Gauge Field Flux Research Articles

Topological monopole's gauge field‐induced anomalous Hall effect in artificial honeycomb lattice

AbstractVortex magnetic structure in artificial honeycomb lattice provides a unique platform to explore emergent properties due to the additional Berry phase curvature imparted by chiral magnetization to circulating electrons via direct interaction. We argue that while the perpendicularly aligned magnetic component leads to the quantized flux of monopole at the center of the Berry sphere, the in‐plane vortex circulation of magnetization gives rise to unexpected nontrivial topological Berry phase due to the gauge field transformation. The unprecedented effect signifies the importance of vector potential in multiply connected geometrical systems. Experimental confirmations to proposed hypotheses are obtained from Hall resistance measurements on permalloy honeycomb lattice. Investigation of the topological gauge transformation due to the in‐plane chirality reveals anomalous quasi‐oscillatory behavior in Hall resistance as a function of perpendicular field. The oscillatory nature of is owed to the fluctuation in equilibrium current as a function of Fermi wave‐vector , envisaged under the proposed new formulation in this article. Our synergistic approach suggests that artificially tunable nanostructured material provides new vista to the exploration of topological phenomena of strong fundamental importance.Key PointsDemonstration of gauge field flux due to vortex magnetism.Anomalous Hall effect in magnetic honeycomb lattice.Topological monopole‐induced magnetic flux.

Bosonic Hofstadter butterflies in synthetic antiferromagnetic patterns

The emergence of Hofstadter butterflies for bosons in synthetic-gauge-field antiferromagnetic (AFM) patterns is theoretically studied. We report on a specific tight-binding model of artificial AFM structures incorporating both nearest and next-to-nearest neighbour tunnelings and allowing for the formation of the fractal spectra even with the vanishing gauge field flux through the lattice. The model is applied to square and honeycomb lattices. Possible experimental realization is suggested for the lattices of microring resonators connected by waveguides. Finally, the structure of the butterflies is analyzed for different points in the magnetic Brillouin zone for both the ferromagnetic and AFM patterns.

T-branes and G2 backgrounds

Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial gauge field flux as well as normal deformations to the three-manifold captured by non-commuting matrix coordinates, a signal of T-brane phenomena. Solutions of the 3D gauge theory on a three-manifold are given by a deformation of the Hitchin system on a marked Riemann surface which is fibered over an interval. We present explicit examples of such backgrounds as well as the profile of the corresponding zero modes for localized chiral matter. We also provide a purely algebraic prescription for characterizing localized matter for such T-brane configurations. The geometric interpretation of this gauge theory description provides a generalization of twisted connected sums with codimension seven singularities at localized regions of the geometry. It also indicates that geometric codimension six singularities can sometimes support 4D chiral matter due to physical structure "hidden" in T-branes.

Gauge Field Fluxes and Bianchi Identities in Extended Field Theories

Tensor hierarchy of Exceptional Field Theories contains gauge fields satisfying certain Bianchi identities with source part governing interaction with standard and exotic branes. These are responsible for tadpole cancellation in compactification schemes and provide consistency constraints for cosmological model building. Analysis of reduction of (10+10)-dimensional DFT into (D+d+d)-dimensional split DFT allows to consider all Bianchi identities of the theory in the form analogous to the ExFT approach. Here we review in details and elaborate on these ideas.

Gauge field fluxes and Bianchi identities in extended field theories

Тензорная иерархия исключительных теорий поля содержит калибровочные поля, которые удовлетворяют определенным тождествам Бьянки с источником, управляющим взаимодействием со стандартными и экзотическими бранами. Данные тождества отвечают за сокращение диаграмм типа головастик в схемах компактификации и обеспечивают условия согласованности при построении космологической модели. Подробно описывается и развивается подход, согласно которому анализ редукции ($10+10$)-мерной двойной теории поля к ($D+d+d$)-мерной расщепленной двойной теории поля позволяет рассматривать все тождества Бьянки этой теории в виде, аналогичном тому, который получается в расширенной теории поля.

Electronic properties of single and double napped carbon nanocones

In this paper we study the electronic properties of carbon nanocones with one and two nappes, with pentagonal and heptagonal defects in their lattices. We use the continuum model, which is based on a Dirac-like Hamiltonian with the topological effects described by localized non-Abelian gauge field fluxes. We develop a geometrical approach that can describe the two nappes of the double cone surface simultaneously, by extending the radial coordinate to the complete set of real numbers. We show that, for some combinations of different nanocones, forming the double conical surface, the local density of states near the apex of the cone does not vanish at the Fermi energy and presents a strong dependence on the angular momentum. We also obtain the energy spectrum for finite-sized nanocones and verify that it depends on the choice of topological defect on the surface, which suggests that a double nanocone can be used to control the electronic transport in carbon-based electronic devices.

Monodromy relations in higher-loop string amplitudes

New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point (planar and non-planar) one-loop amplitudes described by a world-sheet cylinder and derive a set of relations between subamplitudes of different color orderings. Various consistency checks are performed by matching α′-expansions of planar and non-planar amplitudes involving elliptic iterated integrals with the resulting periods giving rise to two sets of multiple elliptic zeta values. The latter refer to the two homology cycles on the once-punctured complex elliptic curve and the monodromy equations provide relations between these two sets of multiple elliptic zeta values. Furthermore, our monodromy relations involve new objects for which we present a tentative interpretation in terms of open string scattering amplitudes in the presence of a non-trivial gauge field flux. Finally, we provide an outlook on how to generalize the new monodromy relations to the non-oriented case and beyond the one-loop level. Comparing a subset of our results with recent findings in the literature we find therein several serious issues related to the structure and significance of monodromy phases and the relevance of missed contributions from contour integrations.

Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations

We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of mathcal{N} = 4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux. This involves several types of two-point functions which are vanishing in the theory without the defect, such as two-point functions of operators of unequal conformal dimension. We furthermore exploit the operator product expansion (OPE) and the boundary operator expansion (BOE), which form the basis of the boundary conformal bootstrap equations, to extract conformal data both about the defect CFT and about mathcal{N} = 4 SYM theory without the defect. From the knowledge of the one- and two-point functions of the defect theory, we extract certain structure constants of mathcal{N} = 4 SYM theory using the (bulk) OPE and constrain certain bulk-to-boundary couplings using the BOE. The extraction of the former relies on a non-trivial, polynomial k dependence of the one-point functions, which we explicitly demonstrate. In addition, it requires the knowledge of the one-point functions of SU(2) descendant operators, which we likewise explicitly determine.

AdS vacua from dilaton tadpoles and form fluxes

We describe how unbounded three-form fluxes can lead to families of AdS3×S7 vacua, with constant dilaton profiles, in the USp(32) model with “brane supersymmetry breaking” and in the U(32) 0'B model, if their (projective-)disk dilaton tadpoles are taken into account. We also describe how, in the SO(16)×SO(16) heterotic model, if the torus vacuum energy Λ is taken into account, unbounded seven-form fluxes can support similar AdS7×S3 vacua, while unbounded three-form fluxes, when combined with internal gauge fields, can support AdS3×S7 vacua, which continue to be available even if Λ is neglected. In addition, special gauge field fluxes can support, in the SO(16)×SO(16) heterotic model, a set of AdSn×S10−n vacua, for all n=2,..,8. String loop and α′ corrections appear under control when large form fluxes are allowed.

AdS/dCFT one-point functions of the SU(3) sector

We propose a closed formula for the tree-level one-point functions of non-protected operators belonging to an SU(3) sub-sector of the defect CFT dual to the D3-D5 probe brane system with background gauge field flux, k, valid for k=2. The formula passes a number of non-trivial analytical and numerical tests. Our proposal is based on expressing the one-point functions as an overlap between a Bethe eigenstate of the SU(3) spin chain and a certain matrix product state, deriving various factorization properties of the Gaudin norm and performing explicit computations for shorter spin chains. As its SU(2) counterpart, the one-point function formula for the SU(3) sub-sector is of determinant type. We discuss the the differences with the SU(2) case and the challenges in extending the present formula beyond k=2.

Hadamard function and the vacuum currents in braneworlds with compact dimensions: Two-brane geometry

We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field in the region between two co-dimension one branes on the background of locally AdS spacetime with an arbitrary number of toroidally compactified spatial dimensions. Along compact dimensions periodicity conditions are considered with general values of the phases and on the branes Robin boundary conditions are imposed for the field operator. In addition, we assume the presence of a constant gauge field. The latter gives rise to Aharonov-Bohm type effect on the vacuum currents. There exists a range in the space of the Robin coefficients for separate branes where the vacuum state becomes unstable. Compared to the case of the standard AdS bulk, in models with compact dimensions the stability condition imposed on the parameters is less restrictive. The current density has nonzero components along compact dimensions only. These components are decomposed into the brane-free and brane-induced contributions. The component along a given compact dimension is a periodic function of the gauge field flux, enclosed by that dimension, with the period of the flux quantum. An important feature, that distinguishes the current density from the expectation values of the field squared and energy-momentum tensor, is its finiteness on the branes. In particular, for Dirichlet boundary condition the current density vanishes on the branes. We show that, depending on the constants in the boundary conditions, the presence of the branes may either increase or decrease the current density compared with that for the brane-free geometry. Applications are given to the Randall--Sundrum 2-brane model with extra compact dimensions.

Vacuum currents in braneworlds on AdS bulk with compact dimensions

The two-point function and VEV of the current density are investigated for a massive charged scalar field with arbitrary curvature coupling in the geometry of a brane on background of AdS spacetime with partial toroidal compactification.The presence of a gauge field flux enclosed by compact dimensions is assumed.On the brane the field obeys Robin boundary condition and along compact dimensions periodicity conditions with general phases are imposed.There is a range in the space of values for the coefficient in the boundary condition where Poincare vacuum is unstable.This range depends on the brane location.In models with compact dimensions the stability condition is less restrictive than for AdS bulk with trivial topology.Vacuum charge density and components of current along non-compact dimensions vanish. VEV of the current density along compact dimensions is a periodic function of the gauge field flux with a period equal to the flux quantum.It is decomposed into the boundary-free and brane-induced contributions.The asymptotic behavior of the latter is investigated near the brane, AdS boundary and horizon.In contrast to VEVs of the field squared and energy-momentum tensor, current density is finite on brane and vanishes for the special case of Dirichlet boundary condition.Both boundary-free and brane-induced contributions vanish on AdS boundary.Brane-induced contribution vanishes on the horizon and for points near the horizon the current is dominated by the boundary-free part.In the near-horizon limit, the latter is connected to the corresponding quantity for a massless field in the Minkowski bulk by a simple conformal relation.Depending on the value of the Robin coefficient, the presence of the brane can either increase or decrease the vacuum currents. Applications are given for a higher-dimensional version of the Randall-Sundrum 1-brane model

Tuning the Hall conductivity with rotation

In this work we investigate the effects of rotation in the integer quantum Hall effect. We verify that the quantization of the Hall conductivity comes from the quantization of a generalized gauge field flux as predicted by Fischer and Schopohl (Europhys. Lett., 54 (2001) 502) and show that rotation can be used to fine-tune the conductivity plateaus.

Gauge-covariant extensions of Killing tensors and conservation laws

In classical and quantum mechanical systems on manifolds with gauge-field fluxes, constants of motion are constructed from gauge-covariant extensions of Killing vectors and tensors. This construction can be carried out using a manifestly covariant procedure, in terms of covariant phase space with a covariant generalization of the Poisson brackets, c.q. quantum commutators. Some examples of this construction are presented.

Induced vacuum currents in anti-de Sitter space with toral dimensions

We investigate the Hadamard function and the vacuum expectation value of the current density for a charged massive scalar field on a slice of anti-de Sitter (AdS) space described in Poincaré coordinates with toroidally compact dimensions. Along compact dimensions periodicity conditions are imposed on the field with general phases. Moreover, the presence of a constant gauge field is assumed. The latter gives rise to Aharonov–Bohm-like effects on the vacuum currents. The current density along compact dimensions is a periodic function of the gauge field flux with the period equal to the flux quantum. It vanishes on the AdS boundary and, near the horizon, to the leading order, it is conformally related to the corresponding quantity in Minkowski bulk for a massless field. For large values of the length of the compact dimension compared with the AdS curvature radius, the vacuum current decays as power-law for both massless and massive fields. This behavior is essentially different from the corresponding one in Minkowski background, where the currents for a massive field are suppressed exponentially.

Stringy holography at finite density

We consider an exactly solvable worldsheet string theory in the background of a black brane with a gauge field flux. Holographically, such a system can be interpreted as a field theory with finite number of degrees of freedom at finite temperature and density. We construct closed string vertex operators which holographically represent the U(1) gauge field and the stress energy tensor and compute their two-point functions. At finite density the system behaves like a sum of two noninteracting fluids.

Stringy holography at finite density

We consider an exactly solvable worldsheet string theory in the background of a black brane with a gauge field flux. Holographically, such a system can be interpreted as a field theory with finite number of degrees of freedom at finite temperature and density. This is to be contrasted with more conventional holographic models which involve gravity in the bulk and possess infinite number of degrees of freedom and mean field critical exponents. We construct closed string vertex operators which holographically represent the U(1) gauge field and the stress-energy tensor and compute their two-point functions. At finite temperature and vanishing charge density the low-energy excitations are described by hydrodynamics. As the density is raised, the system behaves like a sum of two non-interacting fluids. We find low-energy excitations in the shear and sound channels of each fluid.

Chiral primary one-point functions in the D3-D7 defect conformal field theory

We compute the one-point functions of chiral primary operators in the non-supersymmetric defect conformal field theory that is dual to the IIB string theory on $AdS_5\times S^5$ background with a probe D7 brane with internal gauge field flux, both in perturbative Yang-Mills theory and in the string theory dual. The former is expected to be accurate at weak coupling whereas the latter should be accurate in the planar strong coupling limit of the gauge theory. We consider the distinct cases where the D7 brane has geometry $AdS_4\times S^4$ with an instanton bundle of the worldvolume gauge fields on $S^4$ and $AdS_4\times S^2\times S^2$ with Dirac monopole bundles on each $S^2$. The gauge theory computation and the string theory computation can be compared directly in the planar limit and then a subsequent limit where the worldvolume flux is large. We find that there is exact agreement between the two in the leading order.

The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere

We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a biaxially squashed three-sphere, with a non-trivial background gauge field. This is described by a 1/2 BPS Euclidean solution of four-dimensional N=2 gauged supergravity, consisting of a Taub–NUT–AdS metric with a non-trivial instanton for the graviphoton field. The holographic free energy of this solution agrees precisely with the large N limit of the free energy obtained from the localized partition function of a class of Chern–Simons quiver gauge theories. We also discuss a different supersymmetric solution, whose boundary is a biaxially squashed Lens space S3/Z2 with a topologically non-trivial background gauge field. This metric is of Eguchi–Hanson–AdS type, although it is not Einstein, and has a single unit of gauge field flux through the S2 cycle.

Non-Abelian structures in compactifications of M-theory on seven-manifolds with SU(3) structure

We study M-theory compactified on a specific class of seven-dimensional manifolds with SU(3) structure. The manifolds can be viewed as a fibration of an arbitrary Calabi-Yau threefold over a circle, with a U-duality twist around the circle. In some cases we find that in the four dimensional low energy effective theory a (broken) non-Abelian gauge group appears. Furthermore, such compactifications are shown to be dual to previously analyzed compactifications of the heterotic string on K3 x T^2, with background gauge field fluxes on the T^2.