non-Abelian Fields Research Articles

Multiple Scattering with fully coherent scattering in pA and AA collisions

A new energy loss mechanism model is presented. Medium multiple scattering is modified by the interaction with a classical non-abelian background field. It is shown that the obtained gluon radiation spectrum has a symmetric structure in x (the outgoing radiation energy over incident parton energy) and (1 − x) and the appropriate sign.

Topological Nonsymmorphic Metals from Band Inversion

We introduce the notion of a band-inverted, topological semimetal in two-dimensional nonsymmorphic crystals. This notion is materialized in the monolayers of MTe$_2$ (M $=$ W, Mo) if spin-orbit coupling is neglected. We characterize the Dirac band touching topologically by the Wilson loop of the non-Abelian Berry gauge field. An additional feature of the Dirac cone in monolayer MTe$_2$ is that it tilts over in a Lifshitz transition to produce electron and hole pockets, a type-II Dirac cone. These pockets, together with the pseudospin structure of the Dirac electrons, suggest a unified, topological explanation for the recently-reported, non-saturating magnetoresistance in WTe$_2$, as well as its circular dichroism in photoemission. We complement our analysis and first-principle bandstructure calculations with an $\textit{ab-initio}$-derived-derived tight-binding model for the WTe$_2$ monolayer.

Free energy for a damped cold atom in SU(2) non-Abelian gauge potentials

Our main aim in this work is to find out the exact formula of the equilibrium free energy for a cold atom subjected to a harmonic potential in the background of an artificial non-Abelian uniform magnetic field and linearly coupled to a heat bath. The heat bath consists of a collection of independent quantum harmonic oscillators, while its interaction with the cold atom is modeled in terms of bilinear coupling between the coordinate variables of the cold atom and the oscillators. The main thermodynamic properties of such a system are modified in comparison with the Abelian case. For a non-Abelian magnetic field generated from the laser methods employing degenerate dark states, we evaluate the effect of the non-Abelian dynamics on the magnetic moment of the cold atom.

Non-Abelian bubbles in microstate geometries

We find the first smooth microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of $\mathcal{N}=1$, $d=5$ Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.

The Gribov problem in presence of background field for SU(2) Yang–Mills theory

The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.

Local subsystems in gauge theory and gravity

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.

Vortex states in a non-Abelian magnetic field

A type-II superconductor survives in an external magnetic field by admitting an Abrikosov lattice of quantized vortices. This is an imprint of the Aharonov-Bohm effect created by the Abelian U(1) gauge field. The simplest non-Abelian analogue of such a gauge field, which belongs to the SU(2) symmetry group, can be found in topological insulators. Here we discover a superconducting ground state with a lattice of SU(2) vortices in a simple two-dimensional model that presents an SU(2) "magnetic" field (invariant under time-reversal) to attractively interacting fermions. The model directly captures the correlated topological insulator quantum well, and approximates one channel for instabilities on the Kondo topological insulator surface. Due to its simplicity, the model might become amenable to cold atom simulations in the foreseeable future. The vitality of low-energy vortex states born out of SU(2) "magnetic" fields is promising for the creation of incompressible vortex liquids with non-Abelian fractional excitations.

Large field excursions from a few site relaxion model

Relaxion models are an interesting new avenue to explain the radiative stability of the Standard Model scalar sector. They require very large field excursions, which are difficult to generate in a consistent UV completion and to reconcile with the compact field space of the relaxion. We propose an $N$-site model which naturally generates the large decay constant needed to address these issues. Our model offers distinct advantages with respect to previous proposals: the construction involves non-Abelian fields, allowing for controlled high-energy behavior and more model building possibilities, both in particle physics and inflationary models, and also admits a continuum limit when the number of sites is large, which may be interpreted as a warped extra dimension.

Towards a fully stringy computation of Yukawa couplings on non-factorized tori and non-abelian twist correlators (I): The classical solution and action

We consider the simplest possible setting of non-abelian twist fields which corresponds to SU(2) monodromies. We first review the theory of hypergeometric function and of the solutions of the most general Fuchsian second order equation with three singularities. Then we solve the problem of writing the general solution with prescribed U(2) monodromies. We use this result to compute the classical string solution corresponding to three D2 branes in R4. Despite the fact that the configuration is supersymmetric the classical string solution is not holomorphic. Using the equation of motion and not the KLT approach we give a very simple expression for the classical action of the string. We find that the classical action is not proportional to the area of the triangle determined by the branes intersection points since the solution is not holomorphic. Phenomenologically this means that the Yukawa couplings for these supersymmetric configurations on non-factorized tori are suppressed with respect to the factorized case.

An explicit quasiplatonic curve with non-abelian moduli field

We give an example of a regular dessin d'enfant whose field of moduli is not an abelian extension of the rational numbers, namely it is the field generated by a cubic root of 2. This answers a previous question. We also prove that the underlying curve has non-abelian field of moduli itself, giving an explicit example of a quasiplatonic curve with non-abelian field of moduli. In the last section, we note that two examples in previous literature can be used to find other examples of regular dessins d'enfants with non-abelian field of moduli.

Duality and ‘particle’ democracy

Weak/strong duality is usually accompanied by what seems a puzzling ontological feature: the fact that under this kind of duality what is viewed as ‘elementary’ in one description gets mapped to what is viewed as ‘composite’ in the dual description. This paper investigates the meaning of this apparent ‘particle democracy’, as it has been called, by adopting an historical approach. The aim is to clarify the nature of the correspondence between ‘dual particles’ in the light of a historical analysis of the developments of the idea of weak/strong duality, starting with Dirac׳s electric-magnetic duality and its successive generalizations in the context of (Abelian and non-Abelian) field theory, to arrive at its first extension to string theory. This analysis is then used as evidential basis for discussing the ‘elementary/composite’ divide and, after taking another historical detour by analyzing an instructive analogy case (DHS duality and related nuclear democracy), drawing some conclusions on the particle-democracy issue.

Gauge invariant method for maximum simplification of the field strength in non-Abelian Yang–Mills theories

A new local gauge invariant method is introduced in order to maximally simplify the expression for a SU(2) non-Abelian field strength. The new tetrads introduced in previous works are going to play a fundamental role in the algorithm presented in this paper. Three new local gauge invariant objects are going to guide us through the process of making a field strength block diagonal. The process is also covariant. Any nontrivial isospace field strength projection will become block diagonal through this gauge invariant algorithm. As an application we will find new local observables in Yang–Mills theories.

Energy problem in the Einstein–Cartan theory

The Einstein–Cartan–Kibble–Sciama equations are presented in the following form: the codifferential of the differential of a tetrad is the tetrad current with the ordinary conservation law. This form is an analogue of the form for non-Abelian quantum field theory. A canonical gauge tetrad is proposed for six two-directions with extreme sectional Riemannian curvature. A nonlocal conservation law for the contracted Bianchi identities is presented. The physical and geometric meaning of the Gibbons-Hawking Lagrangian and surface term are proposed. Application of the tetrad current concept is illustrated for the Schwarzschild and de Sitter metrics.

Time-dependent non-Abelian Aharonov-Bohm effect

In this article, we study the time-dependent Aharonov-Bohm effect for non-Abelian gauge fields. We use two well known time-dependent solutions to the Yang-Mills field equations to investigate the Aharonov-Bohm phase shift. For both of the solutions, we find a cancellation between the phase shift coming from the non-Abelian "magnetic" field and the phase shift coming from the non-Abelian "electric" field, which inevitably arises in time-dependent cases. We compare and contrast this cancellation for the time-dependent non-Abelian case to a similar cancellation which occurs in the time-dependent Abelian case. We postulate that this cancellation occurs generally in time-dependent situations for both Abelian and non-Abelian fields.

Strongly correlated states of trapped ultracold fermions in deformed Landau levels

We analyze the strongly correlated regime of a two-component trapped ultracold fermionic gas in a synthetic non-Abelian U(2) gauge potential, that consists of both a magnetic field and a homogeneous spin-orbit coupling. This gauge potential deforms the Landau levels (LLs) with respect to the Abelian case and exchanges their ordering as a function of the spin-orbit coupling. In view of experimental realizations, we show that a harmonic potential combined with a Zeeman term, gives rise to an angular momentum term, which can be used to test the stability of the correlated states obtained through interactions. We derive the Haldane pseudopotentials (HPs) describing the interspecies contact interaction within a lowest LL approximation. Unlike ordinary fractional quantum Hall systems and ultracold bosons with short-range interactions in the same gauge potential, the HPs for sufficiently strong non-Abelian fields show an unconventional non-monotonic behaviour in the relative angular momentum. Exploiting this property, we study the occurrence of new incompressible ground states as a function of the total angular momentum. In the first deformed Landau level (DLL) we obtain Laughlin and Jain states. Instead, in the second DLL three classes of stabilized states appear: Laughlin states, a series of intermediate strongly correlated states and finally vortices of the integer quantum Hall state. Remarkably, in the intermediate regime, the non-monotonic HPs of the second DLL induce two-particle correlations which are reminiscent of paired states such as the Haffnian state. Via exact diagonalization in the disk geometry, we compute experimentally relevant observables such as density profiles and correlations, and we study the entanglement spectra as a further tool to characterize the obtained strongly correlated states.

Supersymmetry: Early Roots That Did Not Grow

This paper is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of “partners” in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincaré group, were not known. There were, of course, no supersymmetric nonabelian quantum field theories in those days.

Non-Abelian fields inAdS4spacetime: Axially symmetric, composite configurations

We construct new finite energy regular solutions in Einstein-Yang-Mills-SU(2) theory. They are static, axially symmetric and approach at infinity the anti-de Sitter spacetime background. These configurations are characterized by a pair of integers $(m, n)$, where $m$ is related to the polar angle and $n$ to the azimuthal angle, being related to the known flat space monopole-antimonopole chains and vortex rings. Generically, they describe composite configurations with several individual components, possesing a nonzero magnetic charge, even in the absence of a Higgs field. Such Yang-Mills configurations exist already in the probe limit, the AdS geometry supplying the attractive force needed to balance the repulsive force of Yang-Mills gauge interactions. The gravitating solutions are constructed by numerically solving the elliptic Einstein-DeTurck--Yang-Mills equations. The variation of the gravitational coupling constant $\alpha$ reveals the existence of two branches of gravitating solutions which bifurcate at some critical value of $\alpha$. The lower energy branch connects to the solutions in the global AdS spacetime, while the upper branch is linked to the generalized Bartnik-McKinnon solutions in asymptotically flat spacetime. Also, a spherically symmetric, closed form solution is found as a perturbation around the globally anti-de Sitter vacuum state.

The supersymmetric Wong equations and the non-abelian Landau problem

A Lagrangian formulation is given extending to supersymmetry, or the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge potential. As an illustration, a specific gauge is fixed, enabling canonical quantization and the study of the supersymmetric non-abelian Landau problem. The spectrum of the quantum Hamiltonian operator follows in accordance with the supersymmetric structure.

Finite BRST–antiBRST transformations in Lagrangian formalism

We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λa, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λa. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λa=saΛ, induced by a finite even-valued functional Λ(ϕ,π,λ) and by the generators sa of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕa⁎,ϕ¯ and auxiliary variables πa,λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λa, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.

Pair creation by an external non-Abelian field

The problem of the creation of particle pairs of spin 0 and 1/2 from the vacuum by an external field of a non-Abelian type plane wave on the light cone is considered following the approach of Schwinger. Using simple shifts and only by an algebraic calculation, it is shown that with this form of interaction, there is no creation of particles.