The density profile of the QCD flux tube is investigated within the framework of the Lüscher-Weisz (LW) string action with two boundary terms. The transverse action profile and potential between static quarks are considered using Wilson's loop overlap formalism at zero temperature in SU(2) Yang-Mills theory. We find the predictions of the LW string matching the lattice data for the width of the energy-density and $Q\bar{Q}$ potential up to a small color-source separation of $R=0.32$\,fm.
This is the second paper on hadronic wave functions in the light front formulation. We first consider only confinement effects, using the classical Nambu-Gotto string with massive end points in the light cone gauge. We derive the light-front Hamiltonian and show how to solve it, using an expansion in suitable basis functions. We next discuss the correlators of Wilson lines on the light front, leading to an effective Hamiltonian that includes spin effects. At the end, we consider a separate problem of instanton-induced interactions, at the origin of the pion as a massless Goldstone mode on the …
We test gauge/string duality by evaluating expectation values of small Wilson loops in pure Yang-Mills theories. On the gauge-theory side, there exists rich phenomenology. The dual formulation provides with a universal language to evaluate the gluon condensate and quadratic correction in terms of the metric in the fifth coordinate. Quantitatively, the estimated value of the gluon condensate is approximately 0.010 GeV^4.
Numerical experiments on most gauge theories coupled with matter failed to observe string-breaking effects while measuring Wilson loops only. We show that, under rather mild assumptions, the overlap of the Wilson loop operator with the broken-string state obeys a natural upper bound implying that the signal of string-breaking is in general too weak to be detected by the conventional updating algorithms. In order to reduce the variance of the Wilson loops in 3-D Z_2 gauge Higgs model we use a new algorithm based on the Lüscher-Weisz method combined with a non-local cluster algorithm which allow…
Recently, we proposed a new method to extract the string tension from 4-dimensionally smeared Wilson loops. In this talk, we first show that the results obtained using this smearing method are identical to those obtained by Wilson flow, once the time step is sufficiently small. We then demonstrate the practical advantage of our method by applying it to the calculation of string tension in SU(3) Yang-Mills theory.
In the framework of Matrix theory we show that Wilson loops can serve as interpolating fields to define string scattering amplitudes as gauge theory observables.
We compute the one-loop string corrections to the Wilson loop, glueball Regge trajectory and stringy hadron masses in the Witten model of non supersymmetric, large-N Yang-Mills theory. The classical string configurations corresponding to the above field theory objects are respectively: open straight strings, folded closed spinning strings, and strings orbiting in the internal part of the supergravity background. For the rectangular Wilson loop we show that besides the standard Luescher term, string corrections provide a rescaling of the field theory string tension. The one-loop corrections to …
Critical values of Wilson lines and general background fields for toroidal compactifications of heterotic string theories are constructed systematically using Dynkin diagrams.
We consider the description of form factors of local and Wilson line operators (reggeon amplitudes) in N=4 SYM within the framework of four dimensional ambitwistor string theory. We present the explicit expressions for string composite operators corresponding to stress-tensor operator supermultiplet and Wilson line operator insertion. It is shown, that corresponding tree-level string correlation functions correctly reproduce previously obtained Grassmannian integral representations. As by product we derive four dimensional tree-level scattering equations representations for the mentioned form …
Target space modular symmetries relevant to string loop threshold corrections are studied for $Z_N$ orbifold compactified string theories containing Wilson line background fields.
We look at energies of the low lying states of the hadronic string in three dimensional SU(2) lattice gauge theory by forming correlation matrices among different sources. We are able to go to previously inaccessible time separations. This is made possible by using a new algorithm proposed by Lüscher and Weisz which lets us measure the exponentially small values of large Wilson loops with sufficient accuracy.
Compact string expressions are found for non-intersecting Wilson loops in SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a weighted sum over covers of the surface. All terms from the coupled chiral sectors of the 1/N expansion of the Wilson loop expectation values are included.
The vacuum expectation value of the Wilson loop in the dual representation is calculated in the dual Higgs model with dual Dirac strings. It is shown that the averaged value of the Wilson loop in the dual representation obeys the area-law falloff. Quantum fluctuations of the dual-vector and the Higgs field around Abrikosov flux lines induced by dual Dirac strings in a dual superconducting vacuum and string shape fluctuations are taken into account.
We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the…
This work is about pure Yang-Mills theory in four Euclidean dimensions with gauge group SU(N). We study rectangular smeared Wilson loops on the lattice at large N and relatively close to the large-N transition point in their eigenvalue density. We show that the string tension can be extracted from these loops but their dependence on shape differs from the asymptotic prediction of effective string theory.
Using smeared Creutz ratios we extract the string tension for SU(N) pure gauge theory and $N$=3,4,5,6,8. We employ these results to extrapolate to large N. The same methodology is applied to the single-site Twisted Eguchi Kawai model. The corresponding string tension matches perfectly within errors with the extrapolated one, providing strong evidence in favour of the twisted reduction framework. Interesting results are also obtained on the behaviour of Creutz ratios for large sizes.
Recent progresses in the computation of quantum string corrections to holographic Wilson loops are extended to the case of strings in $AdS_{4}\times CP^{3}$. For this, the ratio of 1/2-BPS circular and 1/6-BPS latitude fermionic Wilson loops in ABJM is considered at strong coupling by studying the corresponding semiclassical string partition functions. Explicit evaluation of fluctuation determinants using phaseshifts and diffeomorphism invariant regulators leads to exact matching with the recent field theory proposal. Key to this computation is the choice of boundary conditions for massless fe…
We use the string sigma model action in AdS_5 \times S^5 to reconstruct the open string solution ending on the Wilson loop in S^3\times R parametrized by a geometric angle in S^3 and an angle in flavor space. Under the interchange of the world sheet space and time coordinates and the T-duality transformation with the radial inversion, the static open string configuration associated with the BPS Wilson loop with two equal angle parameters becomes a long open spinning string configuration which is produced by taking the equal limit of two frequencies for the folded spinning closed string with tw…
We study stringy fluctuations as a source for corrections to the Wilson loop as obtained from the superstrings on (adS_5 x S^5)/ N=4 SYM correspondence. We give a formal expression in terms of determinants of two dimensional operators for the leading order correction.
We explore the consequences of imposing Polyakov's zig/zag-invariance in the search for a confining string. We first find that the requirement of zig/zag-invariance seems to be incompatible with spacetime supersymmetry. We then try to find zig/zag-invariant string backgrounds on which to implement the minimal-area prescription for the calculation of Wilson loops considering different possibilities.
We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in ${\cal N}=4$ SYM to large $N$ QCD by deriving a general relation between QCD meson scattering amplitudes and Wilson loops. We then investigate properties of the open-string disk amplitude integrated over reparametrizations. When the Wilson loop is approximated by the area behavior, we find that the QCD scattering amplitude is a convolution of the standard Koba-Nielsen integrand and a kernel. As usual poles originate from the first factor, whereas no (momentum dependent) poles can arise from the kerne…
Wilson loop elements on torus are introduced into the partition function of open strings as Polyakov's path integral at one-loop level. Mass spectra from compactification and expected symmetry breaking are illustrated by choosing the correct weight for the contributions from annulus and Möbius strip. We show that Jacobi's imaginary transformation connects the mass spectra with the Wilson loops. The application to thermopartition function and cosmological implications are briefly discussed.
We discuss a semiclassical string description to circular Wilson loops without/with local operator insertions. By considering a semiclassical approximation of type IIB string theory on AdS_5 X S^5 around the corresponding classical solutions, quadratic actions with respect to fluctuations are computed. Then the dual corresponding operators describing the fluctuations are discussed from the point of view of a small deformation of the Wilson loops. The result gives new evidence for AdS/CFT correspondence.
We consider the VEV of Wilson loop operators by studying the behavior of string probes in solutions of Type IIB string theory generated by Nc D5 branes wrapped on an internal manifold. In particular, we focus on solutions to the background equations that are dual to field theories with a walking gauge coupling as well as for flavored systems. We present in detail our walking solution and emphasize various general aspects of the procedure to study Wilson loops using string duals. We discuss the special features that the strings show when probing the region associated with the walking of the fie…
In the world line representation of the fermionic effective action for QCD the interaction between Fermions and the gauge field is contained in the fermionic Wilson loop, namely the Wilson loop for a spin-half particle. It is argued that a string representation of the fermionic Wilson loop can provide a link connecting QCD with a dual description of a meson as a quark and an antiquark connected by a string. This is illustrated by obtaining such a representation in compact U(1) gauge theories. The resulting description contains information about the interaction of the spin of the quark with the…
Using covariant phase space formulations for the natural topological invariants associated with the world-surface in closed string theory, we find that certain Wilson loops defined on the world-surface and that preserve topological invariance, correspond to wave functionals for the vacuum state with zero energy. The differences and similarities with the 2-dimensional QED proposed by Schwinger early are discussed.
The nonabelian Stokes theorem, representing a Wilson loop as an integral over all the orientations in colour space, and the cumulant expansion are used for derivation of the string effective action in SU(2) gluodynamics. The obtained theory is the theory of the rigid string interacting with the rank two antisymmetric Kalb-Ramond fields. In this model there exists a phase where there are no problems of crumpling and wrong high temperature behaviour of the string tension, which are present in the free rigid string theory. The Langevin approach to stochastic quantization of the obtained theory is…
Schwarz-Christoffel (SC) mapping plays a crucial role in the calculation of the large-size expansion for polygonal Wilson loops in confining gauge theories using effective string theory (EST). Recently a new analytical regularization based on SC mapping was suggested and successfully applied to the calculation of the two-loop contribution of EST in the case of triangular Wilson loops. We prove that this analytical renormalization produces finite results for arbitrary polygonal Wilson loops and show that the result of the analytical renormalization for a given polygonal contour is independent o…
We consider d=4, N=2 compactifications of heterotic strings with an arbitrary number of Wilson lines. In particular, we focus on known chains of candidate heterotic/type II duals. We give closed expressions for the topological amplitudes F^g in terms of automorphic forms of SO(2+k,2,Z), and find agreement with the geometric data of the dual K3 fibrations wherever those are known.
We address the implementation of non-Abelian Wilson lines in D=4 N=1 Type IIB orientifold constructions. We present an explicit three-family example with the gauge group (U(4)xU(2)xSU(2)xSU(2))^2x(U(6)xSp(4))^2 and give the particle spectrum and the trilinear superpotential. Emphasizing the new subtleties associated with the introduction of non-Abelian Wilson lines, we show that the Abelian gauge anomalies are cancelled by the Green-Schwarz-type mechanism, and calculate the Fayet-Iliopoulos terms and gauge coupling corrections. The analysis thus sets a stage for further investigations of the p…
Previous attempts to match the exact N=4 super Yang-Mills expression for the expectation value of the 1/2-BPS circular Wilson loop with the semiclassical AdS(5)xS(5) string theory prediction were not successful at the first subleading order. There was a missing prefactor ~ lambda^(-3/4) which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing the ratio of the string partition functions corresponding to the circular Wilson loop and the special 1/4-supersymmetric latitude Wilson loop. The fact that the latter has a triv…
We find 1/6 BPS string configurations in AdS_4 x CP^3, which we identify as the duals of certain 1/6 BPS circular Wilson loops in N=6 super Chern-Simons-matter gauge theory. We use our results to verify -in the strong coupling limit- a proposal made in arXiv:1402.4128 for a relation between the expectation value of these Wilson loops and the Bremsstrahlung function from deforming 1/2 BPS Wilson lines with a cusp. We also derive an analogous relation between the expectation value of some particular 1/12 BPS Wilson loops and the Bremsstrahlung function from deforming 1/6 BPS Wilson lines with an…
By employing the symmetries of the underlying conformal field theory, the tree-level Kähler potentials for untwisted moduli of the heterotic string compactifications on orbifolds with continuous Wilson lines are derived. These symmetries act linearly on bosonic (toroidal and $E_8\times E_8$ gauge) string coordinates as well as on the untwisted (toroidal and continuous Wilson lines) moduli; they correspond to the scaling of toroidal moduli, the axionic shift of toroidal moduli and the shift of the continuous Wilson line moduli. In turn such symmetries provide sufficient constraints to determine…
We investigate stationary string solutions with spacelike worldsheet in a five-dimensional AdS black hole background, and find that there are many branches of such solutions. Using a non-perturbative definition of the jet quenching parameter proposed by Liu et. al., hep-ph/0605178, we take the lightlike limit of these solutions to evaluate the jet quenching parameter in an N=4 super Yang-Mills thermal bath. We show that this proposed definition gives zero jet quenching parameter, independent of how the lightlike limit is taken. In particular, the minimum-action solution giving the dominant con…
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 set up the Montecarlo evaluation, in the 3d Ising gauge model, of an observable (the ratio of two Wilson loops with the same perimeter) for which boundary effec…
We construct exact classical solutions in cubic open string field theory. By the redefinition of the string field, we find that the solutions correspond to finite deformations of the Wilson lines. The solutions have well-defined Fock space expressions, and they have no branch cut singularity of marginal parameters which was found in the analysis using level truncation approximation in Feynman-Siegel gauge. We also discuss marginal tachyon lump solutions at critical radius.
We review, in a self-contained and pedagogical manner, recent developments and techniques for the evaluation of the scattering amplitudes of planar N=4 SYM theory at both weak and strong coupling. Special emphasis is placed on the newly discovered connection between a special class of amplitudes and the expectation values of particular cusped light-like Wilson loops.
For the asymptotic string solution in AdS_3 which is represented by the AdS_3 Poincare coordinates and yields the planar multi-gluon scattering amplitude at strong coupling in arXiv:0904.0663, we express it by the AdS_4 Poincare coordinates and demonstrate that the hexagonal and octagonal Wilson loops surrounding the string surfaces take closed contours consisting of null vectors in R^{1,2} owing to the relations of Stokes matrices. For the tetragonal Wilson loop we construct a string solution characterized by two parameters by solving the auxiliary linear problems and demanding a reality cond…
We study the Wegner-Wilson loops in the string-net model of Levin and Wen in the presence of a string tension. The latter is responsible for a phase transition from a topological deconfined phase (weak tension) to a trivial confined phase (strong tension). We analyze the behavior of all Wegner-Wilson loops in both limiting cases for an arbitrary input theory of the string-net model. Using a fluxon picture, we compute perturbatively the first contributions to a perimeter law in the topological phase as a function of the quantum dimensions. In the trivial phase, we find that Wegner-Wilson loops …
A recently proposed connection between closed string field and an open Wilson line defined on an arbitrary contour is further explored here. We suggest that reparametrization invariance of a Wilson line is the principle which determines the coupling of non-commutative gauge theory/matrix model to the modes of the closed string. An analogue of the level matching condition on the gauge theory/matrix model operators emerges quite naturally from the cyclic symmetry of the straight Wilson line. We show that the generating functional of correlation functions of these operators has the space-time gau…
We calculate the moduli dependent part of string one-loop threshold corrections to gauge couplings for the heterotic string theory compactified on abelian toroidal orbifolds, allowing for arbitrary discrete Wilson lines. We show that the knowledge of threshold corrections for any such compactification is equivalent to solving a class of integrals. We solve a sub-class of these integrals and show how any model can be mapped onto this class by fractional linear transformations of its fixed plane moduli. Modular symmetries of the final expression are discussed.
We present the results of a high statistics analysis of smeared Wilson loops in 4 dimensional SU(N) Yang-Mills theory for various values of N. The data is used to analyze the behaviour of smeared Creutz ratios, extracting from them the value of the string tension and other asymptotic parameters. A scaling analysis allows us to extrapolate to the continuum limit for N=3,5,6 and 8. The results are consistent with a $1/N^2$ approach towards the large N limit. The same analysis is done for the TEK model (one-point lattice) for N=841 and a non-minimal symmetric twist with flux of $k=9$. The results…
We present a theorem that determines the value of the Wilson loop associated with a Nambu-Goto action which generalizes the action of the $AdS_5\times S_5$ model. In particular we derive sufficient conditions for confining behavior. We then apply this theorem to various string models. We go beyond the classical string picture by incorporating quadratic quantum fluctuations. We show that the bosonic determinant of $D_p$ branes with 16 supersymmetries yields a Luscher term. We confirm that the free energy associated with a BPS configuration of a single quark is free from divergences. We show tha…
We present a general set-up for inflation in string theory where the inflaton field corresponds to Wilson lines in compact space in the presence of magnetic fluxes. T-dualities and limits on the value of the magnetic fluxes relate this system to the standard D-brane inflation scenarios, such as brane-antibrane inflation, D3/D7 brane inflation and different configurations of branes at angles. This can then be seen as a generalised approach to inflation from open string modes. Inflation ends when the Wilson lines achieve a critical value and an open string mode becomes tachyonic. Then hybrid-lik…
According to the standard prescriptions, zero-temperature string theories can be extended to finite temperature by compactifying their time directions on a so-called "thermal circle" and implementing certain orbifold twists. However, the existence of a topologically non-trivial thermal circle leaves open the possibility that a gauge flux can pierce this circle --- i.e., that a non-trivial Wilson line (or equivalently a non-zero chemical potential) might be involved in the finite-temperature extension. In this paper, we concentrate on the zero-temperature heterotic and Type I strings in ten dim…
We study string quantum corrections to the ratio of latitude and circular Wilson loops in N=4 super-Yang-Mills theory at strong coupling. Conformal gauge for the corresponding minimal surface in AdS(5)xS(5) is singular and we show that an IR anomaly associated with the divergence in the conformal factor removes previously reported discrepancy with the exact field-theory result. We also carefully check conformal anomaly cancellation and recalculate fluctuation determinants by directly evaluating phaseshifts for all the fluctuation modes.
We investigate the lightlike limit of stationary spacelike string configurations on a large class of five-dimensional asymptotically AdS backgrounds. Specific examples include gravity duals which incorporate finite 't Hooft coupling, curvature-squared corrections, and chemical potentials. A universal feature of these AdS/CFT models is that the string solution with minimum action yields a lightlike Wilson loop whose leading behavior is exponentially linear, rather than quadratic, in the width of the loop. Unless there is a compelling reason for discarding the leading saddlepoint contribution to…
We construct non-geometric string compactifications by using the F-theory dual of the heterotic string compactified on a two-torus with two Wilson line parameters, together with a close connection between modular forms and the equations for certain K3 surfaces of Picard rank $16$. We construct explicit Weierstrass models for all inequivalent Jacobian elliptic fibrations supported on this family of K3 surfaces and express their parameters in terms of modular forms generalizing Siegel modular forms. In this way, we find a complete list of all dual non-geometric compactifications obtained by the …
In the AdS/CFT correspondence, an AdS_2 x S^2 D3-brane with electric flux in AdS_5 x S^5 spacetime corresponds to a circular Wilson loop in the symmetric representation or a multiply wound one in N=4 super Yang-Mills theory. In order to distinguish the symmetric loop and the multiply wound loop, one should see an exponentially small correction in large 't Hooft coupling. We study semi-classically the disk open string attached to the D3-brane. We obtain the exponent of the term and it agrees with the result of the matrix model calculation of the symmetric Wilson loop.
Inequalities are derived for Wilson loops generalizing the well-known Bachas inequality for rectangular contours. The inequalities are compatible with the area law for large contours. The Polyakov cusp anomalous dimension of Wilson lines (playing an important role in QCD applications to hard processes) has a convex angular dependence. This convexity is crucial for the consistency of the inequalities with renormalization. Some parallel properties can be found in the string theory. The Kac-Ray cusp term from the "shape of a drum" problem has the same angular convexity property and plays the role…
In gauge systems coupled to matter, the static potential flattens out at a scale where the confining string breaks by formation of a dynamical pair of particles. Surprisingly, such a breaking is invisible in Wilson loops even when the inter-charge separation is much larger than the flattening scale. Observing string breaking also requires using different operators. A known string mechanism provides us with a simple explanation, leading to the area law for large Wilson loops, as observed in most gauge models coupled to whatever kind of matter. It is also pointed out that in a simple 3D Z_2 gaug…
We compute the 1-loop partition function for strings in $AdS_4\times\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
We investigate a Π-shape Wilson loop in N=4 super Yang--Mills theory, which lies partially at the light-cone, and consider an associated open superstring in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous dimensions of conformal operators with large Lorentz spin and present an explicit calculation in perturbation theory to order λ. We find the minimal surface in the supergravity approximation, that reproduces the Gubser, Klebanov and Polyakov prediction for the anomalous dimensions at large λ=g_YM^2 N, and discuss its quantum-mechanical interpretation.
We discuss the impact of quadratic quantum fluctuations on the Wilson loop extracted from classical string theory. We show that a large class of models, which includes the near horizon limit of D_p branes with 16 supersymmetries, admits a Lüscher type correction to the classical potential. We confirm that the quantum determinant associated with a BPS configuration of a single quark in the AdS_5 \times S^5 model is free from divergences. We find that for the Wilson loop in that model, unlike the situation in flat space-time, the fermionic determinant does not cancel the bosonic one. For string …
In these lectures we describe the attempt to extract the expectation values of Wilson loops from the string/gauge correspondence. We start with the original calculation in $AdS_5$. It is then extended to the non-conformal background of $D_p$ in the near horizon limit. We discuss the computation at finite temperature. Supergravity models that admit confinement in 3d and 4d are described. A theorem that determines the classical values of loops associated with a generalized background is derived.In particular we determine sufficient conditions for confining behavior. We then apply the theorem to …
We compute the 1-loop correction to the effective action for the string solution in AdS_5 x S^5 dual to the circular Wilson loop. More generically, the method we use can be applied whenever the two dimensional spectral problem factorizes, to regularize and define the fluctuation determinants in terms of solutions of one-dimensional differential equations. A such it can be applied to non-homogeneous solutions both for open and closed strings and to various boundary conditions. In the case of the circular Wilson loop, we obtain, for the 1-loop partition function a result which up to a factor of …
We reconsider a gravity dual of a 1/4 BPS Wilson loop. In the case of an expectation value of the Wilson loop, it is known that broken zero modes of a string world sheet in the gravity side play important roles in the limit $λ\to \infty$ with keeping the combination $λ\cos^2 θ_0$ finite. Here, $λ$ is the 't Hooft coupling constant and $θ_0$ is a parameter of the Wilson loop. In this paper, we reconsider a gravity dual of a correlation function between the Wilson loop and a 1/2 BPS local operator with R charge $J$. We take account of contributions coming from the same configurations of the abov…
