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We observe significant, 6.5 - 12%, differences between skyrmion and antiskyrmion Hall angles in existing experimental data. To account for them, the Thiele equation is generalized with the transverse velocity component in the collective coordinate of magnetization vector. The corresponding generalized Hall angle is formulated, and its consequences are compared to the data. A plausible physical origin is provided for explaining the Hall angle differences., Comment: 2 pages, 3 figures

We generalize the Thiele equation with a transverse velocity to the skyrmion motion described by the collective coordinate of magnetization vector. It is applied to investigate significant disparity in the existing data sets of skyrmion and antiskyrmion Hall angles. Our analysis further reveals interesting differences of these Hall angles near the angular momentum compensation point. We identify a possible physical quantity that is responsible for the disparity., Comment: 6 pages, 3 figures, published version

Entanglement and the R\'enyi entropies for Dirac fermions on 2 dimensional torus in the presence of chemical potential, current source, and topological Wilson loop are unified in a single framework by exhausting all the ingredients of the electromagnetic vertex operators of $\mathbb{Z}_n$ orbifold conformal field theory. We employ different normalizations for different topological sectors to organize various topological phase transitions in the context of entanglement entropy. Pictorial representations for the topological transitions are given for the $n=2$ R\'enyi entropy. Our analytic computations reveal numerous novelties and provide resolutions for existing issues. We have settled to provide non-singular entanglement entropies that are also continuous across the topological sectors. Surprisingly, in infinite space, these entropies become exact and depend only on the Wilson loop. On a circle, we resolve to find the entropies subtly depend on the chemical potential at zero temperature, which is useful for probing the ground state energy levels of quantum systems., Comment: 7+3 pages, 7 figures. Here entanglement entropy is continuous across the Wilson loop topological transitions, while arXiv:1705.01859 realizes its discontinuous version

Magnetic skyrmions are topologically stable objects that are made with a bunch of spins tightly arranged in a smooth fashion. Their topological nature provides unusual and complex transport properties, such as the skyrmion Hall effect. Extensive Hall data have further revealed asymmetry between skyrmion and antiskyrmion Hall angles, which cannot be accounted by known mechanisms. Here, we explain this asymmetry by utilizing another universal transport coefficient called `Hall viscosity,' extensively studied in quantum Hall systems. Hall viscosity is modeled in steady-state skyrmions motion by generalizing the Thiele equation with a transverse velocity component and is independent of the skyrmion charge. Our analyses, based on available asymmetric Hall angle data, reveal this transverse force amounts 3\% - 5.4\% of the force due to the skyrmion Hall effect. Further clarification of Hall viscosity will be essential for designing next generation storage devices properly, not to mention for our deeper understanding of fundamental properties of nature., Comment: 5 pages, 2 figures. A short presentation can be found in APS March Meeting page, https://absuploads.aps.org/presentation.cfm?pid=16434

We review recent progresses towards an understanding of the Skyrmion Hall transport in insulating as well as conducting materials. First, we consider a theoretical breakthrough based on the quantum field theory Ward identity, a first principle analysis, relying on symmetries and conservation laws. Broken parity (inversion) symmetry plays a crucial role in Skyrmion Hall transport. In addition to the well known thermal and electric Hall conductivities, our analysis has led us to the discovery of a new and unforeseen physical quantity, Hall viscosity - an anti-symmetric part of the viscosity tensor. We propose a simple way to confirm the existence of Hall viscosity in the measurements of Hall conductivity as a function of momentum. We provide various background materials to assist the readers to understand the quantum field theory Ward identity. In the second part, we review recent theoretical and experimental advancements of the Skyrmion Hall effects and the topological (Magnon) Hall effects for conducting (insulting) magnets. For this purpose, we consider two enveloping themes: spin torque and thermo-electromagnetic effect. First, we overview various spin torques, such as spin transfer torque, spin-orbit torque, and spin Hall torque, and generalized Landau-Lifshitz-Gilbert equations and Thiele equations using a phenomenological approach. Second, we consider irreversible thermodynamics to survey possible thermo-electromagnetic effects, such as Seebeck, Peltier and Thompson effects in the presence of the electric currents, along with the Hall effects in the presence of a background magnetic field. Recently developed spin Seebeck effects are also a significant part of the survey. We also accommodate extensive background materials to make this review self-contained. Finally, we revisit the Skyrmion Hall transport from the Ward identity view point., Comment: 66 pages and 34 figures. Invited topical review (including new results) published in J. Phys.: Condens. Matter

We study both entanglement and the R\'enyi entropies for the 2 dimensional massless Dirac fermions in the presence of topological Wilson loops, which are qualitatively different from those with a chemical potential and a current source. In the language of $\mathbb{Z}_n$ orbifold theories, the Wilson loop is interpreted as an electric operator while the orbifold twist operator as a magnetic operator. Generalized topological transitions for the entropies are driven by both electric and magnetic parameters via the restriction on the operator's conformal weight. By adapting different normalizations for different topological sectors, we achieve two goals: entanglement entropy can be obtained with a smooth limit from the R\'enyi entropy, and the entropies are continuous across the different topological sectors that include general Wilson loops winding sectors. We provide exact results for the entropies in infinite space, which depend only on the topological Wilson loops, independent of the chemical potential and the current source., Comment: 42 pages and 7 figures. Conclusions not changed. Complete revision including the connection to the topological winding numbers

We discuss the contribution of magnetic Skyrmions to the Hall viscosity and propose a simple way to identify it in experiments. The topological Skyrmion charge density has a distinct signature in the electric Hall conductivity that is identified in existing experimental data. In an electrically neutral system, the Skyrmion charge density is directly related to the thermal Hall conductivity. These results are direct consequences of the field theory Ward identities, which relate various physical quantities based on symmetries and have been previously applied to quantum Hall systems., Comment: 10 pages, based on the invited talk at the 62nd Annual Conference on Magnetism and Magnetic Materials (MMM conference), November 6-10, Pittsburgh, PA

We study the entanglement entropy, the R\'enyi entropy, and the mutual (R\'enyi) information of Dirac fermions on a 2 dimensional torus in the presence of constant gauge fields. We derive their general formulas using the equivalence between twisted boundary conditions and the background gauge fields. Novel and interesting physical consequences have been presented in arXiv:1705.01859. Here we provide detailed computations of the entropies and mutual information in a low temperature limit, a large radius limit, and a high temperature limit. The high temperature limit reveals rather different physical properties compared to those of the low temperature one: there exist two non-trivial limits that depend on a modulus parameter and are not smoothly connected., Comment: 37 pages, v2: some formulas in section 4.3 are corrected

We examine the behavior of entanglement entropy of a subsystem $A$ in a fully backreacted holographic model of a $1+1$ dimensional $p$ wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size $l$ smaller than a critical size $l_{c1}$, entanglement entropy continues to increase as a function of the charge density as we cross the phase transition. When $l$ lies between $l_{c1}$ and another critical size $l_{c2}$ the entanglement entropy displays a non-monotonic behavior, while for $l > l_{c2}$ it decreases monotonically. At large charge densities entanglement entropy appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system., Comment: 16 pages, 17 figures, v2: references added, section 3.1 added, JHEP style

We construct and analytically compute entanglement and the R\'enyi entropies of Dirac fermions on a 2 dimensional torus in the presence of background chemical potential, current source and Wilson loop, by employing correlation functions of the electromagnetic vertex operators of $\mathbb{Z}_n$ orbifold theory. The entropies reveal numerous novelties. They probe the energy levels of compact fermions through the chemical potential, demonstrate interference phenomena with the current source being `beat frequency,' and experience topological phase transitions by dialing the Wilson loop, in the low temperature limit. In the large radius limit, they depend only on the Wilson loop via topological transitions, which are tightly linked to conformal dimension of the electromagnetic operators., Comment: 5+4 pages, 5 figures, v2: improved introduction, v3: major revision with Wilson loop contribution to Entanglement entropy

We generalize the boundary value problem with a mixed boundary condition that involves the gauge and scalar fields in the context of Einstein-Maxwell-Dilaton theories. In particular, the expectation value of the dual scalar operator can be a function of the expectation value of the current operator. The properties are prevalent in a fixed charge ensemble because the conserved charge is shared by both fields through the dilaton coupling, which is also responsible for non-Fermi liquid properties. We study the on-shell action and the stress energy tensor to note practical importances of the boundary value problem. In the presence of the scalar fields, physical quantities are not fully fixed due to the finite boundary terms that manifest in the massless scalar or the scalar with mass saturating the Breitenlohner-Freedman bound., Comment: 39+1 pages. Improved discussions, typos fixed and references added

We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the 2+1 dimensional momentum algebra, which includes a central extension proportional to the topological charge density. In the presence of topological objects like Skyrmions, we observe that the central term leads to a direct relation between the thermal Hall conductivity and the topological charge density. We extend this relation to incorporate the effects of a magnetic field and an electric current. The topological charge density produces a distinct signature in the electric Hall conductivity, which is identified in existing experimental data, and yields further novel predictions. For insulating materials with translation invariance, the Hall viscosity can be directly determined from the Skyrmion density and the thermal Hall conductivity to be measured as a function of momentum., Comment: 6+1 pages including Supplemental Material. Version to appear in Physical Review Letters

We use the Ward identities corresponding to general linear transformations, and derive relations between transport coefficients of $(2+1)$-dimensional systems. Our analysis includes relativistic and Galilean invariant systems, as well as systems without boost invariance such as Lifshitz theories. We consider translation invariant, as well as broken translation invariant cases, and include an external magnetic field. Our results agree with effective theory relations of incompressible Hall fluid, and with holographic calculations in a magnetically charged black hole background., Comment: 17 pages, references and conclusions added. Published version

We derive quantum field theory Ward identities based on linear area preserving and conformal transformations in 2+1 dimensions. The identities relate Hall viscosities, Hall conductivities and the angular momentum. They apply both for relativistic and non relativistic systems, at zero and at finite temperature. We consider systems with or without translation invariance, and introduce an external magnetic field and viscous drag terms. A special case of the identities yields the well known relation between the Hall conductivity and half the angular momentum density., Comment: 35 pages, 1 figure, minor changes. Published version

We consider relativistic non-Abelian superfluids, where the expectation value of the global symmetry currents relate space and internal indices, thus creating a "locked" phase. Locking a superfluid with SU(2) internal symmetry in 2+1 dimensions breaks parity spontaneously, and introduces parity-odd terms in the constitutive relations. We show that there are qualitatively different extensions of the rest frame locking to non-zero velocities. We construct the resulting superfluid hydrodynamics up to the first derivative order. Using an expansion close to the critical point, we estimate the ratio of the Hall viscosity and the angular momentum density. Our general hydrodynamic results are compatible with the holographic p-wave calculations in arXiv:1311.4882., Comment: 44 pages, updated references, new appendix with discussion about entropy current, conclusions unchanged. Published version

We compute the bulk viscosity in holographic models dual to theories with Lifshitz scaling and/or hyperscaling violation, using a generalization of the bulk viscosity formula derived in arXiv:1103.1657 from the null focusing equation. We find that only a class of models with massive vector fields are truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other holographic models with scalars and/or massless vector fields we find a universal formula in terms of the dynamical exponent and the hyperscaling violation exponent., Comment: 24 pages

We consider a covariant formulation of field theories with Lifshitz scaling, and analyze the energy-momentum tensor and the scale symmetry Ward identity. We derive the equation of state and the ideal Lifshitz hydrodynamics in agreement with arXiv:1304.7481, where they were determined by using thermodynamics and symmetry properties. We construct the charged ideal Lifshitz hydrodynamics in the generating functional framework as well as in the gravitational holographic dual description. At the first viscous order, an analysis of the entropy current reveals two additional transport coefficients (one dissipative and one dissipationless) compared to the neutral case, contributing to the charge current and to the asymmetric part of the energy-momentum tensor., Comment: v2, 38 pages, improved discussion of dissipative terms, published version

We construct the hydrodynamics of quantum critical points with Lifshitz scaling. There are new dissipative effects allowed by the lack of boost invariance. The formulation is applicable, in general, to any fluid with an explicit breaking of boost symmetry. We use a Drude model of a strange metal to study the physical effects of the new transport coefficient. It can be measured using electric fields with non-zero gradients, or via the heat production when an external force is turned on. Scaling arguments fix the resistivity to be linear in the temperature., Comment: 11 pages, 1 figure, acceleration term corrected

We analytically compute correlation and response functions of scalar operators for the systems with Galilean and corresponding aging symmetries for general spatial dimensions $d$ and dynamical exponent $z$, along with their logarithmic and logarithmic squared extensions, using the gauge/gravity duality. These non-conformal extensions of the aging geometry are marked by two dimensionful parameters, eigenvalue $\mathcal M$ of an internal coordinate and aging parameter $\alpha$. We further perform systematic investigations on two-time response functions for general $d$ and $z$, and identify the growth exponent as a function of the scaling dimensions $\Delta$ of the dual field theory operators and aging parameter $\alpha$ in our theory. The initial growth exponent is only controlled by $\Delta$, while its late time behavior by $\alpha$ as well as $\Delta$. These behaviors are separated by a time scale order of the waiting time. We attempt to make contact our results with some field theoretical growth models, such as Kim-Kosterlitz model at higher number of spatial dimensions $d$., Comment: 1+35 pages, 11 figures, v2 : minor corrections, published version

We investigate systematic classifications of low energy and lower dimensional effective holographic theories with Lifshitz and Schr\"odinger scaling symmetries only using metrics in terms of hyperscaling violation ($\theta$) and dynamical ($z$) exponents. Their consistent parameter spaces are constrained by null energy and positive specific heat conditions, whose validity is explicitly checked against a previously known result. From dimensional reductions of many microscopic string solutions, we observe the classifications are tied with the number of scales in the original microscopic theories. Conformal theories do not generate a nontrivial $\theta$ for a simple sphere reduction. Theories with Lifshitz scaling with one scale are completely fixed by $\theta$ and $z$, and have a universal emblackening factor at finite temperature. Dimensional reduction of intersecting M2-M5 requires, we call, spatial anisotropic exponents ($\sharp$), along with $z$=1, $\theta$=0, because of another scale. Theories with Schr\"odinger scaling show similar simple classifications at zero temperature, while require more care due to an additional parameter being a thermodynamic variable at finite temperature., Comment: 1+63 pages, 12 figures, v2 : typos corrected, published version

We consider logarithmic extensions of the correlation and response functions of scalar operators for the systems with aging as well as Schr\"odinger symmetry. Aging is known to be the simplest nonequilibrium phenomena, and its physical significances can be understood by the two-time correlation and response functions. Their logarithmic part is completely fixed by the bulk geometry in terms of the conformal weight of the dual operator and the dual particle number. Motivated by recent experimental realizations of Kardar-Parisi-Zhang universality class in growth phenomena and its subsequent theoretical extension to aging, we investigate our two-time correlation functions out of equilibrium, which show several qualitatively different behaviors depending on the parameters in our theory. They exhibit either growing or aging, i.e. power-law decaying, behaviors for the entire range of our scaling time. Surprisingly, for some parameter ranges, they exhibit growing at early times as well as aging at later times., Comment: 1+26 pages, 15 figures

We study the properties of the Schr\"odinger-type non-relativistic holography for general dynamical exponent z with and without hyperscaling violation exponent \theta. The scalar correlation function has a more general form due to general z as well as the presence of \theta, whose effects also modify the scaling dimension of the scalar operator. We propose a prescription for minimal surfaces of this "codimension 2 holography," and demonstrate the (d-1) dimensional area law for the entanglement entropy from (d+3) dimensional Schr\"odinger backgrounds. Surprisingly, the area law is violated for d+1 < z < d+2, even without hyperscaling violation, which interpolates between the logarithmic violation and extensive volume dependence of entanglement entropy. Similar violations are also found in the presence of the hyperscaling violation. Their dual field theories are expected to have novel phases for the parameter range, including Fermi surface. We also analyze string theory embeddings using non-relativistic branes., Comment: 62 pages and 6 figures, v2: several typos in section 5 corrected, references added, v3: typos corrected, references added, published version

We construct the gravity background which describes the dual field theory with aging invariance. We choose the decay modes of the bulk scalar field in the internal spectator direction to obtain the dissipative behavior of the boundary correlation functions of the dual scalar fields. In particular, the two-time correlation function at zero temperature has the characteristic features of the aging system: power law decay, broken time translation and dynamical scaling. We also construct the black hole backgrounds with asymptotic aging invariance. We extensively study characteristic behavior of the finite temperature two-point correlation function via analytic and numerical methods., Comment: 38 pages and 5 figures, expanded discussions on correlator, one mistake is fixed, modified discussion on shear viscosity, to appear in JHEP

We briefly explain the consistency conditions imposed on the effective holographic theories, which are parameterized by two real exponents $(\gamma,\delta)$ that control the IR dynamics. The general scaling of DC resistivity with temperature at low temperature and AC conductivity at low frequency across the whole $(\gamma,\delta)$ plane are explained. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for $(2+1)$-dimensional systems. Regions are identified where the theory at finite density is a Mott-like insulator. This contribution is based on arXiv:1005.4690 with emphasis on the transport properties of charged dilatonic black holes with potential., Comment: 6 pages and 6 figures. Contribution to the proceedings of the XVIth European Workshop on String Theory, Madrid, Spain, June 14-18 2010

We review a recent holographic analysis arXiv:1005.4690 of charged black holes with scalar hair in view of their applications to the cuprate high temperature superconductors. We show in particular that these black holes show an interesting phase structure including critical behaviour at zero temperature or charge, describe both conductors and insulators (including holographic Mott-like insulators), generically have no residual entropy and exhibit experimentally observed scaling relations between electronic entropy, specific heat and (linear) DC resistivity. Transport properties are discussed in the companion contribution to these proceedings., Comment: 6 pages, 6 figures, to appear in "Proceedings of the XVIth European Workshop on String Theory", Madrid, June 2010, to be published in Fortsch. Phys

A holographic model of a quantum critical theory at a finite but low temperature, and finite density is studied. The model exhibits non-relativistic z=2 Schr\"odinger symmetry and is realized by the Anti-de-Sitter-Schwarzschild black hole in light-cone coordinates. Our approach addresses the electrical conductivities in the presence or absence of an applied magnetic field and contains a control parameter that can be associated to quantum tuning via charge carrier doping or an external field in correlated electron systems. The Ohmic resistivity, the inverse Hall angle, the Hall coefficient and the magnetoresistance are shown to be in good agreement with experimental results of strange metals at very low temperature. The holographic model also predicts new scaling relations in the presence of a magnetic field., Comment: 39 pages, 7 figures, (v2) Major revision that considers a wider range of phenomena, explanations and comparisons to experimental data. arXiv admin note: text overlap with arXiv:1107.2116

Properties of Schroedinger black holes are derived from AdS black holes expressed in light-cone coordinates with a particular normalization. The advantages of this method over the direct analysis of the Schroedinger geometry are the simplicity and the well-defined Brown-York procedure with the standard counterterms. The method is demonstrated for several physical interests, including the computation of the DC conductivity and the derivation of the R-charged black hole thermodynamic properties., Comment: 27 pages, 4 figures, minor changes, published version

We consider a (supersymmetric) bosonization of general commuting matter $\beta\gamma$ CFT. Unlike the conventional ghost $\beta\gamma$ CFT bosonization, which is typically described in terms of one scalar and one set of $\xi\eta$ CFT, the matter $\beta\gamma$ CFT is naturally bosonized to two scalar CFTs. Surprisingly, there exists an independent subsector, which satisfies a constraint necessary for consistent bosonization, while the usual sector has a description in terms of two compact coordinates. The subsector itself is a complete system which is equivalent to the original $\beta\gamma$ CFT. Furthermore, a non-compact coordinate naturally emerges in this "non-compact subsector". As an immediate application, we consider the bosonization of matter $\beta\gamma$ CFT in the context of full string theory and find the connection to noncritical string theories in the light-cone gauge., Comment: 11 pages

We construct a supersymmetric version of the ``critical'' non-relativistic bosonic string theory\cite{Kim:2007hb} with its manifest global symmetry. We introduce the anticommuting $bc$ CFT which is the super partner of the $\beta\gamma$ CFT. The conformal weights of the $b$ and $c$ fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of Type IIB superstring theory. There is one notable difference: the fermions are non-chiral. We further consider ``noncritical'' generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical non-relativistic string theory and the lightlike Linear Dilaton theory., Comment: Typos corrected, references added. A version to appear in Phys. Rev. D

We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri\cite{Gomis:2000bd} and Danielsson et. al. \cite{Danielsson:2000gi, Danielsson:2000mu}. Our theory is much simpler than their theory and does not assume a compact coordinate. This non-relativistic string theory has a bosonic matter $\beta\gamma$ CFT with the conformal weight of $\beta$ as 1. It is natural to identify time as a linear combination of $\gamma$ and $\bar{\gamma}$ through an explicit realization of the Galilean boost symmetry. The angle between $\gamma$ and $\bar{\gamma}$ parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a non-relativistic dispersion relation without a nontrivial topology in the non-relativistic setup, which is one of the major differences from the previous works\cite{Gomis:2000bd, Danielsson:2000gi, Danielsson:2000mu}. This simple theory is the non-relativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the $\beta\gamma$ CFT. We also mention supersymmetric generalizations of these theories., Comment: 26 pages

We describe some features of the recently constructed "Puff Field Theory," and present arguments in favor of it being a field theory decoupled from gravity. We construct its supergravity dual and calculate the entropy of this theory in the limit of large 't Hooft coupling. We also determine the leading irrelevant operator that governs its deviation from N=4 super Yang-Mills theory., Comment: 31 pages, 1 figure

Super twistor space admits a certain (super) complex structure deformation that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in twistor string theory this deformation corresponds to augmenting N=4 super Yang-Mills theory by a mass term for the left-chirality spinors. In this paper we analyze this proposal in more detail. We calculate 4-particle scattering amplitudes of fermions, gluons and scalars and show that they are supported on holomorphic curves in the deformed twistor space., Comment: 52 pages, 15 figures

We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space--the reduction of D=4 twistor space to D=3. We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model, we identify the enhanced R-symmetry. We then construct B-model topological string theories that, we propose, correspond to D=3 Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits's model. Some of our constructions can be lifted to D=4, where infinitesimal mass terms correspond to VEVs of certain superconformal gravity fields., Comment: 69 pages; Typos corrected

We have constructed nonrelativistic fermion and scalar field theories coupled to a Maxwell-Chern-Simons gauge field which admit static multi-vortex solutions. This is achieved by introducing a magnetic coupling term in addition to the usual minimal coupling., Comment: 13 pages, Title was changed and References were added