We present a two-loop calculation of the supersymmetric circular Wilson loop in the N=2* super Yang-Mills theory on the four-sphere. We develop an efficient framework for computing contributing Feynman graphs that relies on using the embedding coordinates combined with the Mellin-Barnes techniques for propagator-like integrals on the sphere. Our results exactly match predictions of supersymmetric localization providing a nontrivial consistency check for the latter in non-conformal settings.
We show that a certain class of light-like Wilson loops exhibits a Yangian symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills theory in a certain kinematical regime. The fact that we find a Yangian symmetry constraining their functional form can be thought of as the effect of the original conformal symmetry associated to the scattering amplitudes in the N=4 theory.
The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian gauge theory, in particular, it actually deduces the Ward-Takahashi identity for Wilson action recently derived by Sonoda.
The N=2* Super-Yang-Mills theory (SYM*) undergoes an infinite sequence of large-N quantum phase transitions. We compute expectation values of Wilson loops in k-symmetric and antisymmetric representations of the SU(N) gauge group in this theory and show that the same phenomenon that causes the phase transitions at finite coupling leads to a non-analytic dependence of Wilson loops on k/N when the coupling is strictly infinite, thus making the higher-representation Wilson loops ideal holographic probes of the non-trivial phase structure of SYM*.
We construct the D3-brane solution in the holographic dual of the N = 2* theory that describes Wilson lines in symmetric representations of the gauge group. The results perfectly agree with the direct field-theory predictions based on localization.
The large-N limit of the expectation values of the Wilson loops corresponding to two-dimensional U(N) Yang-Mills and generalized Yang-Mills theories on a sphere are studied. The behavior of the expectation values of the Wilson loops both near the critical area and for large areas are investigated. It is shown that the expectation values of the Wilson loops at large areas behave exponentially with respect to the area of the smaller region the boundary of which is the loop; and for the so called typical theories, the expectation values of the Wilson loops exhibit a discontinuity in their second …
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 study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the noncommutativity scale. At large momentum scale, the Wilson loops in noncommmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in low energy limit. The correlation functions on D-branes in IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also expla…
We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N=4 super Yang-Mills theory are invariant under a Yangian symmetry Y[psu(2,2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS_5 x S^5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the …
We analyze the operator product expansion T_{μν}(z) W[C] in N=4 4-dimensional Super-Yang-Mills (SYM) theory with U(N) gauge group, and clarify that the closed Wilson loop does not possess an anomalous dimension and that only the shape of the loop is changed by the conformal transformation.
Based on the AdS/CFT correspondence, string theory has given exact predictions for circular Wilson loops in U(N) ${\cal N}=4$ supersymmetric Yang-Mills theory to all orders in a 1/N expansion. These Wilson loops can also be derived from Random Matrix Theory. In this paper we show that the result is generically insensitive to details of the Random Matrix Theory potential. We also compute all higher $k$-point correlation functions, which are needed for the evaluation of Wilson loops in arbitrary irreducible representations of U(N).
We compute the expectation value of the circular Wilson loop in N=2 supersymmetric Yang-Mills theory with N_f=2N hypermultiplets. Our results indicate that the string tension in the dual string theory scales as the logarithm of the 't Hooft coupling.
We compute the expectation values of both the time-like and the light-like Wilson loops in a strongly coupled plasma of (p+1)-dimensional Yang-Mills theories using gravity/gauge theory correspondence. From the time-like Wilson loop we obtain the velocity dependent quark-antiquark potential where the dipole is moving through the plasma with an arbitrary velocity 0<v<1 and also obtain expressions for the screening lengths. When the velocity v--> 1, the Wilson loop becomes light-like and we obtain the form of the jet quenching parameter in those strongly coupled plasma.
A light-like Wilson loop is computed in perturbation theory up to ${\cal O} (g^4)$ for pure Yang--Mills theory in 1+1 dimensions, using Feynman and light--cone gauges to check its gauge invariance. After dimensional regularization in intermediate steps, a finite gauge invariant result is obtained, which however does not exhibit abelian exponentiation. Our result is at variance with the common belief that pure Yang--Mills theory is free in 1+1 dimensions, apart perhaps from topological effects.
We argue that the string theory dual to a certain sector of the four-dimensional Yang-Mills theory at large-N is the A-model wrapping N-Lagrangian D-branes on the twistor space of the complex two-dimensional projective space, with certain fluxes and Wilson loops, by finding that the target-space beta function of this A-model coincides with the large-N beta function of the Yang-Mills theory
A field theoretic description of monopole condensation in strongly coupled gauge theories is given by actions involving antisymmetric tensors B_{μν} of rank 2. We rederive the corresponding action for 4d compact QED, summing explicitly over all possible monopole configurations. Its gauge symmetries and Ward identities are discussed. Then we consider the Wilsonian RGs for Yang-Mills theories in the presence of collective fields (again tensors B_{μν}) for the field strengths F_{μν} associated to the U(1) subgroups. We show that a ``vector-like'' Ward identity for the Wilsonian action involving B…
We formulate the canonical structure of Yang--Mills theory in terms of Poisson brackets of gauge invariant observables analogous to Wilson loops. This algebra is non--trivial and tractable in a light--cone formulation. For U(N) gauge theories the result is a Lie algebra while for SU(N) gauge theories it is a quadratic algebra. We also study the identities satsfied by the gauge invariant observables. We suggest that the phase space of a Yang--Mills theory is a co--adjoint orbit of our Poisson algebra; some partial results in this direction are obtained.
We present results for the three-loop universal anomalous dimension of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory. These expressions are obtained by extracting the most complicated contributions from the three-loop anomalous dimensions in QCD. This result is in an agreement with the hypothesis of the integrability of N=4 Supersymmetric Yang-Mills theory in the context of AdS/CFT-correspondence.
The instanton contributions to the partition function and to homologically trivial Wilson loops for a U(N) Yang-Mills theory on a torus $T^2$ are analyzed. An exact expression for the partition function is obtained as a sum of contributions localized around the classical solutions of Yang-Mills equations, that appear according to the general classification of Atiyah and Bott. Explicit expressions for the exact Wilson loop averages are obtained when N=2, N=3. For general $N$ the contribution of the zero-instanton sector has been carefully derived in the decompactification limit, reproducing the…
The vacuum expectation value of the Wilson loop functional in pure Yang-Mills theory on an arbitrary two-dimensional orientable manifold is studied. We consider the calculation of this quantity for the abelian theory in the continuum case and for the arbitrary gauge group and arbitrary lattice action in the lattice case. A classification of topological sectors of the theory and the related classification of the principal fibre bundles over two-dimensional surfaces are given in terms of a cohomology group. The contribution of SU(2)-invariant connections to the vacuum expectation value of the Wi…
The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the flow of the marginal couplings is studied. Our results indicate that higher-derivative terms of the color-unit-vector $\mathbf{n}$ field are necessary for the description of topologically stable knotlike solitons which have been conjectured to be the large-distance degrees of freedom.
We test the unified-gauge formalism by computing a Wilson loop in Yang-Mills theory to one-loop order. The unified-gauge formalism is characterized by the abritrary, but fixed, four-vector $N_μ$, which collectively represents the light-cone gauge $(N^2 = 0)$, the temporal gauge $(N^2 > 0)$, the pure axial gauge $(N^2 < 0)$ and the planar gauge $(N^2 < 0)$. A novel feature of the calculation is the use of distinct sets of vectors, $\{ n_μ, n_μ^{\ast} \}$ and $\{N_μ, N_μ^{\ast}\}$, for the path and for the gauge-fixing constraint, respectively. The answer for the Wilson loop is independent of $N…
Wilson loops on the Coulomb branch of $N=4$ super-Yang-Mills
Vrije Universiteit Brussel（布鲁塞尔自由大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Nordita（北欧理论天体物理学研究所）；Copenhagen University（哥本哈根大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）
We demonstrate that the large-N expansion of Wilson loop expectation values in SO(N) and Sp(N) Yang-Mills theory on orientable and nonorientable surfaces has a natural description as a weighted sum over covers of the given surface. The sum takes the form of the perturbative expansion of an open string theory. The derivation makes contact with the classification of branched covers by Gabai and Kazez. Comparison with the analogous results for the chiral sectors of QCD_2 is instructive for both cases.
We present a three-loop O(g^6) calculation of the difference between the expectation values of Wilson loops evaluated in N=4 and superconformal N=2 supersymmetric Yang-Mills theory with gauge group SU(N) using dimensional reduction. We find a massive reduction of required Feynman diagrams, leaving only certain two-matter-loop corrections to the gauge field and associated scalar propagator. This "diagrammatic difference" leaves a finite result proportional to the bare propagators and allows the recovery of the zeta(3) term coming from the matrix model for the 1/2 BPS circular Wilson loop in the…
We consider double-winding, triple-winding and multiple-winding Wilson loops in the $SU(N)$ Yang-Mills gauge theory. We examine how the area law falloff of the vacuum expectation value of a multiple-winding Wilson loop depends on the number of color $N$. In sharp contrast to the difference-of-areas law recently found for a double-winding $SU(2)$ Wilson loop average, we show irrespective of the spacetime dimensionality that a double-winding $SU(3)$ Wilson loop follows a novel area law which is neither difference-of-areas nor sum-of-areas law for the area law falloff and that the difference-of-a…
Pure Yang-Mills theories on the $S_1\times R$ cylinder are quantized in light-cone gauge $A_-=0$ by means of ${\bf equal-time}$ commutation relations. Positive and negative frequency components are excluded from the ``physical" Hilbert space by imposing Gauss' law in a weak sense. Zero modes, related to the winding on the cylinder, provide non trivial topological variables of the theory. A Wilson loop with light-like sides is studied: in the abelian case it can be exactly computed obtaining the expected area result, whereas difficulties are pointed out in non abelian cases.
We report a perturbative calculation of the expectation value of the infinite straight line Maldacena-Wilson loop in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to order $g^6$. Thus, we extend the previous perturbative result by one order. The vacuum expectation value is reformulated in terms of a non-linear and non-local transformation, the Nicolai map, mapping the full functional measure of the interacting theory to that of a free bosonic theory. The results are twofold. The perturbative cancellations of the different contributions to the Maldacena-Wilson loop are by no means trivial an…
We calculate various Wilson loop averages in a pure $SU(N)$-gauge theory on a two-dimensional sphere, in the large $N$ limit. The results can be expressed through the density of rows in the most probable Young tableau. They are valid in both phases (small and large areas of the sphere). All averages for self-intersecting loops can be reproduced from the average for a simple (non self-intersecting) loop by means of loop equations.
We give a simple diagrammatic algorithm for writing the chiral large $N$ expansion of intersecting Wilson loops in $2D$ $SU(N)$ and $U(N) $Yang Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of holomorphic maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral $YM2$ partition functions. We briefly discuss finite $N$…
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple one- and two- parametric integrals over a single propagator in configuration space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of the configuration-space propagator and loop Feynma…
We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors with two scalars and an arbitrary number of positive-helicity gluons. These quantities resemble closely the MHV scattering amplitudes, including holomorphicity of the tree-level form factor, and the expansion in terms of two-mass easy box functions of the one-loop result. Next, we compare our result for these form factors to the calculation of a particular …
We study the correlator of two parallel Wilson lines in two-dimensional noncommutative Yang-Mills theory, following two different approaches. We first consider a perturbative expansion in the large-N limit and resum all planar diagrams. The second approach is non-perturbative: we exploit the Morita equivalence, mapping the two open lines on the noncommutative torus (which eventually gets decompacted) in two closed Wilson loops winding around the dual commutative torus. Planarity allows us to single out a suitable region of the variables involved, where a saddle-point approximation of the gener…
We propose an alternative method to study the saddle point equation in the strong coupling limit for the Wilson loop in $\mathcal{N}=2$ D=4 super Yang-Mills with an SU(N) gauge group and 2N hypermultiplets. This method is based on an approximation of the integral equation kernel which allows to solve the simplified problem exactly. To determine the accuracy of this approximation, we compare our results to those obtained recently by Passerini and Zarembo. Although less precise, this simpler approach provides an explicit expression for the density of eigenvalues that is used to derive the planar…
We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed $AdS_5\times S_5$ spacetime, which corresponds to 4D $\mathcal{N}=4$ non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual $AdS_5\times S_5$ but with the constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop)…
By using the gauge/gravity duality and the Maldacena prescription we compute the expectation values of the Wilson loops in noncommutative Yang-Mills (NCYM) theory in (3+1) dimensions. We consider both the time-like and the light-like Wilson loops. The gravity dual background is given by a particular decoupling limit of (D1,D3) bound state of type IIB string theory. We obtain the velocity dependent quark-antiquark potential and numerically study how the dipole length and the potential change with velocity (for 0 < v < 1, i.e., the Wilson loop is time-like) of the dipole as well as noncommutativ…
The derivation of the explicit formula for the vacuum expectation value of the Wilson loop functional for an arbitrary gauge group on an arbitrary orientable two-dimensional manifold is considered both in the continuum case and on the lattice. A contribution to this quantity, coming from the space of invariant connections, is also analyzed and is shown to be similar to the contribution of monopoles.
A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang-Mills continuum theories with gauge groups $SU(N)$ and $U(1)$ and space-time topologies $\Rl^1\times\Rl^1$ and $\Rl^1\times S^1$. (For the $U(1)$ theory, we also consider the $S^1\times S^1$ topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Oster…
A perturbative calculation of the correlator of three parallel open Wilson lines is performed for the U(N) theory in two non-commutative space-time dimensions. In the large-N planar limit, the perturbative series is fully resummed and asymptotically leads to an exponential increase of the correlator with the lengths of the lines, in spite of an interference effect between lines with the same orientation. This result generalizes a similar increase occurring in the two-line correlator and is likely to persist when more lines are considered provided they share the same direction.
The S-matrix for planar N = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand via MHV diagrams in twistor space. We show that at MHV, this formulation leads directly to expressions for loop integrands in d log form; i.e., the integrand is a product of exterior derivatives of logarithms of rational functions. For higher MHV degree, it is in d log form multiplied by delta functions. The parameters appearing in the d log form arise geometrically…
Supersymmetric circular Wilson loops in $\mathcal{N}=4$ Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is necessary to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, t…
We calculate circular Wilson loop expectation value of pure ${\cal N}=1$ super Yang-Mills from the Klebanov-Strassker-Tseytlin solution of supergravity and the proposed gauge/gravity duality. The calculation is performed numerically via searching world-sheet minimal surface. It is shown that Wilson loop exhibits area law for large radius which implies that ${\cal N}=1$ super Yang-Mills is confined at large distance or low energy scale. Meanwhile, Wilson loop exhibits logarithmic behavior for small radius and it indicates asymptotical freedom of ${\cal N}=1$ super Yang-Mills at short distance o…
We derive an infinite sequence of Schwinger-Dyson equations for $N=1$ supersymmetric Yang-Mills theory. The fundamental and the only variable employed is the Wilson-loop geometrically represented in $N=1$ superspace: it organizes an infinite number of supersymmetrizing insertions into the ordinary Wilson-loop as a single entity. In the large $N_{c}$ limit, our equation becomes a closed loop equation for the one-point function of the Wilson-loop average.
The Yangian level-one hypercharge generator for the super Wilson loop in N = 4 supersymmetric Yang-Mills theory is constructed. Moreover, evidence for the presence of a corresponding symmetry generator at all higher levels is provided. The derivation is restricted to the strong-coupling description of the super Wilson loop and based on the construction of novel conserved charges for type IIB superstrings on AdS_5 x S^5.
We perform a detailed study of the Yangian symmetry of smooth supersymmetric Maldacena-Wilson loops in planar N=4 super Yang-Mills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A gauge-covariant action of the Yangian generators on the Wilson line is established that generalizes previous constructions built upon path variations. Employing these generators the Yangian symmetry is proven for general paths in non-chiral N=4 superspace at the first perturbative order. The bi-local piece of the level-one generators requires the use of a regula…
Null Wilson loops in $\mathcal{N}=4$ super Yang-Mills are dual to planar scattering amplitudes. This duality implies hidden symmetries for both objects. We consider closely related infrared finite observables, defined as the Wilson loop with a Lagrangian insertion, normalized by the Wilson loop itself. Unlike ratio and remainder functions studied in the literature, this observable is non-trivial already for four scattered particles and bears close resemblance to (finite parts of) scattering processes in non-supersymmetric Yang-Mills theory. We study the general structure of the Wilson loop wit…
We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a two-sphere S^2. We show that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S^2 in the 4d N=4 SYM is captured by the 2d cHYM theory. We further argue that expectation values of Wilson loops in the cHYM theory agree with the prescription "two-dimensional bosonic Yang-Mills excluding instanton contributions". Hence, we support the recent conjecture by Drukker, Giombi, Ricci and Trancanelli on the 1/8 BPS Wilson loops on…
The uniquess of the effective actions describing 4D SU(2) and SU(3) continuum, infinite-volume Yang-Mills thermodynamics in their deconfining and preconfining phases is made explicit. Subsequently, the spatial string tension is computed in the approach proposed by Korthals-Altes. This SU(2) calculation is based on a particular, effective two-loop correction to the pressure needed for the extraction of the hypothetic number density of isolated and screened magnetic monopoles or antimonopoles in the deconfining phase. By exponentiating the exchange of the tree-level massless but one-loop dressed…
$QCD_2$ with fermions in the adjoint representation is invariant under $SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure (k-sectors). The static potential between adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang-Mills theory with the same non-trivial structure. When the (Euclidean) space-time is compactified on a sphere $S^2$, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and…
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with $n$ windings a non trivial scaling intertwines $n$ and $N$. In the non-commutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger gauge group $U(\infty)$. We perform an explicit perturbative calculation of such a loop up to ${\cal O}(g^6)$; rather surprisingly, we find that in the contribution from the crossed graphs (the genuine non-commutative te…
We examine the one-loop partition function describing the fluctuations of the superstring in a Schwarzschild-AdS$_5\times S^5$ background. On the bosonic side, we demonstrate the one-loop equivalence of the Nambu-Goto action and the Polyakov action for a general worldsheet, while on the fermionic side, we consider the reduction of the ten-dimensional Green-Schwarz fermion action to a two-dimensional worldsheet action. We derive the partition functions of the worldsheets corresponding to both straight and parallel Wilson lines. We show that the UV divergences of the functional determinants in t…
A rectangular Wilson loop centered at the origin, with sides parallel to space and time directions and length $2L$ and $2T$ respectively, is perturbatively evaluated ${\cal O}(g^4)$ in Feynman gauge for Yang--Mills theory in $1+(D-1)$ dimensions. When $D>2$, there is a dependence on the dimensionless ratio $L/T$, besides the area. In the limit $T \to \infty$, keeping $D>2$, the leading expression of the loop involves only the Casimir constant $C_F$ of the fundamental representation and is thereby in agreement with the expected Abelian-like time exponentiation (ALTE). At $D= 2$ the result depen…
We compute the two-loop result for the null pentagonal Wilson loop with a Lagrangian insertion (normalized by the Wilson loop without insertion) in planar, maximally supersymmetric Yang-Mills theory. This finite observable is closely related to the Amplituhedron, and it is reminiscent of finite parts of planar two-loop five-particle scattering amplitudes. We verify that, up to this loop order, the leading singularities are given by the same conformally invariant expressions that appear in all-plus pure Yang-Mills amplitudes. The accompanying weight-four transcendental functions are expressed i…
We perform a perturbative ${\cal O}(g^4)$ Wilson loop calculation for the U(N) Yang-Mills theory defined on non-commutative one space - one time dimensions. We choose the light-cone gauge and compare the results obtained when using the Wu-Mandelstam-Leibbrandt ($WML$) and the Cauchy principal value ($PV$) prescription for the vector propagator. In the $WML$ case the $θ$-dependent term is well-defined and regular in the limit $θ\to 0$, where the commutative theory is recovered; it provides a non-trivial example of a consistent calculation when non-commutativity involves the time variable. In th…
We propose that, in N=4 Super Yang-Mills theory, correlation functions of certain 1/8 BPS Wilson loops and local operators inserted on a S^2 in space-time may be computed in terms of analogous observables in the "zero-instanton" sector of 2d Yang-Mills theory. The Wilson loops are mapped to the standard Wilson loops of the 2d theory, as recently conjectured, while the local operators are mapped to powers of the 2d field strength. We give several perturbative checks of the correspondence, and derive from 2d Yang-Mills a two-matrix model for the correlator of a local operator and a Wilson loop o…
We discuss the relation between the Gell-Mann-Low beta function and the ``flowing couplings'' of the Wilsonian action $S_Ł[ϕ]$ of the exact renormalization group (RG) at the scale $Ł$. This relation involves the ultraviolet region of $Ł$ so that the condition of renormalizability is equivalent to the Callan-Symanzik equation. As an illustration, by using the exact RG formulation, we compute the beta function in Yang-Mills theory to one loop (and to two loops for the scalar case). We also study the infrared (IR) renormalons. This formulation is particularly suited for this study since: $i$) $Ł$…
Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, $<W>\sim\exp((constant)\sqrt{g^2N})$. For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of $\sqr…
Using holography we have studied the time-dependent potential of a quark-antiquark pair in a dynamical strongly coupled plasma. The time-dependent plasma, whose dynamics is originated from the energy injection, is dual to AdS-Vaidya background. The quark-antiquark pair is represented by the endpoints of a string stretched from the boundary to the bulk. The evolution of the system is studied by evaluating the potential between quark and anti-quark, extracted from the expectation value of the Wilson loop, throughout the process. Our results show that the time-dependent potential depends on the s…
We examine how the average of double-winding Wilson loops depends on the number of color $N$ in the $SU(N)$ Yang-Mills theory. In the case where the two loops $C_1$ and $C_2$ are identical, we derive the exact operator relation which relates the double-winding Wilson loop operator in the fundamental representation to that in the higher dimensional representations depending on $N$. By taking the average of the relation, we find that the difference-of-areas law for the area law falloff recently claimed for $N=2$ is excluded for $N \geq 3$, provided that the string tension obeys the Casimir scali…
AI for Pattern Hunter: Application in Wilson Loop of 2D Lattice Yang-Mills Theory
Peking University（北京大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Physics, Beijing Normal University（北京师范大学物理学院）；State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University（华南师范大学量子物质研究院核物理与技术国家重点实验室）；Beijing Computational Science Research Center（北京计算科学研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）
