String theory, knot theory, thermal QCD and string cosmology

弦理论、纽结理论、热 QCD 和弦宇宙学

• 批准号: SAPIN-2019-00039
• 负责人: Dasgupta, Keshav
• 金额: $ 3.64万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=718424
• 关键词: String; theory; knot; thermal; QCD

My research proposal may be divided into four broad categories: string cosmology, string theory, thermal QCD and knot theory. Let me start by string cosmology. A recent challenge is to construct de Sitter vacua, i.e a vacua with positive cosmological constant, from string theory. This has turned out to be very challenging due to certain no-go conditions, also called the swampland criteria. One of my aim is to find a concrete way to overcome the no-go conditions and show how de Sitter vacua may come about or justify that there could be no de Sitter solution possible in string theory. My second research proposal is in string theory. One of the issue that is important in string theory is the choice of the stable vacuum. Stabilization of moduli require switching on background fluxes, and also non-perturbative effects, leading to non-Calabi-Yau manifolds, or more generically, non-Kahler manifolds. Despite ubiquitous, concrete constructions of these manifolds are harder because they require sophisticated techniques in differential geometry. Thus one of my proposal here is to have generic constructions of these vacua. This is important otherwise string theory will be unable to reproduce the standard model. My third proposal is related to thermal QCD. We have been able to construct the dual gravitational description that can explain the dynamics of QCD like theories at all energy scales. However many things remain to be shown. For example it is as yet unknown how bulk viscosity in such a theory works at intermediate couplings, i.e couplings between weak and strong 't Hooft couplings. Knowing this will be an immense progress in the literature because the present techniques used to study dynamics at intermediate couplings are pretty much inconclusive. Another related thing is color superconductivity which may be studied using the same dual gravitational model. Interestingly, the gravity dual constructed by us is not just to study QCD, but also to study other holographic questions like entanglement entropies etc. Since our model gives rise to the gravity dual of a theory that is non-conformal, answering questions related to entanglement entropies (EE) etc. will shed light on these issues when non-conformality is switched on. My last proposal is on knot theory. This is a new direction that I have started recently, and is based on our findings that many of the results of topological field theory my be derived from certain gravitational background in M-theory. This surprising construction not only explains the concept of topological twisting, but also directly reproduces the boundary Chern-Simons theory as well as the knot invariants. However the puzzling thing is that the coefficients of a given knot polynomial have one-to-one correspondence to the number of solutions of a certain differential equation. One of my proposal is to prove this conjecture. Related topics like the construction of the colored Jones and Kaufmann polynomials require further research.

我的研究计划可以分为四大类：弦宇宙学、弦理论、热QCD和纽结理论。让我从弦宇宙学开始。最近的一个挑战是从弦理论中构造德西特真空，即具有正宇宙学常数的真空。由于某些禁止通行的条件（也称为沼泽地标准），这被证明是非常具有挑战性的。我的目标之一是找到一种具体的方法来克服不可行条件，并说明德西特真空是如何产生的，或者证明在弦理论中不可能有德西特解。我的第二个研究计划是弦理论。弦理论中的一个重要问题是稳定真空的选择。模的稳定化需要切换背景通量，以及非微扰效应，导致非卡拉比-丘流形，或者更一般地，非卡勒流形。尽管无处不在，这些流形的具体结构是困难的，因为它们需要微分几何中的复杂技术。因此，我在这里的一个建议是，对这些真空进行一般性的构造。这一点很重要，否则弦理论将无法重现标准模型。我的第三个建议与热QCD有关。我们已经能够构造对偶引力描述，它可以解释所有能量尺度下的QCD类理论的动力学。然而，还有许多东西有待展示。例如，在这种理论中，体粘滞系数在中间耦合，即在弱和强特胡夫特耦合之间的耦合下是如何工作的，这一点还不清楚。了解这一点将是一个巨大的进步，在文献中，因为目前的技术用于研究动态在中间耦合是非常不确定的。另一个相关的东西是颜色超导性，可以使用相同的对偶引力模型进行研究。有趣的是，我们构造的引力对偶不仅是为了研究QCD，而且还可以研究其他全息问题，如纠缠熵等。由于我们的模型产生了一个非共形理论的引力对偶，当非共形性打开时，回答与纠缠熵（EE）等有关的问题将有助于解决这些问题。这是我最近开始的一个新方向，它是基于我们的发现，即拓扑场论的许多结果可以从M理论的某些引力背景中导出。这个令人惊讶的构造不仅解释了拓扑扭曲的概念，而且直接再现了边界Chern-Simons理论以及纽结不变量。然而令人困惑的是，给定的纽结多项式的系数与某个微分方程的解的个数一一对应。我的建议之一就是证明这个猜想。相关的主题，如有色琼斯和考夫曼多项式的建设需要进一步的研究。