SL(2,Z) duality transformations in asymptotically AdS4 x S7 act nontrivially on the three-dimensional superconformal field theory of coincident M2-branes on the boundary. We show how S-duality acts away from the IR fixed point.We develop a systematic method to holographically obtain the deformations of the boundary CFT and show how electric-magnetic duality relates different deformations. We analyze in detail marginal deformations and deformations by dimension 4 operators. In the case of massive deformations, the renormalization group flow relates S-dual CFT’s. Correlation functions in the CFT are computed by varying magnetic bulk sources, whereas correlation functions in the dual CFT are computed by electric bulk sources. Under massive deformations, the boundary effective action is generically minimized by massive self-dual configurations of the U(1) gauge field. We show that a self-dual choice of boundary conditions exists, and it corresponds to the self-dual topologically massive gauge theory in 2 + 1 dimensions. Thus, self-duality in three dimensions can be understood as a consequence of electric-magnetic invariance in the bulk of AdS4.
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机译:渐近AdS4 x S7中的SL(2,Z)对偶变换对边界上重合的M2脑的三维超保形场理论不起作用。我们展示了S-对偶性如何在远离IR不动点的地方起作用。我们开发了一种系统方法来全息获取边界CFT的形变,并展示了电磁对偶性如何与不同形变相关。我们将详细分析边际变形和4维算子的变形。如果发生大的变形,则重归一化组流与S-dual CFT有关。 CFT中的相关函数是通过改变磁性体源来计算的,而双CFT中的相关函数是通过电体源来计算的。在大量变形下,通常通过U(1)规范场的大量自对偶配置将边界有效作用最小化。我们表明存在边界条件的自我对偶选择,并且它对应于2 + 1维的自我对偶拓扑量规理论。因此,可以将三维自对偶性理解为大量AdS4的电磁不变性的结果。
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