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arXiv 1603.08770hep-thcond-mat.str-elhep-phnucl-th
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高阶导数全息理论中反常电导率的普适性

Universality of anomalous conductivities in theories with higher-derivative holographic duals

Sašo Grozdanov, Napat Poovuttikul

摘要:

在具有全局反常的理论中,反常手征电导率与它们是否在弱耦合量子(或热)场论、流体力学或全息术的无限耦合中计算无关。虽然存在的动力学规范场和混合,规范全球异常可以破坏这种普遍性,在他们的情况下,非重整化的异常沃德恒等式预计将遵守在所有中间耦合强度。在全息术中,具有高阶导数修正的体理论将耦合常数修正纳入到无限耦合附近的扩展中的边界理论观测值中。在这项工作中,我们调查的耦合常数的依赖性和普遍性的异常电导率(从而异常的沃德恒等式)在一般情况下,四维系统,具有渐近反德西特全息图与非极值黑膜在五维,和异常输运引入到边界理论通过散装陈-西蒙斯行动。我们表明,在散装理论与任意规范和非对称不变的高导数行动,反常电导率,它可以纳入一个无限系列的(逆)耦合常数修正,仍然普遍。由于膜范式的存在,证明简化为在视界和边界上构造体有效理论。它只要求我们在场上施加视界正则性条件和正确的边界条件。我们还讨论了如何违反膜范式的有效性违反条件的普遍性,特别是,通过增加质量的矢量场(一个混合的情况下,规范全球异常)和散装几何与裸奇点。

英文摘要:

Anomalous chiral conductivities in theories with global anomalies are independent of whether they are computed in a weakly coupled quantum (or thermal) field theory, hydrodynamics, or at infinite coupling from holography. While the presence of dynamical gauge fields and mixed, gauge-global anomalies can destroy this universality, in their absence, the non-renormalisation of anomalous Ward identities is expected to be obeyed at all intermediate coupling strengths. In holography, bulk theories with higher-derivative corrections incorporate coupling constant corrections to the boundary theory observables in an expansion around infinite coupling. In this work, we investigate the coupling constant dependence and universality of anomalous conductivities (and thus of the anomalous Ward identities) in general, four-dimensional systems that possess asymptotically anti-de Sitter holographic duals with a non-extremal black brane in five dimensions, and anomalous transport introduced into the boundary theory via the bulk Chern-Simons action. We show that in bulk theories with arbitrary gauge- and diffeomorphism-invariant higher-derivative actions, anomalous conductivities, which can incorporate an infinite series of (inverse) coupling constant corrections, remain universal. Owing to the existence of the membrane paradigm, the proof reduces to a construction of bulk effective theories at the horizon and the boundary. It only requires us to impose the condition of horizon regularity and correct boundary conditions on the fields. We also discuss ways to violate the universality by violating conditions for the validity of the membrane paradigm, in particular, by adding mass to the vector fields (a case with a mixed, gauge-global anomaly) and in bulk geometries with a naked singularity.

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