Rectangular Wilson Loop Research Articles

Wilson loops and random matrices

Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories.

Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory

In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the first-principle calculation of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD using the formulation of large momentum effective theory. We provide appropriate RI′-type conditions that address the power and logarithmic divergences, as well as the mixing among staple operators of different Dirac structures, using a number of different possible projectors. A variant of RI′, including calculations of rectangular Wilson loops, which cancel the pinch-pole singularities of the staple operators at infinite length and reduce residual power divergences, is also employed. We calculate at one-loop order the conversion matrix, which relates the quasi-TMDPDFs in the RI′-type schemes to the reference scheme MS¯ for arbitrary values of the renormalization momentum scale and of the dimensions of the staple. Published by the American Physical Society 2024

Schwinger-Type Pair Production in Non-SUSY AdS/CFT

We study pair production of particles in the presence of an external electric field in a large N non-supersymmetric Yang-Mills theory using the holographic duality. The dual geometry we consider is asymptotically AdS and is effectively parametrized by two parameters, u 0 and − 5 / 2 < δ ≤ 0 , both of which can be related to the effective mass of quark/antiquark for non-supersymmetric theories. We numerically calculate the interquark potential profile and the effective potential to study pair production and analytically find out the threshold electric field beyond which one gets catastrophic pair creation by studying rectangular Wilson loops using the holographic method. We also find out the critical electric field from DBI analysis of a probe brane. Our initial investigations reveal that the critical electric field necessary for spontaneous pair production increases or decreases w.r.t. its non-supersymmetric value depending on the parameter δ . Ultimately, we find out the pair production rate of particles in the presence of an external electric field by evaluating circular Wilson loops using perturbative methods. From the later investigation, we note the resemblance with our earlier prediction. However, we also see that for and below another certain value of the parameter δ , the pair production rate of particle/antiparticle pairs blows up as the external electric field is taken to zero. We thus infer that the vacuum of the non-SUSY gauge theory is unstable for a range of non-supersymmetric parameter δ and that the geometry/non-SUSY field theory under consideration has quite different characteristics than earlier reported.

Building bulk from Wilson loops

Abstract We provide formulas for holographically building a bulk metric from given expectation values of rectangular Wilson loops. As a corollary, we prove that any confining quark potential necessarily leads to the existence of a bulk infrared bottom.

Holographic Schwinger effect in a soft wall AdS/QCD model * *Supported by the NSFC (11705166) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGL180402)

We perform a potential analysis for the holographic Schwinger effect in a deformed model with conformal invariance broken by a background dilaton. We evaluated the static potential by analyzing the classical action of a string attached to a rectangular Wilson loop on a probe D3 brane located at an intermediate position in the bulk AdS space. We observed that the inclusion of the chemical potential tends to enhance the production rate, which is opposite to the effect of the confining scale. In addition, we calculated the critical electric field based on the Dirac-Born-Infeld (DBI) action.

1/N correction in holographic Wilson loop from quantum gravity

We study 1/N corrections to a Wilson loop in holographic duality. Extending the AdS/CFT correspondence beyond the large N limit is an important but a subtle issue, as it needs quantum gravity corrections in the gravity side. To find a physical property of the quantum corrected geometry of near-horizon black 0-branes previously obtained by Hyakutake, we evaluate a Euclidean string worldsheet hanging down in the geometry, which corresponds to a rectangular Wilson loop in the SU(N) quantum mechanics with 16 supercharges at a finite temperature with finite N . We find that the potential energy defined by the Wilson loop increases due to the 1/N correction, therefore the quantum gravity correction weakens the gravitational attraction.

Holographic Wilson Loops in the Confining Backgrounds at Zero Temperature

We study Wilson loops in the exact renormalization group ow at zero tempera- ture via the 5d holographic model that reproduces the behavior of the QCD running coupling. Calculating the time-like rectangular Wilson loop we show that the model includes a conning phase at T = 0 in the IR region.

A Classical String in Lifshitz\u2013Vaidya Geometry

We study the time evolution of the expectation value of a rectangular Wilson loop in strongly anisotropic time-dependent plasma using gauge-gravity duality. The corresponding gravity theory is given by describing time evolution of a classical string in the Lifshitz–Vaidya background. We show that the expectation value of the Wilson loop oscillates about the value of the static potential with the same parameters after the energy injection is over. We discuss how the amplitude and frequency of the oscillation depend on the parameters of the theory. In particular, for the transverse case, by raising the anisotropy parameter, we observe that the amplitude and frequency of the oscillation increase. In the longitudinal case, although the amplitude of the oscillation increases for larger values of anisotropy parameter, the frequency is independent of anisotropy parameter.

Thermalization of holographic Wilson loops in spacetimes with spatial anisotropy

In this paper, we study behavior of Wilson loops in the boost-invariant nonequilibrium anisotropic quark–gluon plasma produced in heavy-ion collisions within the holographic approach. We describe the thermalization studying the evolution of the Vaidya metric in the boost-invariant and spatially anisotropic background. To probe the system during this process we calculate rectangular Wilson loops oriented in different spatial directions. We find that anisotropic effects are more visible for the Wilson loops lying in the transversal plane unlike the Wilson loops with partially longitudinal orientation. In particular, we observe that the Wilson loops can thermalizes first unlike to the order of the isotropic model. We see that Wilson loops on transversal contours have the shortest thermalization time. We also calculate the string tension and the pseudopotential at different temperatures for the static quark–gluon plasma. We show that the pseudopotential related to the configuration on the transversal plane has the screened Cornell form. We also show that the jet-quenching parameter related with the average of the light-like Wilson loop exhibits the dependence on orientations.

Instanton effects in correlation functions on the light-cone

We study instanton corrections to four-point correlation correlation function of half-BPS operators in mathcal{N} = 4 SYM in the light-cone limit when operators become null separated in a sequential manner. We exploit the relation between the correlation function in this limit and light-like rectangular Wilson loop to determine the leading instanton contribution to the former from the semiclassical result for the latter. We verify that the light-like rectangular Wilson loop satisfies anomalous conformal Ward identities nonperturbatively, in the presence of instantons. We then use these identities to compute the leading instanton contribution to the light-like cusp anomalous dimension and to anomalous dimension of twist-two operators with large spin.

Holographic Wilson loops in anisotropic quark-gluon plasma.

The nonequilibrium properties of the anisotropic quark-gluon plasma are con- didered from the holographic viewpoint. Lifshitz-like solution is considered as a holo- graphic dual of anisotropic QGP. The black brane formation in such background is con- sidered as a thermalization in dual theory. As a probe of thermalization we consider rectangular spatial Wilson loops with different orientation.

Holographic thermalization with Weyl corrections

We consider holographic thermalization in the presence of a Weyl correction in five dimensional AdS space. We first obtain the Weyl corrected black brane solution perturbatively, up to first order in the coupling. The corresponding AdS-Vaidya like solution is then constructed. This is then used to numerically analyze the time dependence of the two point correlation functions and the expectation values of rectangular Wilson loops in the boundary field theory, and we discuss how the Weyl correction can modify the thermalization time scales in the dual field theory. In this context, the subtle interplay between the Weyl coupling constant and the chemical potential is studied in detail.

Probing Wilson loops in AdS/QCD

We use AdS/QCD to analyze the quark and gluon scalar and pseudo-scalar condensates around static color sources described by a circular Wilson loop. We also derive the static dipole-dipole interactions between rectangular Wilson loops in AdS/QCD and discuss their relevance for static string interactions in QCD at strong coupling.

Probing Wilson loops in the QCD instanton vacuum

We discuss the quark and gluon condensates in the presence of a rectangular Wilson loop using the QCD instanton vacuum with three light dynamical quarks. The scalar quark condensate is found to decrease while the gluon condensate increases. We also derive the static potential between two QCD dipoles and show that it is attractive but short ranged at large distances. Its relevance to static QCD string interactions is discussed.

Renormalization of loop functions in QCD

We give a short overview of the renormalization properties of rectangular Wilson loops, the Polyakov loop correlator and the cyclic Wilson loop. We then discuss how to renormalize loops with more than one intersection, using the simplest non-trivial case as an illustrative example. Our findings expand on previous treatments. The generalized exponentiation theorem is applied to the Polyakov loop correlator and used to renormalize linear divergences in the cyclic Wilson loop.

Nonequilibrium Wilson loops inN=4super Yang-Mills theory

We consider rectangular Wilson loops in certain nonequilibrium quantum states in $\mathcal{N}=4$ super Yang-Mills theory at weak coupling, prepared with a quantum quench. We find that in the ladder approximation, the Bethe-Salpeter equation can be reduced to solving a massive $1+1$ dimensional wave equation with a leaking boundary condition leading to a quasinormal behavior analogous to what is found in studying dynamics of fields in black hole backgrounds. Furthermore, we find that the Wilson loops with size $L$ approach a thermal form after time $T\ensuremath{\approx}L/2$. The thermal form found in the current paper follows from the particular initial state chosen.

Estimates for the thermal width of heavy quarkonia in strongly coupled plasmas from holography

The gauge/gravity duality is used to investigate the imaginary part of the heavy quark potential (defined via the rectangular Wilson loop) in strongly coupled plasmas. This quantity can be used to estimate the width of heavy quarkonia in a plasma at strong coupling. In this paper the thermal worldsheet fluctuation method, proposed in [J.Noronha and A.Dumitru, Phys.\ Rev.\ Lett.\ {\bf 103}, 152304 (2009)], is revisited and general conditions for the existence of an imaginary part for the heavy quark potential computed within classical gravity models are obtained. We prove a general result that establishes the connection between this imaginary part of the potential determined holographically and the area law displayed by the Wilson loop in the vacuum of confining gauge theories. We also determine the imaginary part of the heavy quark potential in a strongly coupled plasma dual to Gauss-Bonnet gravity. This provides an estimate of how the thermal width of heavy quarkonia changes with the shear viscosity to entropy density ratio, $\eta/s$, at strong coupling.

Holographic Wilson loops, dielectric interfaces, and topological insulators

We use holography to study ($3+1$)-dimensional $\mathcal{N}=4$ supersymmetric $\mathrm{SU}({N}_{c})$ Yang-Mills theory (SYM) in the large-${N}_{c}$ and large-coupling limits, with a ($2+1$)-dimensional interface where the Yang-Mills coupling or $\ensuremath{\theta}$ angle changes value, or ``jumps.'' We consider interfaces that either break all supersymmetry or that preserve half of the $\mathcal{N}=4$ supersymmetry thanks to certain operators localized to the interface. Specifically, we compute the expectation values of a straight timelike Wilson line and of a rectangular Wilson loop in the fundamental representation of $\mathrm{SU}({N}_{c})$. The former gives us the self-energy of a heavy test charge while the latter gives us the potential between heavy test charges. A jumping coupling or $\ensuremath{\theta}$ angle acts much like a dielectric interface in electromagnetism: the self-energy or potential includes the effects of image charges. $\mathcal{N}=4$ SYM with a jumping $\ensuremath{\theta}$ angle may also be interpreted as the low-energy effective description of a fractional topological insulator, as we explain in detail. For nonsupersymmetric interfaces, we find that the self-energy and potential are qualitatively similar to those in electromagnetism, despite the differences between $\mathcal{N}=4$ SYM and electromagnetism. For supersymmetric interfaces, we find dramatic differences from electromagnetism which depend sensitively on the coupling of the test charge to the adjoint scalars of $\mathcal{N}=4$ SYM. In particular, we find one special case where a test charge has a vanishing image charge.

Erratum: new numerical results and novel effective string predictions for Wilson loops

We compute the prediction of the Nambu-Goto effective string model for a rectangular Wilson loop up to three loops. This is done through the use of an operatorial, first order formulation and of the open string analogues of boundary states. This result is interesting since there are universality theorems stating that the predictions up to three loops are common to all effective string models. To test the effective string prediction, we use a Montecarlo evaluation, in the 3 d Ising gauge model, of an observable (the ratio of two Wilson loops with the same perimeter) for which boundary effects are relatively small. Our simulation attains a level of precision which is sufficient to test the two-loop correction. The three-loop correction seems to go in the right direction, but is actually yet beyond the reach of our simulation, since its effect is comparable with the statistical errors of the latter.

Dynamics of holographic thermalization

Fil: Baron, Walter Helmut. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - La Plata. Instituto de Fisica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Fisica La Plata; Argentina