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

与E. D'Hoker和D. P. Phong一起，我们在一些物理学感兴趣的不对称轨道真空中，解析地获得了超弦理论中宇宙学常数的两个环的贡献。当时，有人声称这个真空在微扰理论中所有阶的宇宙学常数都为零，这可能导致一种迄今未知的机制，在没有超对称的时空中保持零宇宙学常数。从现象学的观点来看，这个特征是非常可取的。关于这个问题没有明确的声明，主要是由于所涉及的技术困难。通过显式计算，我们证明了在相关情况下，宇宙学常数在双回路水平上不为零，有助于解决这一问题。迄今为止，似乎还没有构建不对称轨道的系统方法。作为一个相关问题，我们还系统地分析了如何构建不对称轨道。有限温度下的非平衡动力学理论是物理学中许多领域的一个重要方面。然而，目前从第一性原理得到的定量结果并不多。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明确行为。特别是，我们定量地说明了在某些理论中，局部平衡和线性响应是如何在热梯度作用下被破坏的。此外，我们还阐明了热梯度下理论的微观方面（如Lyapunov指数）与宏观方面（如相空间维损失和输运现象）之间的关系。上述研究结果已在相关期刊上发表，我们正在准备发表更多相关文章。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.