Effective Action for Noncommutative U（1） Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

Renormalisation of Noncommutative Quantum Field Theories

We sketch our proof that the real Euclidean ⁴-model on the four-dimensional Moyal plane is renormalisable to all orders. The bare action of relevant and marginal couplings of the model is parametrised by four (divergent) quantities which require normalisation to the experimental data. The corresponding physical parameters are the mass, the field amplitude (to be normalised to 1), the coupling constant and—in addition to the commutative version—the frequency of a harmonic oscillator potential.     

Star products from commutative string theory

A boundary-state computation is performed to obtain derivative corrections to the Chern-Simons coupling between a p-brane and the RR gauge potential C ^p −3. We work to quadratic order in the gauge field strength F, but all orders in derivatives. In a certain limit, which requires the presence of a constant B-field background, it is found that these corrections neatly sum up into the *₂ product of (commutative) gauge fields. The result is in agreement with a recent prediction using noncommutativity.     

Noncommutative Sine-Gordon Model

The sine-Gordon model may be obtained by dimensional and algebraic reduction from (2+2)-dimensional self-dual U(2) Yang-Mills through a (2+1)-dimensional integrable U(2) sigma model. It is argued that the noncommutative (Moyal) deformation of this procedure should relax the algebraic reduction from U(2) U(1) to U(2)U(1) × U(1). The result are novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is outlined for constructing its multi-soliton solutions. Finally, the tree-level amplitudes demonstrate that this model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.     

The Geometric Construction of WZW Effective Action in Noncommutative Manifold

By constructing close-one-cochain density Ω^12n in the gauge group space we get the Wess-Zumino-Witten (WZW) effective Lagrangian on high-dimensional noncommutative space.Especially consistent anomalies derived from this WZW effective action in noncommutative four-dimensional space coincide with those obtained by L.Bonora etc.(het-th/0002210).     

Letter: Perturbative Evaluation of the Effective Action for a Self-Interacting Conformal Field on a Manifold with Boundary

In a series of three projects a new technique which allows for higher-loop renormalisation on a manifold with boundary has been developed and used in order to assess the effects of the boundary on the dynamical behaviour of the theory. Commencing with a conceptual approach to the theoretical underpinnings of the, underlying, spherical formulation of Euclidean Quantum Field Theory this overview presents an outline of the stated technique's conceptual development, mathematical formalism and physical significance.     

Drinfeld-Manin instanton and its noncommutative generalization

The Drinfeld-Manin construction of U(N)instanton is reformulated in the ADHM formulism,which gives explicit general solutions of the ADHM constraints for U(N)(N ≥ 2k-1)k-instantons.For the N<2k-1 case,implicit results are given systematically as further constraints.We find that this formulism can easily be generalized to the noncommutative case,where the explicit solutions are also obtained.     

Effective Field Theory for Fermi Systems in a Large N Expansion

A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which particle-hole bubbles are resummed to all orders. For spin-independent interactions, the loop expansion is equivalent to a systematic expansion in 1/N, where N is the spin-isospin degeneracy g. Numerical results at next-to-leading order are presented and the connection to the Bose limit of this system is elucidated.     

Letter: O(d + 1, d + n + 1)-Invariant Formulation of Stationary Heterotic String Theory

We present a pair of symmetric formulations of the matter sector of the stationary effective action of heterotic string theory that arises after the toroidal compactification of d dimensions. The first formulation is written in terms of a pair of matrix potentials Z ₁ and Z ₂ which exhibits a clear symmetry between them and can be used to generate new families of solutions on the basis of either Z ₁ or Z ₂; the second one is an O(d + 1, d + n + 1)-invariant formulation which is written in terms of a matrix vector W endowed with an O(d + 1, d + n + 1)-invariant scalar product which linearizes the action of the O(d + 1, d + n + 1)symmetry group on the coset space O(d + 1, d + n + 1)/[O(d + 1) × O(d + n + 1)]; this fact opens as well a simple solution-generating technique which can be applied on the basis of known solutions.     

Trefoil Symmetry V: Class Representations for the Minimal Clover Extension

We construct four different real representations of the minimal vector clover extension and their covariant derivatives. We determine their relation to the basic representation and initiate the exploration of constrained superfields.     

Trefoil Symmetry IV: Basic Enhanced Superspace for the Minimal Vector Clover Extension

We construct a differential representation and covariant derivatives of the minimal vector clover extension of the Poincaré algebra. In analogous way as in the supersymmetric case, there arises an enhanced superspace which allows to define superfields. The action of group transformations on such superfields determines a representation out of which the covariant derivatives are obtained.     

Center-symmetric dimensional reduction of hot Yang-Mills theory

It is expected that incorporating the center symmetry in the conventional dimensionally reduced effective theory for high-temperature SU(N_c) Yang-Mills theory, EQCD, will considerably extend its applicability towards the deconfinement transition. The construction of such a center-symmetric effective theory for the case of two colors is reviewed and lattice simulation results are presented. The simulations demonstrate that unlike EQCD, the new center-symmetric theory undergoes a second order confining phase transition in complete analogy with the full theory.     

二重非交换时空与二重复对称引力理论

通过引入二重复对称度规张量,建立了一种二重复对称引力理论. 从一个二重实的作用量出发,导出了静态球对称二重复度规的具体表达式. 该理论扩展了Moffat结果,不仅自然地得到了双曲复对称引力理 论,而且把著名的Schwarzschild解作为特殊情况包含在其中,并且在线性化的弱场近似下自动摆脱了Moffat理论中存在的负 能鬼态问题. 进一步,通过将二重复坐标推广到满足二重非对易关系以及将Moyal星积二重 化,由此构造出二重非交换复对称引力场作用量.关键词：非交换几何复对称度规非对易坐标引力场作用量