Non-trivial Gauge Field Research Articles

Rotating AdS3× S3 and dyonic strings from 3-dimensions

We make a general Killing spinor analysis of a particular D = 3, N = 4 gauged supergravity that comes from a consistent S3 reduction of D = 6, N = (1, 0) supergravity coupled to a single chiral tensor multiplet. We then focus on its supersymmetric solutions with a null Killing vector and find three new ones. Two of these, namely the null warped AdS3 (also known as the Schrödinger spacetime) and the charged domain wall solutions, admit non-trivial gauge fields which give rise to rotating solutions in 6-dimensions. The uplift of the first one produces an interesting AdS3 × S3 background with a non-trivial rotation in the U(1) fiber direction of the S3 which retains the Schrödinger scale invariance that the seed solution has. The second one leads to the well-known rotating dyonic string solution. Finally, the uplift of the third one, which is a domain wall solution with no gauge fields, results in a distribution of dyonic strings.

A story of non-conformal branes: spindles, disks, circles and black holes

We consider the (p + 2)-dimensional gauged supergravities arising as a consistent truncation of type II on S8−p, which are associated with the near-horizon limit of Dp-branes, for p = 2, 4, 5, 6 (and NS5-branes for p = 5). In a truncation of these theories with only abelian gauge fields and scalars, we find several classes of new solutions, with and without supersymmetry. Our ansatz for such backgrounds is inspired by the recent progress in the study of branes wrapped on orbifolds, but unlike those examples we consider “non-conformal branes”, i.e. no Anti de Sitter factors in the metric. Focusing on cases with non-trivial gauge fields, we can divide the solutions that we present in three categories: 1) branes wrapping Riemann surfaces, spindles and disks, 2) branes wrapped on a circle with a holonomy for the gauge field along the circle and 3) electrically charged black holes in gauged supergravity, which uplift to rotating branes in ten dimensions. We carefully analyze the conditions for supersymmetry in all these cases.

Democratic Lagrangians from topological bulk

Chiral form fields in d dimensions can be effectively described as edge modes of topological Chern-Simons theories in d+1 dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a d-dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on shell with extra gauge symmetries. A recent work by Arvanitakis demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the (d+1)-dimensional topological Lagrangian automatically leads to d-dimensional Lagrangians with appropriate sets of auxiliary fields. We develop this setup in three distinct directions. First, we demonstrate how arbitrary Abelian self-interactions for chiral forms can be included using nonlinear boundary terms in the Chern-Simons theory. Second, by generalizing the Chern-Simons theory to the BF-theory, we obtain an analogous democratic description of nonchiral form fields, where electric and magnetic potentials appear as explicit dynamical variables. Third, we discuss the effects of introducing topological interactions in the higher-dimensional bulk, which produce extra interaction terms in the boundary theory. When applied to a topological 4-form field in 12 dimensions, this construction results in a democratic description of the 3-form gauge field of the eleven-dimensional supergravity. Published by the American Physical Society 2024

Magnon dynamics in a skyrmion-textured domain wall of antiferromagnets

We theoretically investigate the interaction between magnons and a Skyrmion-textured domain wall in a two-dimensional antiferromagnet and elucidate the resultant properties of magnon transport. Using supersymmetric quantum mechanics, we solve the scattering problem of magnons on top of the domain wall and obtain the exact solutions of propagating and bound magnon modes. Then, we find their properties of reflection and refraction in the Skyrmion-textured domain wall, where magnons experience an emergent magnetic field due to its non-trivial spin texture-induced effective gauge field. Based on the obtained scattering properties of magnons and the domain wall, we show that the thermal transport decreases as the domain wall's chirality increases. Our results suggest that the thermal transport of an antiferromagnet is tunable by modulating the Skyrmion charge density of the domain wall, which might be useful for realizing electrically tunable spin caloritronic devices.

Hall Droplet Sheets in Holographic QCD

In single-flavor QCD, the low energy description of baryons as Skyrmions is not available. In this case, it has been proposed by Komargodski that baryons can be viewed as kinds of charged quantum Hall droplets, or “sheets”. In this paper we propose a string theory description of the sheets in single-flavor holographic QCD, focusing on the Witten-Sakai-Sugimoto model. The sheets have a “hard” gluonic core, described by D6-branes, and a “soft” mesonic shell, dual to non-trivial D8-brane gauge field configurations. We first provide the description of an infinitely extended sheet with massless or moderately massive quarks. Then, we construct a semi-infinite sheet ending on a one-dimensional boundary, a “vortex string”. The holographic description allows for the precise calculation of sheet observables. In particular, we compute the tension and thickness of the sheet and the vortex string, and provide their four dimensional effective actions.

Curved-space Dirac description of elastically deformed monolayer graphene is generally incorrect

Undistorted monolayer graphene has energy bands which cross at protected Dirac points. It elastically deforms, and much research has assumed the Dirac description persists, now in a curved space and coupled to a gauge field related to lattice strain. We show this is incorrect by using a real space gradient expansion to study how the Dirac equation derives from the tight-binding model. Generic spatially varying hopping functions give rise to large magnetic fields which spoil the truncation in derivatives. In the perturbative regime, the only consistent truncation to Dirac is one with nontrivial gauge field but in flat space. One can instead fine-tune the magnetic field to be small, and we derive the resulting differential condition that the hopping functions must satisfy to yield a consistent truncation to Dirac in curved space. We consider whether mechanical effects might impose this fine tuning but find this is not the case for a simple elastic membrane model.

Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes

These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines provides a pedagogical introduction to the theory of non-reciprocal quantum interactions and devices. The goal is connect various approaches and concepts, including Hamiltonians encoding synthetic gauge fields, scattering descriptions, quantum master equations, and non-Hermitian Hamiltonians. The importance of having both non-trivial synthetic gauge fields and dissipation for obtaining non-reciprocal interactions is stressed. Connections to broader topics such as quantum reservoir engineering and the quantum theory of continuous-measurement based feedforward are also discussed.

Gauge symmetry restoration by Higgs condensation in flux compactifications on coset spaces

Extra-dimensional components of gauge fields in higher-dimensional gauge theories will play a role of the Higgs field and become tachyonic after Kaluza-Klein compactifications on internal spaces with (topologically nontrivial) gauge field backgrounds. Its condensation is then expected to break gauge symmetries spontaneously. But, contrary to the expectation, some models exhibit restoration of gauge symmetries. In this paper, by considering all the massive Kaluza-Klein excitations of gauge fields, we explicitly show that some of them indeed become massless at the minimum of the Higgs potential and restore (a part of) the gauge symmetries which are broken by gauge field backgrounds. We particularly consider compactifications on ${S}^{2}$ with monopolelike fluxes and also on ${\mathbb{CP}}^{2}$ with instanton and monopolelike fluxes. In some cases, the gauge symmetry is fully restored, as argued in previous literatures. In other cases, there is a stable vacuum with a partial restoration of the gauge symmetry after Higgs condensation. Topological structure of the gauge field configurations prevent the gauge symmetries from being restored.

Spin(7) and generalized SO(8) instantons in eight dimensions

We present a simple compact formula for a topologically nontrivial map S7→Spin(7) associated with the fiber bundle Spin(7)→G2S7. The homotopy group π7[Spin(7)]=Z brings about the topologically nontrivial 8-dimensional gauge field configurations that belong to the algebra spin(7). The instantons are special such configurations that minimize the functional ∫Tr{F∧F∧⋆(F∧F)} and satisfy non-linear self-duality conditions, F∧F=±⋆(F∧F).Spin(7)⊂SO(8), and Spin(7) instantons represent simultaneously SO(8) instantons of a new type. The relevant homotopy is π7[SO(8)]=Z×Z, which implies the existence of two different topological charges. This also holds for all groups SO(4n) with integer n. We present explicit expressions for two topological charges and calculate their values for the conventional 4-dimensional and 8-dimensional instantons and also for the 8-dimensional instantons of the new type.Similar constructions for other algebras in different dimensions are briefly discussed.

A comment on instantons and their fermion zero modes in adjoint QCD_2

The adjoint 2-dimensional QCD with the gauge group SU(N)/Z_NSU(N)/ZN admits topologically nontrivial gauge field configurations associated with nontrivial \pi_1[SU(N)/Z_N] = Z_Nπ1[SU(N)/ZN]=ZN. The topological sectors are labelled by an integer k=0,\ldots, N-1k=0,…,N−1. However, in contrast to QED_2QED2 and QCD_4QCD4, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument [1] suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of k(N-k) zero mode doublets in the topological sector k. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the conjecture of Ref. [1]. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.

Visualization of center vortex structure

The centre vortex structure of the $SU(3)$ gauge field vacuum is explored through the use of novel visualisation techniques. The lattice is partitioned into 3D time slices, and vortices are identified by locating plaquettes with nontrivial centre phases. Vortices are illustrated by rendering vortex lines that pierce these nontrivial plaquettes. Nontrivial plaquettes with one dimension in the suppressed time direction are rendered by identifying the visible spatial link. These visualisations highlight the frequent presence of singular points and reveal an important role for branching points in $SU(3)$ gauge theory in creating high topological charge density regimes. Visualisations of the topological charge density are presented, and an investigation into the correlation between vortex structures and topological charge density is conducted. The results provide new insight into the mechanisms by which centre vortices generate nontrivial gauge field topology. This work demonstrates the utility of visualisations in conducting centre vortex studies, presenting new avenues with which to investigate this perspective of the QCD vacuum.

New type of string solutions with long range forces

We explore the formation and the evolution of the string network in the Abelian Higgs model with two complex scalar fields. A special feature of the model is that it possesses a global U(1) symmetry in addition to the U(1) gauge symmetry. Both symmetries are spontaneously broken by the vacuum expectation values of the two complex scalar fields. As we will show the dynamics of the string network is quite rich compared with that in the ordinary Abelian Higgs model with a single complex scalar field. In particular, we find a new type of string solutions in addition to the conventional Abrikosov-Nielsen-Olesen (local) string solution. We call this the uncompensated string. An isolated uncompensated string has a logarithmic divergent string tension as in the case of the global strings, although it is accompanied by a non-trivial gauge field configuration. We also perform classical lattice simulations in the 2 + 1 dimensional spacetime, which confirms the formation of the uncompensated strings at the phase transition. We also find that most of the uncompensated strings evolve into the local strings at later time when the gauge charge of the scalar field with a smaller vacuum expectation value is larger than that of the scalar field with a larger vacuum expectation value.

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.

Classifying solutions to Romans supergravity with a zero B-field

Expanding on previous papers, we continue studying Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. Using a set of differential constraints on a SU(2) structure, we look for further geometric solutions to such equations when we turn off the two-form potential B. We find that the six-dimensional space is described by a two-dimensional fibration over a four-dimensional manifold with a Kähler metric. We then classify these types of solutions.

The Different Regimes of Axion Gauge Field Inflation

In axion gauge field inflation an axion-like particle driving cosmic inflation is coupled to the Chern-Simons density of an Abelian or non-Abelian gauge group. In the case of a non-Abelian gauge group, this can lead to the formation of a stable, homogeneous and isotropic gauge field background. We study the dynamics of the inflaton and gauge fields in terms of the two effective coupling parameters: the gauge coupling and the axion decay constant. Starting from the Bunch-Davies vacuum in the far past, we find that the non-trivial gauge field background arises only significantly after the cosmic microwave background (CMB) scales have left the horizon. At these scales, the model thus closely resembles Abelian axion inflation, thereby naturally reconciling the tension of non-Abelian axion gauge field inflation with the latest CMB observations. We further consider two exemplary UV-completions of this setup: multiple Peccei-Quinn axions and axion monodromy in string theory. In both cases we find that the majority of the parameter space is excluded by theoretical or observational constraints. The remaining parameter space can be divided into three regimes. (i) For small gauge couplings we recover natural inflation. For large gauge couplings the non-Abelian gauge theory either (ii) mimics the Abelian theory or (iii) non-linear interactions prohibit a linear analysis of the gauge field perturbations.

Creating lattice gauge potentials in circuit QED: The bosonic Creutz ladder

In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The schemes consist of coupled transmons whose flux are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the fixed phase offset of each site on the complex coupling rate between coupled qubits. These configurations can be directly realised in a superconducting circuit and is easily extendable to a scalable lattice. Due to the intrinsic non-linearity of the transmon qubits such lattices would be an ideal platform for simulating Bose-Hubbard Hamiltonians with non-trivial gauge fields.

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.

Numerical Study of Nonperturbative Corrections to the Chiral Separation Effect in Quenched Finite-Density QCD.

We demonstrate the nonrenormalization of the chiral separation effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows us, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian fields inside instanton cores.

Room-temperature chiral charge pumping in Dirac semimetals

Chiral anomaly, a non-conservation of chiral charge pumped by the topological nontrivial gauge fields, has been predicted to exist in Weyl semimetals. However, until now, the experimental signature of this effect exclusively relies on the observation of negative longitudinal magnetoresistance at low temperatures. Here, we report the field-modulated chiral charge pumping process and valley diffusion in Cd3As2. Apart from the conventional negative magnetoresistance, we observe an unusual nonlocal response with negative field dependence up to room temperature, originating from the diffusion of valley polarization. Furthermore, a large magneto-optic Kerr effect generated by parallel electric and magnetic fields is detected. These new experimental approaches provide a quantitative analysis of the chiral anomaly phenomenon which was inaccessible previously. The ability to manipulate the valley polarization in topological semimetal at room temperature opens up a route towards understanding its fundamental properties and utilizing the chiral fermions.

Bosonic self-energy functional theory

We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean field theory when constraining to local fields, whereas when neglecting kinetic contributions of non-condensed bosons it reduces to the static mean-field approximation. To benchmark the theory we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase-boundaries, and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g. in the presence of non-trivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters, but nevertheless remain computable by modest means.