当前位置: X-MOL 学术Classical Quant. Grav. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Covariant Noether charges for type IIB and 11-dimensional supergravities
Classical and Quantum Gravity ( IF 3.5 ) Pub Date : 2020-12-10 , DOI: 10.1088/1361-6382/abc136
scar J C Dias 1 , Gavin S Hartnett 1, 2 , Jorge E Santos 3, 4
Affiliation  

The covariant Noether charge formalism (also known as the covariant phase method) of Wald and collaborators, including its cohomological extension, is a manifestly covariant Hamiltonian formalism that, in principle, allows one to define and compute the energy, angular momenta, and chemical potentials of generic solutions of gravitational theories. However, it has been observed that for some supergravity solutions the variation of the Noether charge is not (at least manifestably) integrable, and as a result it is unclear whether there are well-defined thermodynamic charges for these solutions. In this work, we derive an expression for the variation of the covariant Noether charges for any solution of Type IIB 10-dimensional supergravity or 11-dimensional supergravity. Although this Noether quantity is not integrable in general, we show that for asymptotically scale-invariant solutions, it is. In particular, the asymptotic scale-invariance allows one to define an energy density and conjugate chemical potentials which obey a first law of thermodynamics and a Smarr relation. These two thermodynamic relations can then be shown to imply that the variation of the Noether charge is integrable, and accordingly the energy and other thermodynamic charges may be defined unambiguously. We explicitly demonstrate and illustrate our claim by computing the thermodynamic charges of two non-trivial supergravity solutions that were recently constructed: 1) the Polchinski-Strassler black brane that is dual to the deconfined phase of $\mathcal{N}=1^*$ theory, and 2) the CGLP black brane that asymptotes to the mass deformed Cveti\v{c}-Gibbons-L\"u-Pope (CGLP) solution.

中文翻译:

IIB 型和 11 维超引力的协变 Noether 电荷

Wald 及其合作者的协变 Noether 电荷形式主义(也称为协变相位法),包括其上同调扩展,是一种明显协变的哈密顿形式主义,原则上允许人们定义和计算能量、角动量和化学势引力理论的一般解法。然而,已经观察到,对于某些超重力解决方案,诺特电荷的变化不是(至少明显)可积分的,因此尚不清楚这些解决方案是否存在明确定义的热力学电荷。在这项工作中,我们导出了协变 Noether 电荷变化的表达式,适用于 IIB 型 10 维超重力或 11 维超重力的任何解。虽然这个 Noether 量一般不可积,我们证明,对于渐近尺度不变的解,它是。特别是,渐近标度不变性允许定义能量密度和共轭化学势,它们遵循热力学第一定律和 Smarr 关系。然后可以证明这两个热力学关系意味着 Noether 电荷的变化是可积分的,因此可以明确定义能量和其他热力学电荷。我们通过计算最近构建的两个非平凡超重力解决方案的热力学电荷来明确证明和说明我们的主张:1) Polchinski-Strassler 黑膜,它与 $\mathcal{N}=1^* 的去约束相是双重的$ 理论,以及 2) 渐近到质量变形的 Cveti\v{c}-Gibbons-L\"u-Pope (CGLP) 解的 CGLP 黑膜。
更新日期:2020-12-10
down
wechat
bug