Bern Zvi, Cheung Clifford, Chi Huan-Hang, Davies Scott, Dixon Lance, Nohle Josh
Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095, USA.
Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev Lett. 2015 Nov 20;115(21):211301. doi: 10.1103/PhysRevLett.115.211301. Epub 2015 Nov 17.
Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R^{3} counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D=4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly-the coefficient of the Gauss-Bonnet operator-changes under p-form duality transformations. We concur and also find that the leading R^{3} divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.
诸如高斯 - 博内项这样的瞬逝算符在精确的(D = 4)维中具有消失的微扰矩阵元。类似地，瞬逝场在(D = 4)中不传播；一个三形式场就属于此类，因为它对偶于宇宙学常数贡献。在本信函中，我们表明瞬逝算符和场会修改纯引力中的主导紫外发散。为了分析这种发散，我们计算了两圈同螺旋度四引力子振幅，并确定了很久以前由戈罗夫和萨尼奥蒂研究的相关（非瞬逝）(R^{3})抵消项的系数。我们比较了在(D = 4)中对偶的两对理论：与无物质或与三形式物质耦合的引力，以及与零形式或与二形式物质耦合的引力。达夫和范纽文惠曾表明，奇怪的是，一圈迹反常——高斯 - 博内算符的系数——在(p)形式对偶变换下会改变。我们认同这一点，并且还发现主导的(R^{3})发散在对偶变换下也会改变。然而，在这两种情况下，物理重整化的两圈同螺旋度四引力子振幅都可以被选择为尊重对偶性。特别地，它对重整化尺度的依赖未被改变。
