Topics in Superstring Perturbation Theory and Non-equilibrium Field Theory at Finite Temperatures

与E.D‘Hoker和D.P.Phong一起，我们解析地得到了超弦理论中的双圈对超弦理论中宇宙常数的贡献，在一些具有物理意义的非对称奥比福尔德真空中。当时，有人声称，在微扰理论中，这种真空对所有阶的宇宙常数都为零，这可能导致了一种迄今未知的机制，可以在没有超对称性的情况下在时空中保持零宇宙常数。从现象学的角度来看，这一特征是非常可取的。关于这一问题没有明确的声明，主要是因为涉及的技术困难。通过显式计算，证明了在相关情况下，宇宙学常数在双圈水平上为非零，有助于解决这一问题。到目前为止，似乎还没有一种系统的方法来构建不对称的奥氏环。作为相关问题，我们还系统地分析了如何构造非对称轨道。有限温度下非平衡理论的动力学是物理学中许多领域的一个重要方面。然而，目前还没有那么多来自第一性原理的定量结果。与D.Kusnezov、H.Spohn等人一起，我们一直在从第一性原理计算非平衡状态下物理量的显式行为。特别是，我们在一些理论中定量地展示了在温度梯度下局域平衡和线性响应是如何被打破的。此外，我们还阐明了该理论的微观方面(如Lyapunov指数)和宏观方面(如相空间维损失和热梯度下的输运现象)之间的关系。上述结果已发表在相关期刊上，我们正在准备更多关于这些方面的出版物。此外，我们相信，我们所获得的结果将作为进一步研究的基础。

With E. D'Hoker and D. P. Phong, we obtained analytically the two loop contribution to the cosmological constant in superstring theory, in some asymmetric orbifold vacua of physics interest. At the time, there were claims that this vacua had zero cosmological constant to all orders in perturbation theory, possibly leading to a hitherto unknown mechanism for preserving zero cosmological constant in spacetimes with no supersymmetry. This feature would be quite desirable from a phenomenological point of view. There was no clear statement on this issue, mostly due to the technical difficulties involved. Through explicit computation, we showed that in the relevant case, the cosmological constant is non-zero at the two loop level, contributing to the resolution of this issue. To date, there seems to be no systematic way of constructing asymmetric orbifolds. As a relevant related issue, we also systematically analyzed how to construct asymmetric orbifolds.Dynamics of non-equilibrium theories at finite temperatures is an important aspect of many fields in physics. However, there currently exist not that many quantitative results from first principles. With D. Kusnezov, H. Spohn and others, we have been computing the explicit behavior of physical quantities in non-equilibrium, from first principles. In particular, we have quantitatively shown how local equilibrium and linear response are broken under thermal gradients in some theories. Also, we elucidated the relationship between the microscopic aspects of the theory, such as Lyapunov exponents, and the macroscopic aspects of the theory, such as phase space dimensional loss and transport phenomena, under thermal gradients.The results mentioned above have been published in refereed journals and we are preparing some more publications on them. Furthermore, we believe that the results we have obtained will serve as the basis for further research.