Ordinary Yang-Mills Theory Research Articles

Non-perturbative Lee-Wick gauge theory: Towards Confinement & RGE with strong couplings

We consider a non-Abelian Lee–Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin invariance. It contains fourth-order derivative as extensions of the kinetic term, leading to massive ghosts in the theory upon quantization. We particularly provide essential clues towards confinement conditions in strongly-coupled regimes, using the Kugo–Ojima approach, and obtain the functions in the non-perturbative regimes. This is achieved using a set of exact solutions of the corresponding local theory in terms of Jacobi elliptical functions. We obtain a similar function just as for the ordinary Yang-Mills theory but the main differences are that now, the cut-off arises naturally from the Lee–Wick heavy mass scales (M). We show that the fate of the ghosts are fixed in these regimes: they are no more the propagating degrees of freedom in the infrared-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit , one recovers the standard results for the local non-Abelian Yang-Mills theory.

Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model

We present the results of an exploratory study of the numerical stochastic perturbation theory (NSPT) applied to the four dimensional twisted Eguchi-Kawai (TEK) model. We employ a Kramers type algorithm based on the Generalized Hybrid Molecular Dynamics (GHMD) algorithm. We have computed the perturbative expansion of square Wilson loops up to O(g8). The results of the first two coefficients (up to O(g4)) have a high precision and match well with the exact values. The next two coefficients can be determined and even extrapolated to large N, where they should coincide with the corresponding coefficients for ordinary Yang-Mills theory on an infinite lattice. Our analysis shows the behaviour of the probability distribution for each coefficient tending to Gaussian for larger N. The results allow us to establish the requirements to extend this analysis to much higher order.

Gluon bound state and asymptotic freedom derived from the Bethe–Salpeter equation

In this paper we study the two-body bound states for gluons and ghosts in a massive Yang-Mills theory which is obtained by generalizing the ordinary massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we give a systematic derivation of the coupled Bethe-Salpeter equations for gluons and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the composite operators within the framework of the path integral quantization. Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude representing the simultaneous bound states of gluons and ghosts by solving the homogeneous Bethe-Salpeter equation in the ladder approximation. We study how the inclusion of ghosts affects the two-gluon bound states in the cases of the standing and running gauge coupling constant. Moreover, we show explicitly that the approximate solutions obtained for the gluon-gluon amplitude are consistent with the ultraviolet asymptotic freedom signaled by the negative $\beta$ function.

Dyson–Schwinger equations and $$\mathcal{N}=4$$ N = 4 SYM in Landau gauge

${\cal N}=4$ Super Yang-Mills theory is a highly constrained theory, and therefore a valuable tool to test the understanding of less constrained Yang-Mills theories. Our aim is to use it to test our understanding of both the Landau gauge beyond perturbation theory as well as truncations of Dyson-Schwinger equations in ordinary Yang-Mills theories. We derive the corresponding equations within the usual one-loop truncation for the propagators after imposing the Landau gauge. We find a conformal solution in this approximation, which surprisingly resembles many aspects of ordinary Yang-Mills theories. We furthermore identify which role the Gribov-Singer ambiguity in this context could play, should it exist in this theory.

Representation of a gauge field via intrinsic “BRST” operator

We show that there exists a representation of a matrix-valued gauge field via intrinsic “BRST” operator assigned to matrix-valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang–Mills theory. In the case of a generating quasigroup/groupoid, we give a natural counterpart to the Yang–Mills action. The latter counterpart does also apply as to the most general case of an involution for matrix-valued gauge generators.

Deformations of Yang-Mills theory

We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has the property that whenever two derivatives act on an internal line propagator, the result is a delta-function and the line collapses to a point. This means that there remains at most one derivative on each internal line, which gives improved ulta-violet behaviour. For many purposes, this class of theories behaves just like ordinary Yang-Mills theory. In particular, they all share the Yang-Mills theory MHV amplitudes. Moreover, these theories remain constructible in the sense that higher-point tree level scattering amplitudes can be obtained from the lower-point amplitudes using the BCFW recursion relations. Also, the square of these gauge-theory amplitudes gives the scattering amplitudes of "deformations" of General Relativity, at least for the low particle numbers that we checked. We compute the one-loop beta-function of the first new coupling constant, and find it to be positive, which signals the associated non-renormalisable interaction becoming important in the ulta-violet.

Supersymmetric duality in superloop space

In this paper we constructed superloop space duality for a four dimensional supersymmetric Yang–Mills theory with \(\mathcal {N} =1\) supersymmetry. This duality reduces to the ordinary loop space duality for the ordinary Yang–Mills theory. It also reduces to the Hodge duality for an abelian gauge theory. Furthermore, the electric charges, which are the sources in the original theory, appear as monopoles in the dual theory. Whereas, the magnetic charges, which appear as monopoles in the original theory, become sources in the dual theory.

Deconfinement in Yang-Mills theory through toroidal compactification with deformation

We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double- trace deformation of toroidally compactified Yang-Mills theory on R2 \times S1_L \times S1_{\beta}. At large N, fixed-L, and arbitrary {\beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {\beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.

One-loop counterterms in the Yang-Mills theory with a gauge-invariant ghost field Lagrangian

One-loop calculations of renormalization constants in the model with gauge invariant ghost field Lagrangian are performed. It is shown that the model is asymptotically free and the renormalization constants satisfy the same equation as in the ordinary Yang-Mills theory.

Supersymmetry inspired QCD beta function

We propose an all orders beta function for ordinary Yang-Mills theories with or without fermions inspired by the Novikov-Shifman-Vainshtein-Zakharov beta function of N=1 supersymmetric gauge theories. The beta function allows us to bound the conformal window. When restricting to one adjoint Weyl fermion we show how the proposed beta function matches the one of supersymmetric Yang-Mills theory. The running of the pure Yang-Mills coupling is computed and the deviation from the two loop result is presented. We then compare the deviation with the one obtained from lattice data also with respect to the two loop running.

Nonabelian localization for gauge theory on the fuzzy sphere

We apply nonabelian equivariant localization techniques to Yang-Mills theory on the fuzzy sphere to write the partition function entirely as a sum over local contributions from critical points of the action. The contributions of the classical saddle-points are evaluated explicitly, and the partition function of ordinary Yang-Mills theory on the sphere is recovered in the commutative limit.

A quantization of twistor Yang-Mills theory through the background field method

Four-dimensional Yang-Mills theory formulated through an action on twistor space has a larger gauge symmetry than the usual formulation, which in previous work was shown to allow a simple gauge transformation between textbook perturbation theory and the Cachazo-Svr\ifmmode \check{c}\else \v{c}\fi{}ek-Witten rules. In this paper we study nonsupersymmetric twistor Yang-Mills theory at loop level using the background field method. For an appropriate partial quantum field gauge choice it is shown that the calculation of the effective action is equivalent to (the twistor lift of) the calculation in ordinary Yang-Mills theory in the Chalmers and Siegel formulation to all orders in perturbation theory. A direct consequence is that the twistor version of Yang-Mills theory is just as renormalizable in this particular gauge. As applications an explicit calculation of the Yang-Mills beta function and some preliminary investigations into using the formalism to calculate S-matrix elements at loop level are presented. In principle the technique described in this paper generates consistent quantum completions of the Cachazo-Svr\ifmmode \check{c}\else \v{c}\fi{}ek-Witten rules. However, by inherent limitations of the partial gauge choice employed here, this offers in its current form mainly simplifications for tree-level forestry. The method is expected to be applicable to a wide class of four-dimensional gauge theories.

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.

Open string with a backgroundBfield as the first order mechanics, noncommutativity, and soldering formalism

To study noncommutativity properties of the open string with constant B field, we construct a mechanical action that reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit B{yields}{infinity}. In particular, it is true for the zero mode of the string coordinate, which means that the noncommutativity is an intrinsic property of this mechanical system. We describe the arbitrariness in the relation existing between the mechanical and the string variables and show that noncommutativity of the string variables on the boundary can be removed. This is in correspondence with the result of Seiberg and Witten on the relation among noncommutative and ordinary Yang-Mills theories. The recently developed soldering formalism helps us to establish a connection between the original open string action and the Polyakov action.

Morita duality and noncommutative Wilson loops in two dimensions

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Analytic expressions for correlators of Wilson loops with infinite winding number are also derived and shown to agree with results from ordinary Yang-Mills theory.

Gauge theory on fuzzyS2×S2and regularization on noncommutative Bbb R4

We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutative limit N -> infinity. The model can be used as a regularization of gauge theory on noncommutative R^4_\theta in a particular scaling limit, which is studied in detail. We also find topologically non-trivial U(1) solutions, which reduce to the known "fluxon" solutions in the limit of R^4_\theta, reproducing their full moduli space. Other solutions which can be interpreted as 2-dimensional branes are also found. The quantization of the model is defined non-perturbatively in terms of a path integral which is finite. A gauge-fixed BRST-invariant action is given as well. Fermions in the fundamental representation of the gauge group are included using a formulation based on SO(6), by defining a fuzzy Dirac operator which reduces to the standard Dirac operator on S^2 x S^2 in the commutative limit. The chirality operator and Weyl spinors are also introduced.

Algebroid Yang-Mills Theories

A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently many E-Killing vectors leads to an astonishingly mild deformation of ordinary Yang-Mills theories: Additional fields turn out to carry no propagating modes. Instead, they serve as moduli parameters gluing together in part different Yang-Mills theories. This leads to a symmetry enhancement at critical points of these fields, as is also typical for String effective field theories.

Stabilization of Yang-Mills chaos in non-Abelian Born-Infeld theory

We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian which arises in superstring theory as a result of summation of all orders in the string slope parameter $\alpha'$. It is shown that generically the Born-Infeld dynamics is less chaotic than that in the ordinary Yang-Mills theory, and at high enough field strength the Yang-Mills chaos is stabilized. More generally, a smothering effect of the string non-locality on behavior of classical fields is conjectured.

Teleparallel gravity and dimensional reductions of noncommutative gauge theory

We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the noncommutativity scale. The effective field theory can also contain higher-curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described.

Dynamics of Wilson observables in non-commutative gauge theory

An equation for the quantum average of the gauge invariant Wilson loop in non-commutative Yang–Mills theory with gauge group U( N) is obtained. In the 't Hooft limit, the equation reduces to the loop equation of ordinary Yang–Mills theory. At finite N, the equation involves the quantum averages of the additional gauge invariant observables of the non-commutative theory associated with open contours in space–time. We also derive equations for correlators of several gauge invariant (open or closed) Wilson lines. Finally, we discuss a perturbative check of our results.