论文标题
非紧凑型双重性，超视力不变性和有效的动作
Non-compact duality, super-Weyl invariance and effective actions
论文作者
论文摘要
在这两个$ {\ cal n} = 1 $和$ {\ cal n} = 2 $ supersymmetry中，众所周知，$ \ Mathsf {sp}（2n，2n，{\ Mathbb r}）$是$ n $ vector的最大二元组，$ n $ vector乘以cOUPLED乘以chiral scalars $ salcar $ sermine $ sermits $ sermits $ sherstry paramits $ camintry paramits $ camintry thy $ x $ x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x $ \ mathsf {sp}（2n，{\ mathbb r}）/ \ mathsf {u}（n）$。如果在Supergravity背景中以$ n $ superCongume量规的耦合到$τ$，则该动作在Super-Weyl转换下也不变。计算弯曲超空间中量规前稳态的路径积分，从而导致有效的动作$γ[τ，\barτ] $具有以下属性：（i）其对数零件在super-weyl和arig-weyl和arig-jird $ \ mathsf {sp}（sp}（2n，2n，\ mathbb r r r and）下是不变的零件。 （ii）重态化时超左转化是异常的。在本文中，我们描述了$ {\ cal n} = 1 $和$ {\ cal n} = 2 $局部超对称的“诱导动作”，该动作确定了相应有效的动作的对数部分。在$ {\ cal n} = 1 $ case中，超级场加热核技术用于计算与手性dilaton-axion倍数耦合的单个矢量多重$（n = 1）$的诱导动作。我们还描述了$ {\ cal n} = 1 $ super-weyl异常的一般结构，该异常包含重量零手性标量倍数$φ^i $在Kähler歧管中取值。明确的异常计算是在$ n = 1 $的情况下进行的。
In both ${\cal N}=1$ and ${\cal N}=2$ supersymmetry, it is known that $\mathsf{Sp}(2n, {\mathbb R})$ is the maximal duality group of $n$ vector multiplets coupled to chiral scalar multiplets $τ(x,θ) $ that parametrise the Hermitian symmetric space $\mathsf{Sp}(2n, {\mathbb R})/ \mathsf{U}(n)$. If the coupling to $τ$ is introduced for $n$ superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action $Γ[τ, \bar τ]$ with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid $\mathsf{Sp}(2n, {\mathbb R})$ transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the ${\cal N}=1$ and ${\cal N}=2$ locally supersymmetric "induced actions" which determine the logarithmically divergent parts of the corresponding effective actions. In the ${\cal N}=1$ case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet $(n=1)$ coupled to a chiral dilaton-axion multiplet. We also describe the general structure of ${\cal N}=1$ super-Weyl anomalies that contain weight-zero chiral scalar multiplets $Φ^I$ taking values in a Kähler manifold. Explicit anomaly calculations are carried out in the $n=1$ case.
