标题： 框架DDF算子和Virasoro约束的一般解 显示英文标题

标题： Framed DDF operators and the general solution to Virasoro constraints

摘要： 我们通过在通常的DDF算符公式中引入局部框架的概念，来定义带框架的DDF算符。这样做可以将DDF算符完全与相关的快子解耦，并表明它们是良好的零维共形算符。这使得能够在实壳和虚壳上明确地表述Virasoro约束的一般解。然后我们精确地实现了直观的想法，即DDF算符可用于将光锥态嵌入协变公式中。这种嵌入不是唯一的，而是依赖于一个陪集。该陪集是光锥嵌入的小群，并与一个框架相关。该框架使我们能够以最一般的方式将$SO(D-2)$光锥物理极化嵌入到$SO(1,D-1)$协变极化中。Virasoro约束的解并不处于通常使用的规范中。这是因为从DDF算符得到的状态通常是由于投影算子的存在而部分横向但不无迹的项以及部分无迹但不横向的项的总和。为了验证识别，我们验证了一些光锥态的庞加莱群第二Casimir算子的期望值与使用带框架DDF构建的相应协变态之间的匹配。 显示英文摘要

摘要： We define the framed DDF operators by introducing the concept of local frames in the usual formulation of DDF operators. In doing so it is possible to completely decouple the DDF operators from the associated tachyon and show that they are good zero-dimensional conformal operators. This allows for an explicit formulation of the general solution of the Virasoro constraints both on-shell and off-shell. We then make precise the realization of the intuitive idea that DDF operators can be used to embed light-cone states in the covariant formulation. This embedding is not unique, but depends on a coset. This coset is the little group of the embedding of the light-cone and is associated with a frame. The frame allows us to embed the $SO(D-2)$ light-cone physical polarizations into the $SO(1,D-1)$ covariant ones in the most general way. The solution to the Virasoro constraints is not in the gauge that is usually used. This happens since the states obtained from DDF operators are generically the sum of terms which are partially transverse due to the presence of a projector but not traceless and terms which are partially traceless but not transverse. To check the identification, we verify the matching of the expectation value of the second Casimir of the Poincar'e group for some light-cone states with the corresponding covariant states built using the framed DDFs.