In a attempt to treat a supergravity as a tensor representation, the 4-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc)graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors[14], with N = p + k: These quaternionic superspaces have 4 + k (N - k) even-quaternionic coordinates and 4N odd- quaternionic coordinates where each coordinate is a quaternion composed by four C-felds (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case the number of felds of the supergravity is determined by the number of components of the tensor representation of the 4-dimensional N-extended quaternionic superspaces. The role of tensorial central charges for any N even USp (N) = Sp (N;HC) \ U (N;HC) is elucidated from this theoretical context.
Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The specific construction contains naturally the supertwistor one of the previous work by Litov and Pervushin [1] and it is shown that in the case of extended supersymmetry such an approach leads to the separation of a class of superspaces and and its groups of motion. We briefly discuss this particular extension to the domain of quaternionic superspaces as nonli…
We give a brief review of the twistor string approach to supersymmetric Yang-Mills theories with an emphasis on the different formulations of (super)string models in supertwistor space and their superspace form. We discuss the classical equivalence among the Siegel closed twistor string and the Lorentz harmonics formulation of the (N=4) tensionless superstring, and notice the possible relation of the twistor string to the D=10 Green-Schwarz superstring action, as well as to models in the enlarged, tensorial superspaces that are relevant in higher spin theories.
We explain some details of the construction of composite operators in N=4 SYM that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC) superspace. We give a step-by-step elementary derivation and show that the result coincides with the recent hypothesis put forward in arXiv:1603.04471 within the twistor approach. We provide the appropriate LHC-to-twistors dictionary.
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）。
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed
We show that the geometry of $4n$-dimensional quaternionic Kähler spaces with a locally free $\mathbb{R}^{n+1}$-action admits a Gibbons-Hawking-like description based on the Galicki-Lawson notion of quaternionic Kähler moment map. This generalizes to higher dimensions a four-dimensional construction, due to Calderbank and Pedersen, of self-dual Einstein manifolds with two linearly independent commuting Killing vector fields. As an application, we use this new Ansatz to give an explicit equivariant completion of the twistor space construction of the local c-map proposed by Roček, Vafa and Vando…
We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate…
Starting with the first-order formulation of the massless superparticle model on the $AdS_5\times S^5$ superbackground and presenting the momentum components tangent to $AdS_5$ and $S^5$ subspaces as bilinear combinations of the constrained $SU(2)$-Majorana spinors allows to bring the superparticle's Lagrangian to the form quadratic in supertwistors. The $SU(2,2|4)$ supertwistors are assembled into a pair of $SU(2)$ doublets, one of which has even $SU(2,2)$ and odd $SU(4)$ components, while the other has odd $SU(2,2)$ and even $SU(4)$ components. They are subject to the first-class constraints…
On Black Hole Effective Potential in 6D/7D N=2 Supergravity
利用调和超空间方法和超多重态的实表示与复表示的对偶性，计算了6D N=2超引力的模空间SO（1，1）x[SO（4，k）/（SO（4）xSO（k））]的四元数度规$G_{mn}$的显式标量场表达式.所获得的度量包括与K3上的10 D IIA型超弦相关联的特定情况k=20。描述了7 D N=2超引力的提升过程，并研究了6D/7 D黑吸引子有效势的若干方面。
