Weyl cohomology and the conformal anomaly in the presence of torsion

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Gregorio Paci, Omar Zanusso
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引用次数: 0

Abstract

Using cohomological methods, we identify both trivial and nontrivial contributions to the conformal anomaly in the presence of vectorial torsion in d=2,4 dimensions. In both cases, our analysis considers two scenarios: one in which the torsion vector transforms in an affine way, i.e., it is a gauge potential for Weyl transformations, and the other in which it is invariant under the Weyl group. An important outcome for the former case in both d=2,4 is the presence of anomalies of a “mixed” nature in relation to the classification of Deser and Schwimmer. For invariant torsion in d=4, we also find a new type of anomaly which we dub Ψ-anomaly. Taking these results into account, we integrate the different anomalies to obtain renormalized anomalous effective actions. Thereafter, we recast such actions in the covariant nonlocal and local forms, the latter being easier to work with. Along the way, we pause to comment on the physical usefulness of these effective actions, in particular to obtain renormalized energy–momentum tensors and thermodynamics of 2d black holes.
Weyl上同调与存在扭转的共形异常
使用上同调方法,我们确定了d=2,4维中矢量扭转存在的共形异常的平凡和非平凡贡献。在这两种情况下,我们的分析考虑了两种情况:一种情况下,扭转向量以仿射方式变换,即,它是Weyl变换的规范势,另一种情况下,它在Weyl群下是不变的。对于前一种情况,d=2,4的一个重要结果是,在Deser和Schwimmer分类中存在“混合”性质的异常。对于d=4的不变扭转,我们还发现了一种新的异常类型,我们称之为Ψ-anomaly。考虑到这些结果,我们整合了不同的异常,以获得重整化的异常有效动作。此后,我们在协变非局部和局部形式中重新定义这些动作,后者更容易使用。在此过程中,我们停下来评论这些有效动作的物理用途,特别是获得二维黑洞的重整化能量-动量张量和热力学。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
期刊介绍: Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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