Wilson Loops Research Articles

Defect correlators in a mathcal{N} = 2 SCFT at strong coupling

We study the correlation function between one single-trace scalar operator and a circular Wilson loop in the 4d mathcal{N} = 2 superconformal field theory with gauge group SU(N) and matter transforming in the symmetric and anti-symmetric representations. By exploiting supersymmetric localization, we resum the perturbative expansion of this correlator in the large-N ’t Hooft limit. Furthermore, using both analytical and numerical techniques, we provide a prediction for the leading term of its strong coupling expansion and we compare this prediction to numerical Padé resummations of the perturbative series.

Chromoelectric field correlator for quarkonium transport in the strongly coupled mathcal{N} = 4 Yang-Mills plasma from AdS/CFT

Previous studies have shown that a gauge-invariant correlation function of two chromoelectric fields connected by a straight timelike adjoint Wilson line encodes crucial information about quark-gluon plasma (QGP) that determines the dynamics of small-sized quarkonium in the medium. Motivated by the successes of holographic calculations to describe strongly coupled QGP, we calculate the analog gauge-invariant correlation function in strongly coupled mathcal{N} = 4 supersymmetric Yang-Mills theory at finite temperature by using the AdS/CFT correspondence. Our results indicate that the transition processes between bound and unbound quarkonium states are suppressed in strongly coupled plasmas, and moreover, the leading contributions to these transition processes vanish in both the quantum Brownian motion and quantum optical limits of open quantum system approaches to quarkonia.

Wilson loops in the abelian lattice Higgs model

We consider the lattice Higgs model on $\mathbb{Z}^4$, with structure group given by $ \mathbb{Z}_n $ for $ n \geq 2 $. We compute the expected value of the Wilson loop observable to leading order when the gauge coupling constant and hopping parameter are both sufficiently large. The leading order term is expressed in terms of a quantity arising from the related but much simpler $ \mathbb{Z}_n $ model, which reduces to the Ising model when $n=2$. As part of the proof, we construct a coupling between the lattice Higgs model and the $ \mathbb{Z}_n $ model.

Probing the holographic model of N=4 SYM rotating quark-gluon plasma

We study Wilson loops in holographic duals of the $\mathcal{N}=4$ SYM quark-gluon plasma. For this we consider the Schwarzschild-$AdS_5$ and Kerr-$AdS_5$ black holes, which are dual to the non-rotating and rotating QGPs, correspondingly. From temporal Wilson loops we find the heavy quark potentials in both backgrounds. For the temperature above the critical one we observe the Coulomb-like behaviour of the potentials. We find that increasing the rotation the interquark distance decreases, we also see that the increase of the temperature yields the similar behaviour. Moreover, at high temperatures values of the potentials in Kerr-$AdS_5$ are close to that one calculated in the Schwarzschild-$AdS_5$ black hole. We also explore holographic light-like Wilson loops from which the jet-quenching parameters of a fast parton propagating in the QGP are extracted. We find that the rotation increases the value of the jet-quenching parameter. However, at high temperatures the jet-quenching parameters have a cubic dependence on the temperature as for the AdS black brane.

Parton decomposition of nucleon spin and momentum: Gluons from dressed quarks

The lowest two Mellin moments of hadronic Generalized Parton Distributions are explored within a model that allows investigation of the inter-related quark and gluon contributions. For light quarks their dynamical connection is strong due to quark dressing. Our principal focus is the angular momentum J of the nucleon. This work employs and extends dynamical insights obtained from our recent model results for quark and gluon momentum fractions 〈x〉q/g in both pion and nucleon. The employed model is based on the Rainbow-Ladder truncation of the Dyson-Schwinger equations of QCD. The special case of a 1-loop treatment of a single hadronic quark is used to motivate several insights and obtain initial estimates such as the Wilson line correction to the established Landau gauge model (−7% for both Jq and 〈x〉q), and the “binding gluon” contribution to 〈x〉g (≤10%). We obtain the proton J within 1% after inclusion of the pion cloud mechanism to produce the sea. The gluon second Mellin moments of the proton reflect similar dynamics; (〈x〉g, Jg) are (26%, 24%) at model scale, and (40%, 38%) at 2 GeV. We also find that Jtot is shared almost equally between the total orbital and total intrinsic spin contributions.

Non-planar corrections in orbifold/orientifold mathcal{N} = 2 superconformal theories from localization

We study non-planar corrections in two special mathcal{N} = 2 superconformal SU(N) gauge theories that are planar-equivalent to mathcal{N} = 4 SYM theory: two-nodes quiver model with equal couplings and mathcal{N} = 2 vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. We focus on two observables in these theories that admit representation in terms of localization matrix model: free energy on 4-sphere and the expectation value of half-BPS circular Wilson loop. We extend the methods developed in arXiv:2207.11475 to derive a systematical expansion of non-planar corrections to these observables at strong ’t Hooft coupling constant λ. We show that the leading non- planar corrections are given by a power series in λ3/2/N2 with rational coefficients. Sending N and the coupling constant λ to infinity with λ3/2/N2 kept fixed corresponds to the familiar double scaling limit in matrix models. We find that in this limit the observables in the two models are related in a remarkably simple way: the free energies differ by the factor of 2, whereas the Wilson loop expectation values coincide. Surprisingly, these relations hold only at strong coupling, they are not valid in the weak coupling regime. We also discuss a dual string theory interpretation of the leading corrections to the free energy in the double scaling limit suggesting their relation to curvature corrections in type IIB string effective action.

Steps towards generalization of tensionless string theory with contact interactions as Wilson loop of non-Abelian Yang–Mills theory

We propose a possible modification to the tensionless string model with contact interactions. The proposed model aims to reproduce the expectation value of a non-Abelian Wilson loop in Yang–Mills theory by integrating out string degrees of freedom with a fixed worldsheet boundary. To reproduce path-ordering along the worldsheet boundary, we introduce Lie algebra-valued fields on the string worldsheet, whose dynamics are determined by the topological BF action. Without bulk contributions, we show that the model describes the non-Abelian Wilson loop, neglecting the effects of self-interactions. Finally, we test the reproduction of the Wilson loop with three-point interaction in the case of SU(2).

Wilson Loops at Large N and the Quantum M2-Brane.

The Wilson loop operator in the U(N)_{k}×U(N)_{-k} Aharony-Bergman-Jafferis-Maldacena theory at large N and fixed level k has a dual description in terms of a wrapped M2-brane in the M-theory given by the product of four-dimensional anti de Sitter space (AdS_{4}) and S^{7}/Z_{k}. We consider the localization result for the 1/2-Bogomol'nyi-Prasad-Sommerfield circular Wilson loop expectation value W in this regime and compare it to the prediction of the M2-brane theory. The leading large N exponential factor is matched as expected by the classical action of the M2-brane solution with AdS_{2}×S^{1} geometry. We show that the subleading k-dependent prefactor in W is also exactly reproduced by the one-loop term in the partition function of the wrapped M2-brane (with all Kaluza-Klein modes included). This appears to be the first case of an exact matching of the overall numerical prefactor in the Wilson loop expectation value against the dual holographic result. It provides an example of a consistent quantum M2-brane computation, suggesting various generalizations.

Memory effects from holonomies

We provide a uniform treatment of electromagnetic and gravitational memory effects, based on the gravito-electromagnetic formulation of GR and a generalization of the geodesic deviation equation. This allows us to find novel results: in gauge theory, we derive relativistic corrections to the well-known kick memory observable, and a general expression for the displacement memory observable, typically overlooked in the literature. In GR, we find relativistic corrections to displacement and kick memory observables. In both theories, we find novel radial memory effects. Next, we show that electromagnetic and gravitational memory observables can be formulated in terms of certain holonomies on a holographic screen in asymptotically flat spacetimes. In gauge theory, the displacement and kick memory effects form a Hamiltonian vector field which is canonically generated by a Wilson loop. In the first order formulation of GR, we show that the holonomy naturally splits into translational and Lorentz parts. While the former encodes the leading and subleading displacement and kick memory observables, the latter reproduces the gyroscopic memory effect.

Holographic operator product expansion of loop operators in the super Yang-Mills theory* *Supported in part by the National Natural Science Foundation of China (11975164, 11935009) and Natural Science Foundation of Tianjin (20JCYBJC00910, 20JCQNJC02030)

In this study, we compute the correlation functions of Wilson(-'t Hooft) loops with chiral primary operators in the supersymmetric Yang-Mills theory with gauge symmetry, which has a holographic dual description of the Type IIB superstring theory on the background. Specifically, we compute the coefficients of the chiral primary operators in the operator product expansion of Wilson loops in the fundamental representation, Wilson-'t Hooft loops in the symmetric representation, Wilson loops in the anti-fundamental representation, and Wilson loops in the spinor representation. We also compare these results to those of the super Yang-Mills theory.

AdS correction to the Faddeev-Kulish state: migrating from the flat peninsula

The IR finiteness of mathcal{S} -matrix in flat spacetime is tied to the Faddeev-Kulish dressed state, which suggests dressing the Fock space scattering state with the soft photon modes. We instigate a construction for the Faddeev-Kulish dressed state in the language of AdS/CFT. A salient feature of AdS spacetime is that it acquits itself as a quintessential IR regulator. The IR divergences will take shape after taking the zoomed in limit. We explore the Faddeev-Kulish dressed state to account for the AdS radius corrections. The Wilson line dressing stands as a guiding principle in the study of AdS radius-corrected Faddeev-Kulish dressing. We construct the modes of the Wilson line dressed massive scalar field implementing vanilla HKLL reconstruction since the field is simply free field. This simplification is owing to the use of soft photon modes in the Wilson line dressing. We map the AdS radius-corrected soft photon modes in terms of CFT current operators. We invert this mapping, use the mapping in the Wilson line dressing, and express the AdS radius-corrected Faddeev-Kulish dressed state.

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.

Topological phonon analysis of the two-dimensional buckled honeycomb lattice: An application to real materials

By means of group theory, topological quantum chemistry, first-principles, and Monte Carlo calculations, we analyze the topology of the 2D buckled honeycomb lattice phonon spectra. Taking the pure crystal structure as an input, we show that eleven distinct phases are possible, five of which necessarily have nontrivial topology according to topological quantum chemistry. Another four of them are also identified as topological using Wilson loops in an analytical model that includes all the symmetry allowed force constants up to third-nearest neighbors, making a total of nine topological phases. We then compute the ab initio phonon spectra for the two-dimensional crystals of Si, Ge, P, As, and Sb in this structure and construct its phase diagram. Despite the large proportion of topological phases found in the analytical model, all of the crystals lie in a trivial phase. By analyzing the force constants space using Monte Carlo calculations, we elucidate why topological phonon phases are physically difficult to realize in real materials with this crystal structure.

On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds

We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in SU(n) or U(n) gauge theories compactified on the orbifolds T2/ℤN (N = 2, 3, 4, 6). We suppose that the theory has a global G′ = U(n) symmetry. Using constraints, unitary transformations and gauge transformations, we examine whether the representation matrices can simultaneously become diagonal or not. We show that at least one diagonal representative necessarily exists in each equivalence class on T2/ℤ2 and T2/ℤ3, but the representation matrices on T2/ℤ4 and T2/ℤ6 can contain not only diagonal matrices but also non-diagonal 2 × 2 ones and non-diagonal 3 × 3 and 2 × 2 ones, respectively, as members of block-diagonal submatrices. These non-diagonal matrices have discrete parameters, which means that the rank-reducing symmetry breaking can be caused by the discrete Wilson line phases.

An off-shell Wilson loop

It is well-known that on-shell maximally helicity-violating gluon scattering amplitudes in planar maximally supersymmetric Yang-Mills theory are dual to a bosonic Wilson loop on a null-polygonal contour. The light-like nature of the intervals is a reflection of the mass-shell condition for massless gluons involved in scattering. Presently, we introduce a Wilson loop prototype on a piece-wise curvilinear contour that can be interpreted in the T-dual language to correspond to nonvanishing gluon off-shellness. We analyze it first for four sites at one loop and demonstrate that it coincides with the four-gluon amplitude on the Coulomb branch. Encouraged by this fact, we move on to the two-loop order. To simplify our considerations, we only focus on the Sudakov asymptotics of the Wilson loop, when the off-shellness goes to zero. The latter serves as a regulator of short-distance divergences around the perimeter of the loop, i.e., divergences when gluons are integrated over a small vicinity of the Wilson loop cusps. It does not however regulate conventional ultraviolet divergences of interior closed loops. This unavoidably introduces a renormalization scale dependence and thus scheme dependence into the problem. With a choice of the scale setting and a finite renormalization, we observe exponentiation of the double logarithmic scaling of the Wilson loop with the accompanying exponent being given by the so-called hexagon anomalous dimension, which recently made its debut in the origin limit of six-leg gluon amplitudes. This is contrary to the expectation for the octagon anomalous dimension to rather emerge from our analysis suggesting that the current object encodes physics different from the Coulomb branch scattering amplitudes.

Meson excitation time as a probe of holographic critical point

We study the time evolution of expectation value of Wilson loop as a non-local observable in a strongly coupled field theory with a critical point at finite temperature and nonzero chemical potential, which is dual to an asymptotically AdS charged black hole via gauge/gravity duality. Due to inject of energy into the plasma, the temperature and a chemical potential increase to finite values and the plasma experiences an out-of-equilibrium process. By defining meson excitation time t_{ex} as a time at which the meson falls into the final excited state, we investigate the behavior of t_{ex} near the critical point as the system evolves towards the critical point. We observe that by increasing the interquark distance the dynamical critical exponent increases smoothly. Also, we obtain for slow quenches different values of the dynamical critical exponent, although for fast quenches our result for the dynamical critical exponent is in agreement with the one that is reported for studying the quasi-normal modes. Consequently, this indicates that in this model for fast quenches and small values of interquark distances the gauge invariant Wilson loop is a good non-local observable to probe the critical point.

Flat equivariant gerbes: holonomies and dualities

We examine the role of global topological data associated to choices of holonomy for flat gauge fields in string compactification. Our study begins with perturbative string compactification on compact flat manifolds preserving 8 supercharges in 5 dimensions. By including non-trivial holonomy for Wilson lines in the heterotic string and for the B-field gerbe in the type II string we find worldsheet dualities that relate these backgrounds to other string compactifications. While our simple examples allow for explicit analysis, the concepts and some of the methods extend to a broader class of compactifications and have implications for string dualities, perturbative and otherwise.

Phases of Wilson Lines in Conformal Field Theories.

We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in 2+1 and 3+1 dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to interesting renormalization group flows and for sufficiently large representations to complete or partial screening by charged fields. This result is universal: in large enough representations, Wilson lines are screened by the charged matter fields. We observe that the onset of the screening instability is associated with fixed-point mergers. We study this phenomenon in a variety of applications. In some cases, the screening of the Wilson lines takes place by dimensional transmutation and the generation of an exponentially large scale. We identify the space of infrared conformal Wilson lines in weakly coupled gauge theories in 3+1 dimensions and determine the screening cloud due to bosons or fermions. We also study QED in 2+1 dimensions in the large N_{f} limit and identify the nontrivial conformal Wilson lines. We briefly discuss 't Hooft lines in 3+1-dimensional gauge theories and find that they are screened in weakly coupled gauge theories with simply connected gauge groups. In non-Abelian gauge theories with S duality, this together with our analysis of the Wilson lines gives a compelling picture for the screening of the line operators as a function of the coupling.

Wilson lines construction of [formula omitted] toroidal conformal blocks

We study W3 toroidal conformal blocks for degenerate primary fields in AdS/CFT context. In the large central charge limit W3 algebra reduces to sl3 algebra and sl3 blocks are defined as contributions to W3 blocks coming from the generators of sl3 subalgebra. We consider the construction of sl3 toroidal blocks in terms of Wilson lines operators of 3d Chern-Simons gravity in the thermal AdS3 space-time. According to the correspondence, degenerate primary fields are associated with Wilson lines operators acting in the corresponding finite-dimensional sl3 representations. We verify this dual construction for one-point toroidal block using sl3 tensor technique in the bulk theory and an algorithm based on AGT correspondence in the boundary CFT.

Holographic entanglement entropy in [formula omitted]-deformed AdS3

In this work, we study the holographic entanglement entropy in AdS3 gravity with the certain mixed boundary condition, which turns out to correspond to TT¯-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in TT¯-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both TT¯-deformed CFTs and cutoff AdS3. Moreover, our result shows that the deformed entanglement entropy for large deformation parameter behaves like the entanglement entropy of CFT at zero temperature. We also consider the entanglement entropy of two intervals and study the effect of TT¯ deformation on phase transition.