Investigating strongly interacting Quantum Field Theories at finite density via holography

在强耦合条件下，相对论区域守恒的有限电荷密度下的量子场理论(如QCD中的重子电荷)并没有得到很好的理解。强耦合下的微扰方法是不充分的，而现有的非微扰方法(格子QFT)受到声名狼藉的符号问题的限制。与此同时，两项发展促使人们对理解有限密度强耦合QFT产生了浓厚的兴趣：计划在未来2-3年发射的新的专门建造的重离子加速器(FAIR和NICA)，以及对中子星和类似天体的专门精确观测。费尔和NICA将在密度不可忽略的区域探索QCD相图，总体目标是找到推测的临界点并研究其附近的核物质。中子星观测的目的是了解超高密度QCD奇异相描述的核心结构。对这些领域的理论理解是非常有限的。建议的研究路线将通过全息术(规范-弦对偶)来研究有限化学势下的强耦合QFT。主要目的是建立相应的量子流体在这一区域的性质，特别是在临界点附近。这包括将手性流体的流体动力学建立到二阶，并使用双重重力方法和专门构建的QFT模型研究其在强耦合条件下的性质。我们希望看到普遍的定性特征，在这种情况下，对该领域的影响将非常重大。至少，我们应该理解在有限密度下的某种类型的强耦合量子傅里叶变换，目前还知之甚少。该计划包括，在经过一段准备阶段后，建立一个具有守恒电荷的已知量子傅里叶变换的全息对偶，并研究其一阶和二阶导数展开时的输运性质。手性流体动力学似乎有许多不同的特征(其中一些是从光学活性介质中已知的)，这些特征可以通过通常用于夸克-胶子等离子体的探针来研究。同时，我们将建立一个具有临界点的自下而上的全息模型，以研究强耦合手征介质临界行为的可能特征。将构建一个包括Kubo关系层次的一般形式主义。第二个更雄心勃勃的阶段将包括计算对第一阶段的任何结果的有限耦合修正。不幸的是，现有的弦理论压缩结果允许人们探索有限密度的系统，在文献中被批评为不可靠的。因此，第一步将是建立一个可靠的压缩方案-这在技术上可能相当具有挑战性，只有在有利的条件下才会尝试。我们计划与加拿大维多利亚大学和爱丁堡大学的理论物理学家合作。该项目主要属于量子场论、弦理论和数学物理的研究领域。

Quantum Field Theories at finite density of charges conserved in the relativistic domain (such as the baryonic charge in QCD) are not well understood in the regime of strong coupling. Perturbative approach at strong coupling is inadequate and the existing non-perturbative methods (lattice QFT) are constrained by the infamous sign problem. Meanwhile, strong interest in understanding finite density strongly coupled QFTs is prompted by two developments: new purpose-built heavy ion accelerators (FAIR and NICA) scheduled for launch in the next 2-3 years and dedicated precision observations of neutron stars and similar objects. FAIR and NICA will explore the phase diagram of QCD in the region of non-negligeable density with an overall aim of finding the conjectured critical point and investigating nuclear matter in its vicinity. Neutron star observations are aimed at understanding the structure of the cores described by exotic phases of QCD at super-high density. Theoretical understanding of these domains is extremely limited.The proposed line of research will investigate strongly coupled QFTs at finite chemical potential via holography (gauge-string duality). The main objective is to establish properties of the corresponding quantum fluid in this regime and especially in the vicinity of a critical point. This involves building fluid dynamics of chiral fluids to second order and investigating its properties at strong coupling using dual gravity methods and purpose-built QFT models. We hope to come across universal qualitative features in which case the impact on the field will be very significant. At the very least, we shall understand strongly coupled QFTs of a certain type at finite density, where very little is known at the moment.The plan involves, after some preparatory period, building a holographic dual of a known QFT with a conserved charge and investigating its transport properties at first and second order of the derivative expansion. Chiral fluid dynamics appears to have a number of distinct features (some of them are known from optically active media) which can be studies via probes normally used for quark-gluon plasma. At the same time, we shall build a bottom-up holographic model with a critical point to investigate possible signatures of critical behaviour of a strongly coupled chiral medium. A general formalism including the hierarchy f Kubo relations will be constructed.A second, more ambitious stage, will include computing finite coupling corrections to any of the results of stage one. Unfortunately, the existing string theory compactification results allowing one to explore systems with finite density were criticized in the literature as unreliable. Therefore, the first step would be establishing a reliable compactification scheme - this may be rather challenging technically and will be attempted only under favourable conditions.We plan to collaborate with theoretical physicists at University Victoria (Canada) and University of Edinburgh. This project falls within Quantum Field Theory (mostly), String Theory and Mathematical Physics research areas.