We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared--ultraviolet mixing problem.
We discuss recent endeavours in connecting twistor theory to higher-spin theories and the IKKT- matrix model. Starting with a brief review on higher-spin algebra hs in four-dimensional target space, we elucidate how higher-spin symmetry can be encoded in hs-valued sections/holomorphic differential forms on (non-commutative) twistor space. This provides an efficient way to construct local higher-spin theories in spacetime from some actions on (non-commutative) twistor space. Remarkably, some higher-spin theories obtained within the framework of twistor theory can have non-trivial scattering amp…
We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed $D=4$ quantum inhomegeneous conformal Hopf algebras $\mathcal{U}_{θ}(su(2,2)\ltimes T^{4}$) and $\mathcal{U}_{\barθ}(su(2,2)\ltimes\bar{T}^{4}$), where $T^{4}$ describe complex twistor coordinatesand $\bar{T}^{4}$ the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently we introduce the quantum deformations of $D=4$ Heisenberg-conformal algebra (H…
We construct massless infinite spin irreducible representations of the six-dimensional Poincaré group in the space of fields depending on twistor variables. It is shown that the massless infinite spin representation is realized on the two-twistor fields. We present a full set of equations of motion for two-twistor fields represented by the totally symmetric $\mathrm{SU}(2)$ rank $2s$ two-twistor spin-tensor and show that they carry massless infinite spin representations. A field twistor transform is constructed and infinite spin fields are found in the space-time formulation with an additional…
受N=2，D=4超引力中黑洞物理的启发，我们研究了由射影特殊Kahler流形M_s通过c-映射构造得到的四元数Kahler流形M的几何性质.改进以前的治疗，我们计算的Kahler势的扭量空间Z和Swann空间S在适应海森堡对称性的复坐标。结果与特殊Kahler流形M_s的Hesse势有简单的关系，从而与BPS黑洞的Bekenstein-Hawking熵有简单的关系.我们显式构造了“协变c-map”和“twistor map”，它们将M x CP ^1（分别）上的实坐标联系起来。M x R^4/Z_2）转换为Z上的复坐标（分别为S）。作为应用，我们求解了M上的一般BPS测地运动，并给出了将H^1（Z，O（-k））中的元素与M上被一阶或二阶微分算子零化的无质量场联系起来的四元数Penrose变换的显式积分公式.最后，我们计算了具有固定电荷和磁荷的BPS黑洞的精确径向波函数（在超引力近似下）。
Large-N Wilsonian beta function in SU(N) Yang-Mills theory by localization on the fixed points of a semigroup contracting the functional measure
在大N SU（N）杨-米尔斯理论的某个（非对易）版本中，存在特殊的威尔逊圈，由于几何原因称为扭量威尔逊圈，其v. e. v.与其算符定义中出现的参数无关。有一个半群通过重新标度作用于参数，并作用于函数测度，通过收缩测度的支持，由尼古拉映射的非超对称版本分解为反自对偶轨道。因此扭量威尔逊圈局部化在压缩半群的不动点上。这种局部化是一种非超对称的模拟局部化，发生在Nekrasov配分函数的n=2超对称YM理论上的固定点上的某个环面行动的模空间（非交换）瞬子。在大N YM的情况下，在n=2超对称YM的情况下，本地化的一个主要后果是，在反自对偶变量的威尔逊耦合常数的β函数是一个循环的准确。因此，大N杨-米尔斯正则β函数具有再现前两个普适微扰系数的NSVZ形式。
Non(anti)commutative superspace with coordinate-dependent deformation
考虑了形变参数与坐标有关的非（反）对易超空间$C^{αβ}$。我们证明了手征${\cal N}=1/2$超对称性可以被定义，并且手征和反手征超场在Moyal-Weyl结合积下仍然是封闭的。只要$C^{αβ}$满足一个适当的条件，并能与形变原点的引力光子背景联系起来，就可以构造一个相容的${\cal N}=1/2$ Super Yang-Mills形变理论.在加入物质后，我们还讨论了Konishi反常和Gluino凝聚。
The Poisson gauge algebra is a semi-classical limit of complete non-commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a corresponding algebra of gauge symmetries. The proposed model is designed to investigate the semi-classical features of the full non-commutative gauge theory with coordinate dependent non-commutativity $Θ^{ab}(x)$, especially whose with a non-constant rank. We derive the expression for the covariant derivative of matter field. The commutator relation for the cov…
In this paper, we derive the non-commutative corrections to the maximal acceleration in the Doplicher-Fredenhagen-Roberts (DFR) space-time and show that the effect of the non-commutativity is to decrease the magnitude of the value of the maximal acceleration in the commutative limit. We also obtain an upper bound on the acceleration along the non-commutative coordinates using the positivity condition on the magnitude of the maximal acceleration in the commutative space-time. From the Newtonian limit of the geodesic equation and Einstein's equation for linearised gravity, we derive the explicit…
In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspective. In order to do so, we consider the graded Lie algebra $\mathfrak{sl}(2|1)$ generated by Hermitian bilinear forms in the non-commutative dynamical variables and the Dirac matrices in $2+1$ dimensions. By further defining a total angular momentum operator, we are able to express a class of Dirac Hamiltonians completely in terms of these operators. In this way, we analyze the energy spectrum of some simple models by constructing and studying the represe…
