Gauge Structure Research Articles

Anomalies in Time-Ordered Products and Applications to the BV–BRST Formulation of Quantum Gauge Theories

We show that every (graded) derivation on the algebra of free quantum fields and their Wick powers in curved spacetimes gives rise to a set of anomalous Ward identities for time-ordered products, with an explicit formula for their classical limit. We study these identities for the Koszul-Tate and the full BRST differential in the BV-BRST formulation of perturbatively interacting quantum gauge theories, and clarify the relation to previous results. In particular, we show that the quantum BRST differential, the quantum antibracket and the higher-order anomalies form an $L_\infty$ algebra. The defining relations of this algebra ensure that the gauge structure is well-defined on cohomology classes of the quantum BRST operator, i.e., observables. Furthermore, we show that one can determine contact terms such that also the interacting time-ordered products of multiple interacting fields are well defined on cohomology classes. An important technical improvement over previous treatments is the fact that all our relations hold off-shell and are independent of the concrete form of the Lagrangian, including the case of open gauge algebras.

Kinetic mixing effect in noncommutative B \u2212 L gauge theory

It is well established that the SU(P)L gauge symmetry for P ≥ 3 can address the question of fermion generation number due to the anomaly cancellation, but it neither commutes nor closes algebraically with electric and baryon-minus-lepton charges. Hence, two U(1) factors that determine such charges are required, yielding a complete gauge symmetry, SU(P)L ⊗ U(1)X ⊗ U(1)N, apart from the color group. The resulting theory manifestly provides neutrino mass, dark matter, inflation, and baryon asymmetry of the universe. Furthermore, this gauge structure may present kinetic mixing effects associated to the U(1) gauge fields, which affect the electroweak precision test such as the ρ parameter and Z couplings as well as the new physics processes. We will construct the model, examine the interplay between the kinetic mixing and those due to the symmetry breaking, and obtain the physical results in detail.

Application of a New Method for Evaluating PDC Bit Anisotropy

Drill bit anisotropy denotes the difference in drilling ability of a bit in the axial and lateral directions, and is an important factor impacting directional drilling efficiency. Quantitative evaluation of PDC bit anisotropy is important for well trajectory control and PDC bit optimization. Based on the structural parameters of PDC bits such as inner cone depth, outer structure height, back-rake angle, and gauge structure, the quantitative evaluation model for determining PDC bit anisotropy is established and a method for solving the model coefficient is given. This model was applied to evaluate bit anisotropy of PDC bit A in the PY35—X well in the South China Sea. The results were used to optimize the design of a new PDC bit, B type. The PDC bit B was then used in the 2450-2850 m section of offset well HZ25—X, with the inclination angle being satisfactorily controlled in the range between 1.2 and 1.95°. Successful application of bit A in the offset well proves the validity of the evaluation model. The model of quantitative evaluation of PDC bit anisotropy helps to overcome the shortcomings of laboratory tests, like complicated test conditions and poor applicability. Basing on this model, the effect of structural parameters of PDC bits on the bit anisotropy index was discussed. It was shown that the bit anisotropy index increases as back rake angle, friction angle between the PDC bit and rock and bit size increase, and decreases as outer structure height, inner cone depth, and friction surface of the gauge increase. When drilling with a pendulum bottom hole assembly, it is recommended to use a PDC bit with high anisotropy index, which helps to minimize the tendency for the well to build angle due to strata deviating forces.

Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks.

We provide a framework for understanding the gapless Kitaev spin liquid (KSL) in the language of the tensor network (TN). Without introducing a Majorana fermion, most of the features of the KSL, including the symmetries, gauge structure, criticality, and vortex freeness, are explained in a compact TN representation. Our construction reveals a hidden string gas structure of the KSL. With only two variational parameters to adjust, we obtain an accurate KSL Ansatz with the bond dimension D=8 in a compact form, where the energy is about 0.007% higher than the exact one.

Gauge structures: From stabilizer codes to continuum models

Stabilizer codes are a powerful method for implementing fault-tolerant quantum memory and in the case of topological codes, they form useful models for topological phases of matter. In this paper, we discuss the theory of stabilizer codes as a discrete version of a linear gauge structure, a concept we introduce here. A linear gauge structure captures all the familiar ingredients of U(1) gauge theory including a generalization of charge conservation, Maxwell equations and topological terms. Using this connection, we prove some important results for stabilizer codes which can be used to characterize their error-correction properties. However, this perspective does not depend on any particular Hamiltonian or Lagrangian, which as a consequence is agnostic to the source of the gauge redundancy. Based upon the connection to stabilizer codes, we view the source of the gauge redundancy as an ambiguity in the tensor product structure of the Hilbert space. That is, the gauge provides a set of equivalent but arbitrary ways to factorize the Hilbert space. We apply this formalism to the d=2 and 3 toric code as well as the paradigm fracton models, X-Cube and Haah’s cubic code. From this perspective, we are able to map all these models to some continuum version which captures all or some of the fractonic and topological features of their parent discrete models.

Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice.

We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and, hence, the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric π-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We discuss possible experimental signatures and, in particular, present finite-temperature MonteCarlo calculations of the specific heat and the static vison structure factor. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model.

Gauge Structure of Teleparallel Gravity

During the conference Teleparallel Universes in Salamanca, we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 2019, 99, 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge theory for the translation group were put forward. This triggered a discussion about the arguments on which those criticisms were based, whose output is described in the present paper. The main conclusion is that to a great extent, those arguments are incorrect, and lack mathematical and physical support.

Quaternionic Formalism for Non-Abelian Gauge Theory of Dyons and Gravito-Dyons

Starting with the Quaternion formulation of SU (2 )× U (1)gauge theory of dyons and gravitodyons, it is shown that the formulation characterizes the abelian and non-Abelian gauge structure of dyons and gravito-dyons in terms of purely real and imaginary units of quaternion.

Quaternionic Formalism for Non-Abelian Gauge Theory of Dyons and Gravito-Dyons

Starting with the Quaternion formulation of SU (2 )× U (1)gauge theory of dyons and gravitodyons, it is shown that the formulation characterizes the abelian and non-Abelian gauge structure of dyons and gravito-dyons in terms of purely real and imaginary units of quaternion.

Higher Gauge Structures in Double and Exceptional Field Theory

AbstractWe review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite‐dimensional) Lie algebra and a choice of representation R. The embedding tensor is a map from the representation space R into satisfying a compatibility condition (‘quadratic constraint'). The Lie algebra structure on is transported to a Leibniz–Loday algebra on R, which in turn gives rise to an ‐structure. We review how the gauge structures of double and exceptional field theory fit into this framework.

Pre‐NQ Manifolds and Correspondence Spaces: the Nilmanifold Example

AbstractCourant algebroids correspond to degree‐2 symplectic differential graded manifolds or NQ‐manifolds for short. We review how a similar construction shows that locally the gauge structure of Double Field Theory corresponds to degree‐2 symplectic pre‐NQ manifolds. To illustrate first steps towards a global understanding of the pre‐NQ case, we apply the local constructions to 3‐dimensional nilmanifolds carrying an abelian gerbe. These are among prime examples where T‐duality is well‐understood and allow us to investigate classic results in the graded language.

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and N\'eel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are an incarnation of exotic states of matter, $i.e.$ the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, $N_f = 4$, our data suggests a continuous quantum phase transition between the VBS and N\'{e}el order. We also provide preliminary theoretical analysis for these quantum phase transitions.

Minimal gauge invariant and gauge fixed actions for massive higher-spin fields

Inspired by the rich structure of covariant string field theory, we propose a minimal gauge invariant action for general massive integer spin n field. The action consists of four totally symmetric tensor fields of order respectively n, n − 1, n − 2 and n − 3, and is invariant under the gauge transformation represented by two also totally symmetric fields of order n − 1 and n − 2. This action exactly has the same gauge structure as for the string field theory and we discuss general covariant gauge fixing procedure using the knowledge of string field theory. We explicitly construct the corresponding gauge fixed action for each of general covariant gauge fixing conditions.

Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points

We study a one-dimensional (1d) system that shows many analogies to proposed two-dimensional (2d) deconfined quantum critical points (DQCP). Our system is a translationally invariant spin-1/2 chain with on-site $Z_2 \times Z_2$ symmetry and time reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the $Z_2$ symmetries and the time reversal are broken, to a valence bond solid (VBS), where all on-site symmetries are restored while the translation symmetry is broken. The other $Z_2$ symmetry remains unbroken throughout, but its presence is crucial for both the direct transition (via specific Berry phase effect on topological defects, also related to a Lieb-Schultz-Mattis-like theorem) and the precise characterization of the VBS phase (which has crystalline-SPT-like property). The transition has a description in terms of either two domain wall species that "fractionalize" the VBS order parameter or in terms of partons that "fractionalize" the FM order parameter, with each picture having its own $Z_2$ gauge structure. The two descriptions are dual to each other and, at long wavelengths, take the form of a self-dual \emph{gauged} Ashkin-Teller model, reminiscent of the self-dual easy-plane non-compact CP$^1$ model that arises in the description of the 2d easy-plane DQCP. We also find an exact reformulation of the transition that leads to a simple field theory description that explicitly unifies the FM and VBS order parameters; this reformulation can be interpreted as a new parton approach that does not attempt to fractionalize either of the two order parameters but instead encodes them in instantons. Besides providing explicit realizations of many ideas proposed in the context of the 2d DQCP, here in the simpler and fully tractable 1d setting with continuous transition, our study also suggests possible new line of approach to the 2d DQCP.

L\u221e algebras and tensor hierarchies in Exceptional Field Theory and Gauged Supergravity

We show how the gauge and field structure of the tensor hierarchies in Double and E7(7) Exceptional Field Theory fits into L∞ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gauging-dependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.

Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation

A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general relativity and scale-invariant scalar-tensor and dilaton theories. Consequently, matter to be coupled to such theories is restricted to be conformal or scale invariant. Standard model-type systems naturally fall into this category. The new loop quantization follows from a novel conformally generalized Holst action principle. In contrast to standard loop quantum gravity, the resulting quantum geometry is not beset by the Immirzi ambiguity and has no definitive area gaps within the considered large class of theories of gravitation. As an additional feature, the scale invariance gives rise to a conserved Weyl current and we discuss briefly its possible implication on the problem of time in quantum gravity.

Properties and application of SO(3) Majorana representation of spin: Equivalence with Jordan-Wigner transformation and exact Z2 gauge theories for spin models

We explore the properties of the SO(3) Majorana representation of spin. Based on its nonlocal nature, it is shown that there is an equivalence between the SO(3) Majorana representation and the Jordan-Wigner transformation in one and two dimensions. From the relation between the SO(3) Majorana representation and one-dimensional Jordan-Wigner transformation, we show that application of the SO(3) Majorana representation usually results in ${Z}_{2}$ gauge structure. Based on lattice Chern-Simons gauge theory, it is shown that the anticommuting link variables in the SO(3) Majorana representation make it equivalent to an operator form of compact ${\text{U(1)}}_{1}$ Chern-Simons Jordan-Wigner transformation in 2D. As examples of its application, we discuss two spin models, namely the quantum XY model on a honeycomb lattice and the ${90}^{\ensuremath{\circ}}$ compass model on a square lattice. It is shown that under the SO(3) Majorana representation both spin models can be exactly mapped into ${Z}_{2}$ gauge theory of spinons, with the standard form of ${Z}_{2}$ Gauss law constraint.

Confronting SUSY GUT With Dark Matter, Sparticle Spectroscopy and Muon (g − 2)

We explore the implications of LHC and cold dark matter searches for supersymmetric particle mass spectra in two different grand unified models with left-right symmetry, $SO(10)$ and $ SU(4)_c \times SU(2)_L \times SU(2)_R$ (4-2-2). We identify characteristic differences between the two scenarios, which imply distinct correlations between experimental measurements and the particular structure of the GUT group. The gauge structure of 4-2-2 enhances significantly the allowed parameter space as compared to $SO(10)$, giving rise to a variety of coannihilation scenarios compatible with the LHC data, LSP dark matter and the ongoing muon g-2 experiment.

SU(2)L doublet vector dark matter from gauge-Higgs unification

A new vector dark matter (DM) scenario in the context of the gauge-Higgs unification (GHU) is proposed. The DM particle is identified with an electric-charge neutral component in an $SU(2)_L$ doublet vector field with the same quantum number as the Standard Model Higgs doublet. Since such an $SU(2)_L$ doublet vector field is incorporated in any models of the GHU scenario, it is always a primary and model-independent candidate for the DM in the scenario. The observed relic density is reproduced through a DM pair annihilations into the weak gauge bosons with a TeV-scale DM mass, which is nothing but the compactification scale of extra-dimensions. Due to the higher-dimensional gauge structure of the GHU scenario, a pair of the DM particles has no direct coupling with a single $Z$-boson/Higgs boson, so that the DM particle evades the severe constraint from the current direct DM search experiments.

Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4

Quantum spin liquids (QSLs) are exotic states of matter characterized by emergent gauge structures and fractionalized elementary excitations. The recently discovered triangular lattice antiferromagnet YbMgGaO4 is a promising QSL candidate, and the nature of its ground state is still under debate. Here we use neutron scattering to study the spin excitations in YbMgGaO4 under various magnetic fields. Our data reveal a dispersive spin excitation continuum with clear upper and lower excitation edges under a weak magnetic field (H = 2.5 T). Moreover, a spectral crossing emerges at the Γ point at the Zeeman-split energy. The corresponding redistribution of the spectral weight and its field-dependent evolution are consistent with the theoretical prediction based on the inter-band and intra-band spinon particle-hole excitations associated with the Zeeman-split spinon bands, implying the presence of fractionalized excitations and spinon Fermi surfaces in the partially magnetized QSL state in YbMgGaO4.