expectation values as a function of the ’t Hooft coupling λ. We use our numerical results to arrive at simple analytic expressions for these correlators valid up to sixth order in the λ−1/2 strong coupling expansion. These results provide explicit field theory predictions for the α′ corrections to the supergravity approximation of type IIB string theory on the AdS5 × S5/ℤ2 orientifold.

On reconstructing finite gauge group from fusion rules

Gauging a finite group 0-form symmetry G of a quantum field theory (QFT) results in a QFT with a Rep(G) symmetry implemented by Wilson lines. The group G determines the fusion of Wilson lines. However, in general, the fusion rules of Wilson lines do not determine G. In this paper, we study the properties of G that can be determined from the fusion rules of Wilson lines and surface operators obtained from higher-gauging Wilson lines. This is in the spirit of Richard Brauer who asked what information in addition to the character table of a finite group needs to be known to determine the group. We show that fusion rules of surface operators obtained from higher-gauging Wilson lines can be used to distinguish infinite pairs of groups which cannot be distinguished using the fusion of Wilson lines. We derive necessary conditions for two non-isomorphic groups to have the same surface operator fusion and find a pair of such groups.

Wilson loop duality and OPE for super form factors of half-BPS operators

We propose a dual Wilson loop description for the MHV super form factors of half-BPS operators in planar N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super-Yang-Mills theory. In this description, the local operators are represented by on-shell states, made out of zero-momentum particles, that are absorbed by a null periodic super Wilson loop. We present evidence for this duality at weak coupling, by performing an explicit calculation of the Wilson loop matrix elements through one loop. At tree level, the interactions localize at the cusps of the loop, revealing a simple connection between the super form factors and the m = 2 tree amplituhedron. At loop level, we show that the Wilson loop calculation reproduces the known results for the super form factors. Inspired by this duality, we extend the OPE program developed for the form factors of the Lagrangian to the super form factors of the higher-charge operators. We introduce non-perturbative axioms and conjectures for the main building blocks that govern the exchange of the lightest flux-tube excitations. These blocks appear as simple refinements of the form factor transitions introduced in earlier OPE studies. They are expressed at any value of the ’t Hooft coupling in terms of the tilted Beisert-Eden-Staudacher kernel. We carry out checks of our conjectures up to two loops at weak coupling for three- and four-point form factors of half-BPS operators of various lengths, finding perfect agreement with perturbative data.

Remarks on BPS Wilson loops in non-conformal N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 gauge theories and localization

We consider 1/2 BPS supersymmetric circular Wilson loops in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SU(N) SYM theories with massless matter content and non-vanishing β-function. Following Pestun’s approach, we can use supersymmetric localization on the sphere S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathbbm{S} $$\\end{document}4 to map these observables into a matrix model, provided that the one-loop determinants are consistently regularized. Employing a suitable procedure, we construct the regularized matrix model for these theories and show that, at order g4, the predictions for the 1/2 BPS Wilson loop match standard perturbative renormalization based on the direct evaluation of Feynman diagrams on S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathbbm{S} $$\\end{document}4. Despite conformal symmetry begin broken at the quantum level, we also demonstrate that the matrix model approaches perfectly captures the expression of the renormalized observable in flat space at this perturbative order. Moreover, we revisit in detail the difference theory approach, showing that when the β-function is non-vanishing, this method does not account for evanescent terms which are made finite by the renormalization procedure and participate to the corrections at order g6.

Large N and large representations of Schur line defect correlators

We study the large N and large representation limits of the Schur line defect correlators of the Wilson line operators transforming in the (anti)symmetric, hook and rectangular representations for \U0001d4a9 = 4 U(N) super Yang-Mills theory. By means of the factorization property, the large N correlators of the Wilson line operators in arbitrary representations can be exactly calculated in principle. In the large representation limit they turn out to be expressible in terms of certain infinite series such as Ramanujan’s general theta functions and the q-analogues of multiple zeta values (q-MZVs). Several generating functions for combinatorial objects, including partitions with non-negative cranks and conjugacy classes of general linear groups over finite fields, emerge from the large N correlators. Also we find conjectured properties of the automorphy and the hook-length expansion satisfied by the large N correlators.

Spin-resolved topology and partial axion angles in three-dimensional insulators

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- (T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{T}}}}}}}}$$\\end{document}-) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{T}}}}}}}}$$\\end{document}-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes.

Holographic renormalized entanglement and entropic c-function

We compute holographic entanglement entropy (EE) and the renormalized EE in AdS solitons with gauge potential for various dimensions. The renormalized EE is a cutoff-independent universal component of EE. Via Kaluza-Klein compactification of S1 and considering the low-energy regime, we deduce the (d − 1)-dimensional renormalized EE from the odd-dimensional counterpart. This corresponds to the shrinking circle of AdS solitons, probed at large l. The minimal surface transitions from disk to cylinder dominance as l increases. The quantum phase transition occurs at a critical subregion size, with renormalized EE showing non-monotonic behavior around this size. Across dimensions, massive modes decouple at lower energy, while degrees of freedom with Wilson lines contribute at smaller energy scales.

Topological edge and corner states in biphenylene photonic crystal.

The biphenylene network (BPN) has a unique two-dimensional atomic structure, where hexagonal unit cells are arranged on a square lattice. Inspired by such a BPN structure, we design a counterpart in the fashion of photonic crystals (PhCs), which we refer to as the BPN PhC. We study the photonic band structure using the finite element method and characterize the topological properties of the BPN PhC through the use of the Wilson loop. Our findings reveal the emergence of topological edge states in the BPN PhC, specifically in the zigzag edge and the chiral edge, as a consequence of the nontrivial Zak phase in the corresponding directions. In addition, we find the localization of electromagnetic waves at the corners formed by the chiral edges, which can be considered as second-order topological states, i.e., topological corner states.

A Wilson line realization of quantum groups

We study Wilson line operators in three-dimensional Chern–Simons theory on a manifold with boundaries and prove to leading order, through a direct calculation of Feynman integrals, that the merging of parallel Wilson lines reproduces the coproduct on the quantum group Uħ(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U_\\hbar ({\\mathfrak {g}})$$\\end{document}. We outline a connection of this theory with the moduli spaces of local systems defined by Goncharov and Shen.

Definition of fragmentation functions and the violation of sum rules

We point out a problem with the formulation and derivations of sum rules for quark fragmentation functions that impacts their validity in QCD, but which potentially points toward an improved understanding of final states in inclusive hard processes. Fragmentation functions give the distribution of final-state hadrons arising from a parton exiting a hard scattering, and the sum rules for momentum, electric charge, etc. express conservation of these quantities. The problem arises from a mismatch between the quark quantum numbers of the initial quark and the fact that all observed final-state hadrons are confined bound states with color zero. We point that, in a confining theory like QCD, the Wilson line in the operator definition of a fragmentation function entails that the final state in a fragmentation function includes a bound state in the external field generated by the Wilson line. We justify this with the aid of general features of string hadronization. The anomalous bound states are restricted to fractional momentum z=0. They tend to invalidate sum rules like the one for charge conservation when applied to the fragmentation functions inferred from experimental data but not the momentum sum rule. We propose to exploit our ideas in future studies as a way to relate the fragmentation functions extracted from inclusive cross sections to more detailed nonperturbative descriptions of final state hadronization. We also describe scenarios wherein the traditional sum rules might remain approximately valid with a reasonably high degree of accuracy. Published by the American Physical Society 2024

Chern, dipole, and quadrupole topological phases of a simple magneto-optical photonic crystal with a square lattice and an unconventional unit cell

For the study of topological phases in photonics, while quantum-Hall-type first-order chiral edge states are routinely realized in magneto-optical photonic crystals, higher-order topological states are mostly explored in all-dielectric photonic crystals. In this work, we study both first- and second-order topological photonic states in magneto-optical photonic crystals. In specific, we revisit a simple magneto-optical photonic crystal in a square lattice with one gyromagnetic cylinder in each unit cell. However, rather than investigating the conventional unit cell where the cylinder is at the center of the square unit cell as previous works have done, we consider a configuration where the cylinders are located at the four corners of the square unit cell and show that this configuration hosts rich topological phases, such as dual-band Chern, dipole, and quadrupole topological phases. Our detailed characterizations of these topological states are based on the Wannier bands and their polarizations via the Wilson loop and nested Wilson loop methods. We study in detail both the edge and corner states of the different topological phases and show that they exhibit a special feature of “spectrum robustness.” For example, though the edge and corner states of the dipole phases living in a band gap could be pushed into the bulk bands by tuning the boundary conditions, they can pass through the bulk bands and reappear within a different band gap. For dual-band quadrupole phases, we can find a regime where both band gaps host a set of corner states simultaneously and, intriguingly, the filling anomaly of one set of corner states can leave their signatures in the filling anomaly of the other set of corner states though they are separated by an extensive number of bulk states. The rich topological physics revealed in a simple magneto-optical photonic crystal not only provides new insights on higher-order topological phases in time-reversal symmetry-broken photonic systems, the results may also find promising applications by harnessing the potentials of both edge and corner states. Published by the American Physical Society 2024