Effective field theories that describes the dynamics of a conserved U(1) current in terms of "hydrodynamic" degrees of freedom of topological phases in condensed matter are discussed in general dimension D = d+1 using the functional bosonization technique. For non-interacting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII) and in the "primary series" of topological insulators in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ-term (when D is even). For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative "fractional" topological insulators and their possible effective field theories, and use them to determine the physical properties of these non-trivial quantum phases.

In spite of the diversity in the equations of state of nuclear matter, the recently discovered I-Love-Q relations [Yagi and Yunes, Science 341, 365 (2013)], which relate the moment of inertia, tidal Love number (deformability) and the spin-induced quadrupole moment of compact stars, hold for various kinds of realistic neutron stars and quark stars. While the physical origin of such universality is still a current issue, the observation that the I-Love-Q relations of incompressible stars can well approximate those of realistic compact stars hints at a new direction to approach the problem. In this paper, by establishing recursive post-Minkowskian expansion for the moment of inertia and the tidal deformability of incompressible stars, we analytically derive the I-Love relation for incompressible stars and show that the so obtained formula can be used to accurately predict the behavior of realistic compact stars from the Newtonian limit to the maximum mass limit.PACS numbers: 04.40. Dg, 04.25.Nx, 97.60.Gb, 95.30.Sf I. INTRODUCTIONRecently, Yagi and Yunes [1, 2] have discovered the so called "I-Love-Q universal relations" prevailing in compact stars, including both neutron stars (NSs) or quark stars (QSs). In such relations, the moment of inertia I, the quadrupole tidal Love number λ (or, more precisely, tidal deformability [3,4]), and the spin-induced quadrupole moment Q of compact stars are expressed in terms of one another, with the stellar mass M playing the role of a scaling parameter. Soon after the discovery of Yagi and Yunes [1,2], the I-Love-Q relations were generalized to several other cases, including binary systems with strong dynamical tidal field [5], magnetized NSs with sufficiently high rotation rates [6], rapidly-rotating stars [7,8], and higher-order multipole moments induced by either tidal forces or rotation [4,9,10].These relations are useful for several reasons [1,2]. First, they provide a link directly connecting the I-Love-Q triplet. Once the mass of a compact star is known, each one of of I, λ and Q can lead to the determination of the other two. Second, in the analysis of gravitational wave signals emitted during the late stages of NS-NS binary mergers, they can break the degeneracy between the contributions due to the quadrupole moment and the spin and hence enable more accurate measurement of the averaged spin of the system [1,2,11,12]. Third, they can identify the validity of other modified gravity theories such as the Chern-Simons gravity and the Eddington-inspired Born-Infeld (EiBI) gravity [1,2,13,14].On the other hand, the emergence of the I-Love-Q relations is also interesting from theoretical point of view. As is well known, the physical characteristics of NSs (or QSs), including mass, radius, and moment of inertia, are usually obscured by various uncertainties in the equation of state (EOS) of nuclear matter (or quark matter). In fact, nuclear physicists have been using different characteristics (e.g., the mass-radius relation, the maximum mass and gravitational wave spectrum) ...

While many features of topological band insulators are commonly discussed at the level of singleparticle electron wave functions, such as the gapless Dirac spectrum at their boundary, it remains elusive to develop a hydrodynamic or collective description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a U (1) gauge field that arises by gauging the continuous symmetry of the target system (the U (1) particle number conservation). Integrating over the U (1) gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the U (1) gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description, and the implication of its duality, of the surface of topological insulators are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction. CONTENTS

The emergence of the I-Love-Q relations, revealing that the moment of inertia, the tidal Love number (deformability) and the spin-induced quadrupole moment of compact stars are, to high accuracy, interconnected in a universal way disregarding the wide variety of equations of state (EOSs) of dense matter, has attracted much interest recently. However, the physical origin of these relations is still a debatable issue. In the present paper, we focus on the I-Love relation for self-bound stars (SBSs) such as incompressible stars and quark stars. We formulate perturbative expansions for the moment of inertia, the tidal Love number (deformability) and the I-Love relation of SBSs. By comparing the respective I-Love relations of incompressible stars and a specific kind of SBSs, we show analytically that the I-Love relation is, to relevant leading orders in stellar compactness, stationary with respect to changes in the EOS about the incompressible limit. Hence, the universality of the I-Love relation is indeed attributable to the proximity of compact stars to incompressible stars, and the stationarity of the relation as unveiled here. We also discover that the moment of inertia and the tidal deformability of a SBS with finite compressibility are, to leading order in compactness, equal to their counterparts of an incompressible star with an adjusted compactness, thus leading to a novel explanation for the I-Love universal relation.

While winding a particlelike excitation around a looplike excitation yields the celebrated Aharonov-Bohm phase, we find a distinctive braiding phase in the absence of such mutual winding. In this Letter, we propose an exotic particle-loop-loop braiding process, dubbed the Borromean rings braiding. In the process, a particle moves around two unlinked loops, such that its trajectory and the two loops form the Borromean rings or more general Brunnian links. As the particle trajectory does not wind with any of the loops, the resulting braiding phase is fundamentally different from the Aharonov-Bohm phase. We derive an explicit expression for the braiding phase in terms of the underlying Milnor's triple linking number. We also propose topological quantum field theories consisting of an AAB-type topological term which realize the braiding statistics.

We discuss (2+1)D topological phases on non-orientable spatial surfaces, such as Möbius strip, real projective plane and Klein bottle, etc, which are obtained by twisting the parent topological phases by their underlying parity symmetries through introducing parity defects. We construct the ground states on arbitrary non-orientable closed manifolds and calculate the ground state degeneracy (GSD). Such degeneracy is shown to be robust against continuous deformation of the underlying manifold. We also study the action of the mapping class group on the multiplet of ground states on the Klein bottle. The physical properties of the topological states on non-orientable surfaces are deeply related to the parity symmetric anyons which do not have a notion of orientation in their statistics. For example, the number of ground states on the real projective plane equals the root of the number of distinguishable parity symmetric anyons, while the GSD on the Klein bottle equals the total number of parity symmetric anyons; in deforming the Klein bottle, the Dehn twist encodes the topological spins whereas the Y-homeomorphism tells the particle-hole relation of the parity symmetric anyons.

Document classification is the detection specific content of interest in text documents. In contrast to the data-driven machine learning classifiers, knowledge-based classifiers can be constructed based on domain specific knowledge, which usually takes the form of a collection of subject related keywords. While typical knowledge-based classifiers compute a prediction score based on the keyword abundance, it generally suffers from noisy detections due to the lack of guiding principle in gauging the keyword matches. In this paper, we propose a novel knowledge-based model equipped with Shannon Entropy, which measures the richness of information and favors uniform and diverse keyword matches. Without invoking any positive sample, such method provides a simple and explainable solution for document classification. We show that the Shannon Entropy significantly improves the recall at fixed level of false positive rate. Also, we show that the model is more robust against change of data distribution at inference while compared with traditional machine learning, particularly when the positive training samples are very limited.

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