标题： Sen形式的共形场论的规范场 显示英文标题

标题： The CFT of Sen's Formulation of Chiral Gauge Fields

摘要： 塞恩在二维空间中对手性标量的行动描述了两个手性标量，其中一个与物理度规耦合，另一个与平直度规耦合。 它有一个推广形式，其中平直度规被替换为任意第二个度规，因此可以在任何弯曲的世界面中进行表述。 当两个度规相等时，该理论退化为一个$\beta \gamma$系统，给出一个非单位的$c=2$二维共形场论。 我们认为，这与相同手性的两个手性标量理论之间的关系可以被视为一个\lq 的玻色化。 我们证明了手性标量的标准顶点算符是塞恩表述中的顶点算符和线性算符，并推导了手性标量理论中相关函数在塞恩理论中的表述。 平直空间的塞恩理论可以通过某种方式与两个不同的世界面度规耦合，使得一个标量与一个度规耦合，另一个与另一个度规耦合，从而得到具有两个度规的一般表述。 在$d=4k+2$维度中，具有自对偶场强的$2k$形规范场的双度规作用量，当两个度规相等时，会简化为一个具有$BF$类型作用量的共形场论，只是$B$是一个自对偶$d/2$形，而$F$是一个$d/2$形场强，$F=dP$。 自对偶性意味着$B$不是一个拓扑理论，而是表示两个自对偶的规范场。 这可以推广到任何维度中的$p$形规范场的民主作用量。 显示英文摘要

摘要： Sen's action for chiral bosons in 2 dimensions describes two chiral scalars, one of which couples to the physical metric and one of which couples to a flat metric. It has a generalisation in which the flat metric is replaced by an arbitrary second metric and so can be formulated on any curved world-sheet. When the two metrics are equal, the theory reduces to a $\beta \gamma$ system, giving a non-unitary $c=2$ conformal field theory. We argue that the relation between this and the theory of two chiral bosonic scalars of the same chirality can be viewed as a \lq bosonisation'. We show that the standard vertex operators for the chiral scalars are vertex operators and line operators in the Sen formulation and derive the formulation in the Sen theory of correlation functions in the chiral scalar theory. The flat space Sen theory can be coupled to two different world-sheet metrics in such a way that one scalar couples to one metric and the other to the other metric, so obtaining the general formulation with two metrics. In $d=4k+2$ dimensions, the bi-metric action for a $2k$-form gauge field with self-dual field strength reduces, when the two metrics are equal, to a conformal field theory with a $BF$-type action, except that $B$ is a self-dual $d/2$-form and $F$ is a $d/2$-form field strength, $F=dP$. The self-duality of $B$ means that this is not a topological theory but instead represents two self-dual gauge fields. This has a generalisation to a democratic action for $p$-form gauge fields in any dimension.