#### Xunyu Liang

Doctor of Philosophy in Physics (PhD)

**Research Topic**

Dark matter in form of the axion quark nuggets

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- Ariel Zhitnitsky

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Calculations in modified gauge theory: testing some ideas from QCD in a toy model (2018)

We use a deformed “center-stablised” gauge theory, which can be brought into a weak coupling regime while remaining confined and gapped, as a toy model to study some ideas from real QCD. The deformed model has the correct nontrivial θ-dependence and degeneracy of topological sectors conjectured for QCD, and is, apparently, smoothly connected to the strongly coupled undeformed Yang-Mills, so that we can perhaps expect to get some qualitative insights into QCD. We demonstrate the presence of a nondispersive contact term in the topological susceptibility, which contributes with the opposite sign to normal dispersive contributions coming from physical propagating degrees of freedom. We further show that, despite the system being completely gapped with no massless physical degrees of freedom, the system has a Casimir-like, power scaling, dependence on boundaries, in contrast with the naive expectation that a system with only massive degrees of freedom should have a weak (exponentially small) dependence on long distance effects. This behaviour suggests the possibility for a solution for the cosmological dark energy problem coming from the strongly coupled QCD sector on a manifold with a boundary, which would have the correct sign and be of the correct order of magnitude. Next, we investigate the interaction between point-like topological charges (monopoles) and extended sheet-like topological defects (domain walls) in attempt to explain some recent lattice QCD results suggesting that extended topological objects are more important to understanding the relevant field configurations in QCD than the instantons traditionally expected. Finally, we derive the existence of excited metastable vacuum states and calculate their decay rate to the true ground state of the theory, comparing with the expected results discussed years ago in proper QCD. The presence of metastable vacuum states with a nonzero effective θ parameter, like those present in the deformed model, could explain P and CP violation in heavy ion collisions observed on an event by event basis, which seem to average away over many events.

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Quark Nugget Dark Matter: Cosmic Evidence and Detection Potential (2015)

I present a dark matter model in which the dark matter is composed of very heavy “nuggets” of Standard Model quarks and antiquarks. This model was originally motivated by the fact that the matter and dark matter mass densities are observed to have similar scales. If these two forms of matter originate through completely distinct physical processes then their densities could easily have existed at vastly different scales. However, if the dark and the visible matter are co-produced, this similarity in scales is a natural outcome. In the model considered here dark matter and the baryonic matter share an origin in Standard Model strong force physics. The main goal of this work is to establish the testable predictions of this model. The physical properties of the nuggets are set by well understood nuclear physics and quantum electrodynamics, allowing many observable consequences to be predicted. To this end, I devote special attention to the structure of the surface layer of the nuggets from which the majority of observable consequences arise. With this basic picture of nugget structure in place, I will discuss the consequences of their interactions with a number of different environments. Particular attention is given to the galactic centre and to the early universe, as both are sufficiently dense to allow for significant levels of matter-dark matter interaction. The emitted radiation, in both cases, is shown to be consistent with observations. Finally, I discuss the consequences of a nugget striking the earth. In this context, I will demonstrate that the nuggets produce effects observable in cosmic ray detectors. Based on these considerations, I discuss the nugget detection potential for experiments primarily devoted to the study of high energy cosmic rays.

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Topological currents in dense matter (2011)

This thesis introduces the idea of a topological current that flows in regions with large magnetic fields, dense matter, and parity violation. We propose that such a current exists in the cores of neutron stars and may be responsible for the large proper motion (kicks) observed in some pulsars. This current is similar to the charge separation effect and chiral magnetic effect that may be responsible for parity (℘) and charge conjugation-parity (C℘) violation observed at the Relativistic Heavy Ion Collider (RHIC). We start by deriving the topological current two ways. The first is a macroscopic derivation where we appeal to an anomaly induced by the presence of a fictitious axial field. The second method is microscopic, in which we consider how the modes of the Dirac equation in a magnetic field and chemical potential contribute to the current. We then discuss in great detail the elements necessary for a topological current to exist in a dense star.Our concern then rests with calculating the magnitude of topological currents in the many phases of matter thought to exist in dense stars. We choose four representative processes to investigate: nuclear matter, hyperons, kaon condensates, and strange quark matter. We then suppose that this current may somehow transfer its momentum out of the star, either by being physically ejected or by emitting radiation, causing a kick. We also discuss how the current may induce magnetic helicity and a toroidal magnetic field in the core of the star.We end by discussing the topological current in terms of the AdS/CFT correspondence, a powerful tool that allows one to obtain results from strongly coupled field theories by transferring the problem to the language of a weakly coupled gravitational theory. We introduce a toy model to how one might introduce topological currents into the AdS/CFT framework.

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The Topological Casimir Effect on a Torus (2013)

The conventional Casimir effect manifests itself as a quantum mechanical force between two plates, that arises from the quantization of the electromagnetic field in the enclosed vacuum. In this thesis the existence is discussed of an extra, topological term in the Casimir energy at finite temperatures. This topological Casimir effect emerges due to the nontrivial topological features of the gauge theory: the extra energy is the result of tunneling transitions between states that are physically the same but topologically distinct. It becomes apparent when examining, for instance, periodic boundary conditions. I explicitly calculate the new term for the simplest example of such a system, a Euclidean 4-torus. By dimensional reduction, this system is closely related to two dimensional electromagnetism on a torus, which is well understood. It turns out that the topological term is extremely small compared to the conventional Casimir energy, but that the effect is very sensitive to an external magnetic field. The external field plays the role of a topological theta parameter, analogous to the theta vacuum in Yang-Mills theory. The topological Casimir pressure and the induced magnetic field show a distinctive oscillation as a function of the external field strength, something that can hopefully be observed experimentally.

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The conformal anomaly and dark energy : how the conformal anomaly can introduce an IR scale into the vacuum energy (2011)

We suggest that the solution to the cosmological vacuum energy puzzle may come from the infrared sector of the low energy eﬀective quantum ﬁeld theory of gravity, where the impact of the conformal anomaly is of the upmost importance. We proceed by introducing two auxiliary ﬁelds, which describe the quantum state by the speciﬁcations of their macroscopic IR boundary conditions, in contrast to UV quantum eﬀects. Our investigation aims at ﬁnding a realistic cosmological solution which interprets the observed dark energy as a well deﬁned deﬁcit in the zero point energy density of the Universe. The energy density arises from a ’phase transition’ that alters the quantum ground state, wherein we give a precise ’renormalization’ scheme and deﬁnition for a ’renormalized vacuum energy’ that we identify with the dark energy.

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