Noncommutative Yang-Mills Theory Research Articles

Two-dimensional non-commutative Yang-Mills theory: coherent effects in open Wilson line correlators

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.

Open Wilson lines and group theory of noncommutative Yang-Mills theory in two dimensions

The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only topological numbers of Heisenberg modules and enables extraction of the weak-coupling limit of the gauge theory. A dual algebraic expansion involves only group theoretic quantities, winding numbers and translational zero modes, and enables analysis of the strong-coupling limit of the gauge theory and the high-momentum behaviour of open Wilson lines. The dual expressions can be interpreted physically as exact sums over contributions from virtual electric dipole quanta.

Note on (D6, D8) bound state, massive duality and non-commutativity

In this paper we study half-supersymmetric (D6, D8) bound state brane configuration of massive type IIA supergravity. We show this bound state can also be generated by using massive T-duality rules of type II strings in D=9 and starting from D7-branes. We write down corresponding Killing spinors and find that these backgrounds indeed preserve 16 supersymmetries like any other D p-brane bound state with B μν field. We also make a point on the massive nature of B μν field in this background. The Seiberg–Witten limits to obtain non-commutative Yang–Mills theories in D=9 are also discussed, but the full understanding of such gauge theories remains unanswered.

Noncommutative Instantons via Dressing and Splitting Approaches

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative Euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques.

NCOS and D-branes in time-dependent backgrounds

We study noncommutative open string (NCOS) theories realized in string theory with time-dependent backgrounds. Starting from a noncommutative Yang–Mills theory (NCYM) with a constant space–space noncommutativity but in a time-dependent background and making an S-dual transformation, we show that the resulting theory is an NCOS also in a time-dependent background but now with a time-dependent time–space noncommutativity and a time-dependent string scale. The corresponding dual gravity description is also given. A general SL(2,Z) transformation on the NCYM results in an NCOS with a time-dependent time-space noncommutativity and a constant space–space noncommutativity, and also in a time-dependent background.

Noncommutative GUTs, Standard Model and C, P, T

Noncommutative Yang–Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter θ, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in θ. We study in detail the reality, Hermiticity and C, P, T properties of the Seiberg–Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg–Witten map.

Scaling properties of the perturbative Wilson loop in two-dimensional noncommutative Yang-Mills theory

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 nontrivial scaling intertwines n and N. In the noncommutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger gauge group $U(\ensuremath{\infty}).$ We perform an explicit perturbative calculation of such a loop up to $\mathcal{O}{(g}^{6});$ rather surprisingly, we find that in the contribution from the crossed graphs (the genuine noncommutative terms) the scaling we mentioned occurs for large n and N in the limit of maximal noncommutativity $\ensuremath{\theta}=\ensuremath{\infty}.$ We present arguments in favor of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.

Tachyon Condensation of D2/D4-Brane System in Noncommutative Gauge Theory

In this paper we construct the 2+1 effective theory of the light states in D2/D4-brane system in the context of noncommutative Yang-Mills theory. This effective theory is noncommutative and tachyonic, however, it is not taking the form of an Abelian Higgs model as naively expected. We solve the classical solutions of the effective theory which are nicely corresponding to different states during the tachyon condensation process of the dissolution of D2-brane into D4-brane. We also find that if the expected stable self-dual D0/D4 configuration as the unit-winding vortex exists, it would be highly calibrated in the effective theory and be out of the reach of the analytic solutions.

Wilson line correlators in two-dimensional noncommutative Yang-Mills theory

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 general Morita expression for the correlator can be performed. In this region the correlator nicely compares with the perturbative result, exhibiting an exponential increase with respect to the momentum p.

Seiberg-Witten maps in the context of the antifield formalism

The formulation of Seiberg-Witten maps from the point of view of consistent deformations of gauge theories in the context of the Batalin-Vilkovisky antifield formalism is reviewed. Some additional remarks on noncommutative Yang-Mills theory are made.

Transport equation and hard thermal loops in noncommutative Yang-Mills theory

We show that the high temperature limit of the noncommutative thermal Yang-Mills theory can be directly obtained from the Boltzmann transport equation of classical particles. As an illustration of the simplicity of the Boltzmann method, we evaluate the two- and the three-point gluon functions in the noncommutative $U(N)$ theory at high temperatures T. These amplitudes are gauge invariant and satisfy simple Ward identities. Using the constraint satisfied at order ${T}^{2}$ by the covariantly conserved current, we construct the hard thermal loop effective action of the noncommutative theory.

Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups

Seiberg-Witten maps and a recently proposed construction of noncommutative Yang-Mills theories (with matter fields) for arbitrary gauge groups are reformulated so that their existence to all orders is manifest. The ambiguities of the construction which originate from the freedom in the Seiberg-Witten map are discussed with regard to the question whether they can lead to inequivalent models, i.e., models not related by field redefinitions.

Non-commutative instantons and the Seiberg-Witten map

We present several results concerning non-commutative instantons and the Seiberg-Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang-Mills theory. These include the two dimensional ``shift operator'' solutions and the four dimensional Nekrasov-Schwarz instantons as special cases. We also study how the Seiberg-Witten map acts on these instanton solutions. The infinitesimal Seiberg-Witten map is shown to take a very simple form in operator language, and this result is used to give a commutative description of non-commutative instantons. The instanton is found to be singular in commutative variables.

A note on half-supersymmetric bound states in M-theory and type IIA string theory

By using O(7,7) transformations, to deform D6-branes, we obtain half-supersymmetric bound state solutions of type IIA supergravity, containing D6, D4, D2, D0, F1-branes and waves. We lift the solutions to M-theory which gives half-supersymmetric M-theory bound states, e.g. KK6–M5–M5–M5– M2–M2–M2–MW. We also take near-horizon limits for the type IIA solutions, which give supergravity duals of seven-dimensional non-commutative open string theory (with spacetime and space–space non-commutativity), non-commutative Yang–Mills theory (with space–space and light-like non-commutativity) and an open D4-brane theory.

(NS5-brane, D5-brane, D3-brane) bound state, open D3-brane, open D5-brane limits, andSL(2,Z)duality

We generalize the nonthreshold bound state in type IIB supergravity of the form (NS5-brane, D5-brane, D3-brane) constructed by the present authors [J. High Energy Phys. 02, 026 (2001)] to a nonzero asymptotic value of the axion $({\ensuremath{\chi}}_{0}).$ We identify the decoupling limits corresponding to both the open D3-brane theory and open D5-brane theory for this supergravity solution as expected. However, we do not find any noncommutative Yang-Mills theory (NCYM) limit for this solution in the presence of NS5-branes. We then study the $\mathrm{SL}(2,Z)$ duality symmetry of type IIB theory for both open D3-brane (OD3) limit and open D5-brane (OD5) limit. We find that for OD3 theory, a generic $\mathrm{SL}(2,Z)$ duality always gives another OD3 theory irrespective of the value of ${\ensuremath{\chi}}_{0}$ being rational or not. This indicates that OD3 theory is self-dual. But, under a special set of $\mathrm{SL}(2,Z)$ transformations for which ${\ensuremath{\chi}}_{0}$ is rational, OD3 theory goes over to a (5+1)-dimensional NCYM theory and these two theories in this case are related to each other by strong-weak duality symmetry. On the other hand, for OD5 theory, a generic $\mathrm{SL}(2,Z)$ duality gives another OD5 theory if ${\ensuremath{\chi}}_{0}$ is irrational, but when ${\ensuremath{\chi}}_{0}$ is rational it gives the little string theory limit indicating that OD5 theory is S dual to the type IIB little string theory.

BPS Bound States Of D0-D6 And D0-D8 Systems In AB-Field

The D0-D6 system, which is not supersymmetric in the absence of a Neveu-Schwarz B-field, becomes supersymmetric if a suitable constant B-field is turned on. On one side of the supersymmetric locus, this system has a BPS bound state, and on the other side it does not. After compactification on T^6, this gives a simple example in which the number of 1/8 BPS states jumps as the moduli of the compactification are changed. The D0-D8 system in a B-field has two different supersymmetric loci, only one of which is continuously connected to the familiar supersymmetric D0-D8 system without a B-field. In a certain range, the D0-D8 system also has a BPS bound state. In the limit in which the B-field goes to infinity, supersymmetric D0-D6 and D0-D8 systems and their bound states can be studied using noncommutative Yang-Mills theory.

Noncommutative supersymmetric Yang-Mills theory in ten dimensions with higher-derivative terms

We present an action for noncommutative supersymmetric Yang-Mills theory in ten dimensions, and confirm its invariance under supersymmetry. We next add higher-order derivative terms to such a noncommutative supersymmetric action. These terms contain fields as high as the quartic order. The resulting action can be regarded as a supersymmetric generalization of the noncommutative non-Abelian Dirac-Born-Infeld action. Some ambiguities related to field redefinitions are also clarified.

Gravity/Non-Commutative Yang-Mills Correspondence and Doubletons

We discuss the gravity dual description for a non-commutative Yang-Mills theory, which reduces to that on AdS_{5} x S_{5} in the commutative limit. It is found that doubletons do not decouple in this dual gravity description unless one takes the commutative limit. The decoupling of the doubletons in AdS_{5} space implies that the dual gauge theory has SU(N) gauge symmetry. Our result implies that this gravity description is dual to non-commutative U(N) gauge theory. It is compatible with the claim that U(1) and SU(N) gauge symmetries can not separate in non-commutative U(N) gauge theory.

Symplectic connections, noncommutative Yang–Mills theory and supermembranes

In built noncommutativity of supermembranes with central charges in eleven dimensions is disclosed. This result is used to construct an action for a noncommutative supermembrane where interesting topological terms appear. In order to do so, we first set up a global formulation for noncommutative Yang–Mills theory over general symplectic manifolds. We make the above constructions following a pure geometrical procedure using the concept of connections over Weyl algebra bundles on symplectic manifolds. The relation between noncommutative and ordinary supermembrane actions is discussed.

Noncommutative differential calculus for a D-brane in a nonconstantBfield background withH=0

In this paper we try to construct noncommutative Yang-Mills theory for generic Poisson manifolds. It turns out that the noncommutative differential calculus defined in an old work is exactly what we need. Using this calculus, we generalize results about the Seiberg-Witten map, the Dirac-Born-Infeld action, the matrix model and the open string quantization for constant B field to a nonconstant background with $H=0.$