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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762439
• 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.

我的研究建议可以分为四个广泛的类别：弦宇宙学，弦理论，热QCD和结理论。让我从字符串宇宙学开始。最近的一个挑战是构建弦理论中的真空吸尘器，即具有正宇宙常数的真空。由于某些禁忌条件，这也称为Swampland标准，因此事实证明这是非常挑战。我的目的之一是找到一种具体的方法来克服不做条件，并展示de Sitter真空可能发生或证明在字符串理论中不可能有De Sitter解决方案。我的第二个研究建议是弦理论。在字符串理论中很重要的问题之一是选择稳定真空。 Modulli的稳定需要打开背景通量以及非扰动效应，导致非卡拉比YAU歧管，或更一般地非卡勒歧管。尽管无处不在，这些流形的具体构造更加困难，因为它们需要不同几何形状的复杂技术。我这里的提议之一是对这些真空的通用结构进行通用结构。这很重要，否则字符串理论将无法重现标准模型。我的第三个建议与热QCD有关。我们已经能够构建双重引力描述，这些描述可以解释QCD的动力学，就像所有能量尺度上的理论一样。但是许多事情仍有待显示。例如，尚不清楚这种理论中的散装粘度如何在中间耦合中起作用，即弱和强'thooft耦合之间的耦合。知道这将是文献中的巨大进步，因为目前用于研究中间耦合的动态的技术几乎没有定论。另一个相关的是颜色超导性，可以使用相同的双重引力模型进行研究。有趣的是，我们构建的重力双重双重不仅是研究QCD，而且还要研究其他全息问题，例如纠缠熵等。因为我们的模型引起了一个理论的重力二重奏，该理论是非符合性的，回答与纠缠熵（EE）相关的问题等。与这些问题相关的问题会阐明这些问题时，当这些问题不合格性更新范围时。我最后的提议是关于结理论。这是我最近开始的一个新方向，它是基于我们的发现，即拓扑场理论的许多结果我来自M理论中的某些引力背景。这种令人惊讶的结构不仅解释了拓扑扭曲的概念，而且还直接再现了边界Chern-Simons理论以及结的不变性。但是，难题是给定结多项式的核心与某个微分方程的溶液数量一对一。我的提议之一是证明这种缔约合。相关主题，例如建造有色琼斯和Kaufmann多项式，需要进一步研究。