PhD-thesis, TU-Vienna 2007, 246 pages. Contains hyperlinks and thesis-index (This time really! Last time it got lost during upload). Corrections in section 5.9 and 5.10 and additional appendix section E.4. Equation and section numbers remained the same. Possible future corrections will be only added as errata
The thesis divides into three parts. The first is devoted to a careful study of very convenient superspace conventions which are a basic tool for the second part. A theorem is formulated that gives a clear statement about when the signs of a superspace calculation can be omitted.
The second part describes the type II superstring using Berkovits' pure spinor formalism. The derivation of the supergravity constraints from classical BRST invariance of Berkovits and Howe is carefully reviewed and new aspects are added. The present derivation uses a covariant variation principle and stays throughout in the Lagrangian formalism. A new result is the explicit form of the BRST transformation of the worldsheet fields for type II. By further deriving the form of the local supersymmetry transformations of the fermionic fields, a connection is established to the starting point of those supergravity calculations, which derive generalized Calabi Yau conditions from effective four-dimensional supersymmetry.
Generalized complex geometry is in turn the motivation for the last part, which is based on the author's paper on derived brackets from sigma models and the relation to integrability of generalized complex structures. Finally there are detailed appendices on geometric brackets, generalized complex geometry, Noether's theorem, Bianchi identities, supergauge transformations and the WZ gauge, gamma-matrices and on some aspects of structure group connections.
We present the massless six-point one-loop amplitudes in the open and closed superstring using BRST cohomology arguments from the pure spinor formalism. The hexagon gauge anomaly is traced back to a class of kinematic factors in pure spinor superspace which were recently introduced as BRST pseudo-invariants. This complements previous work where BRST invariance arguments were used to derive the non-anomalous part of the amplitude. The associated worldsheet functions are non-singular and demonstrated to yield total derivatives on moduli space upon gauge variation. These cohomology considerations…
The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
我们将IIA型超引力的玻色子AdS_4 × CP^3解提升到D=10的具有32个Grassmann奇方向的超空间中。IIA型超空间是从D=11通过陪集超空间OSp（8）的降维得到的|4）/SO（7）x SO（1，3），将后者实现为前者的Hopf纤维化。这种构造将S^7的Hopf纤维化推广到超空间，作为CP ^3上的U（1）丛，并且适合于写出在AdS_4 x CP ^3超背景中编码IIA型弦和膜动力学的格林-施瓦茨型作用量的显式形式。我们证明了OSp（6| 4）/U（3）x SO（1，3）超陪集弦作用量只描述了完整Green-Schwarz超弦的一个子扇区。因此，即使OSp（6）中的超弦运动方程|4）/U（3）x SO（1，3）子扇区是经典可积的，而全AdS_4 x CP^3超空间不是超陪集的事实要求使用更一般的方法来确定全AdS_4 x CP^3超背景中的超弦是否是经典可积的。
Super $T\bar{T}$ deformation and the RNS non-critical superstring
ICTP-SAIFR（国际理论物理中心-巴西基础与应用物理研究所）；Instituto de Física Teórica, UNESP-Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）；C.N. Yang Institute for Theoretical Physics, S.U.N.Y. Stony Brook University（纽约州立大学石溪分校陈省身理论物理研究所）
The covariant and kappa-symmetric action for superstring in direct product of two flat D=10 N=1 superspaces is presented. It is given by the sum of supersymmetric generalization of two copies of chiral boson actions constructed with the use of the Pasti-Sorokin-Tonin (PST) technique. The chirality of 8 `left' bosons and 8 `left' fermions and the anti-chirality of their `right' counterparts are obtained as gauge fixed version of the equations of motion, so that the physical degrees of freedom are essentially those of the II Green-Schwarz superstring. Our action is manifestly T-duality invariant…
Consistency of Superspace Low Energy Equations of Motion of 4D Type II Superstring with Type II Sigma Model at Tree-Level
我们导出了超空间中四维II型超引力的挠率约束，并证明了其运动方程与II型西格玛模型的一致性。这是通过将四维紧化的Type II Berkovits超弦耦合到N=2的弯曲背景，并要求σ模型在树级具有超共形不变性来实现的。我们以明显的4D N=2超对称方式计算这个。这些约束打破了目标共形和SU（2）不变性，并且该子将是共形的、$SU(2)\times U(1)$补偿器。对于四维的II型超弦，世界面超对称性需要两个不同的补偿子。一种类型是由手征和反手征超场描述。这个补偿器可以用一个矢量多重态来表示。另一个II型补偿器由扭曲手征和扭曲反手征超场描述，可以用张量超多重态来识别。此外，在树水平的超共形不变性选择一个特定的规范，在那里的物质是固定的，但不是补偿。在施加现实条件后，我们证明了树能级的II型西格玛模型与弦规范中的II型超引力运动方程是一致的。
We study supersymmetry conditions for the heterotic pure superstring preserving and N=1 supersymmetry in four dimensions directly from the curved superspace defined by the Berkovits-Howe constraints.
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.
University of Cambridge（剑桥大学）；International Centre for Theoretical Sciences-TIFR（国际理论科学中心-印度理论研究所）；ETH Zürich（苏黎世联邦理工学院）；Weizmann Institute of Science（魏茨曼科学研究所）
