We develop a new superfield approach to N=4 supersymmetric mechanics based on the concept of biharmonic superspace (bi-HSS). It is an extension of the N=4,d=1 superspace by two sets of harmonic variables associated with the two SU(2) factors of the R-symmetry group SO(4) of the N=4, d=1 super Poincaré algebra. There are three analytic subspaces in it: two of the Grassmann dimension 2 and one of the dimension 3. They are closed under the infinite-dimensional "large" N=4 superconformal group, as well as under the finite-dimensional superconformal group D(2,1;α). The main advantage of the bi-HSS approach is that it gives an opportunity to treat N=4 supermultiplets with finite numbers of off-shell components on equal footing with their ``mirror'' counterparts. We show how such multiplets and their superconformal properties are described in this approach. We also define nonpropagating gauge multiplets which can be used to gauge various isometries of the bi-HSS actions. We present an example of nontrivial N=4 mechanics model with a seven-dimensional target manifold obtained by gauging an U(1) isometry in a sum of the free actions of the multiplet (4,4,0) and its mirror counterpart.
We suggest the $su(1,N|M)$-superconformal mechanics formulated in terms of phase superspace given by the non-compact analogue of complex projective superspace $\mathbb{CP}^{N|M}$. We parameterized this phase space by the specific coordinates allowing to interpret it as a higher-dimensional super-analogue of the Lobachevsky plane parameterized by lower half-plane (Klein model). Then we introduced the canonical coordinates corresponding to the known separation of the "radial" and "angular" parts of (super)conformal mechanics. Relating the "angular" coordinates with action-angle variables we demo…
这些讲座已于2005年3月在Nazionali di Frascati大学举行。主要的想法是提供我们的年轻同事，谁加入了我们的尝试，以了解结构的$N$ -扩展超对称一维系统，与简短的描述的方法和技术，我们使用。这反映在材料的选择和介绍的风格上。我们的处理主要基于超场的观点。此外，我们更倾向于处理N=4和N=8的超场。目前，存在着广泛的文献组件的方法来扩展超对称理论在$d=1$，而明显的超对称制定适当的约束超场是鲜为人知的。然而，我们认为，正是这种提法更可取。为了使这些讲座或多或少自洽，我们从一维超对称理论的最简单例子开始，并对$d=1$超对称的特性给予了大量关注。我们不时地以非常详细的方式介绍计算结果。在其他情况下，我们省略了细节，只给出了最后的答案。无论如何，这些讲座在任何方面都不能被视为教科书。它们可以被认为是我们对一维超场论和我们认为重要的方法和技术的个人观点。特别是，所有这些都涉及第3节，我们讨论的非线性实现方法。我们在本节中没有提出任何证据。相反，我们专注于计算的细节。最后，我们对绝对不完整的参考文献列表表示歉意。
We construct models of coupled semi-dynamical (spin) and dynamical mirror multiplets of ${\cal N}=4$ supersymmetric mechanics in $d=1$ harmonic superspace. Specifically, we consider a semi-dynamical mirror multiplet ${\bf (3,4,1)}$ coupled to dynamical mirror multiplets ${\bf (1, 4, 3)}$ and ${\bf (2, 4, 2)}$. Coupling of the multiplets ${\bf (3, 4, 1)}$ and ${\bf (1, 4, 3)}$ yields a mirror counterpart of the earlier constructed model implying the Nahm equations for the spin variables with the bosonic component of the multiplet ${\bf (1, 4, 3)}$ as an evolution parameter. We also couple the m…
We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to $c=1$ matter. Our motivation is to understand whether some form of averaging is essential for the boundary theory, if we wish to describe the bulk quantum gravity path integral of this two dimensional example. The analysis hence, is in a spirit similar to the recent studies of Jackiw-Teitelboim (JT)-gravity. Macroscopic loop operators define the asymptotic region on which the holographic boundary dual resides. Matrix quant…
In this work, we analyze an extended $\mathcal{N}=2$ supersymmetry with central charge and develop its superspace formulation under two distinct viewpoints. Initially, in the context of classical mechanics, we discuss the introduction of deformed supersymmetric derivatives and their consequence on the deformation of one-dimensional non-linear sigma model. After that, considering a field-theoretical framework, we present an implementation of this superalgebra in two dimensions, such that one of the coordinates is related to the central charge. As an application, in this two-dimensional scenario…
