Massless Bosonic Fields Research Articles

Absence of ground states in the renormalized massless translation-invariant Nelson model

We consider a model for a massive uncharged non-relativistic particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known that an ultraviolet renormalized Hamilton operator exists in this case. Further, due to translation-invariance, it decomposes into fiber operators. In this paper, we treat the renormalized fiber operators. We give a description of the operator and form domains and prove that the fiber operators do not have a ground state. Our results hold for any non-zero coupling constant and arbitrary total momentum. Our proof for the absence of ground states is a new generalization of methods recently applied to related models. A major enhancement we provide is that the method can be applied to models with degenerate ground state eigenspaces.

Open F-branes

We include in F-theory, through open Type I F-theory branes (F-branes), string theories with N = 1 supersymmetry, both Type I and heterotic. Type I branes are distinguished from Type II by worldvolume parity projection. The same open Type I branes describe both open Type I superstrings and closed heterotic upon different sectionings from F-branes to worldsheets, while closed Type I superstrings arise from closed Type I branes. (Type II superstrings come from closed Type II branes, as described previously.)F-theory manifests the exceptional-group U-duality symmetry, with all massless bosonic fields in a single gauge coset. This coset branches to the usual bosonic supergravity fields upon sectioning. We examine in detail the simple case of D = 3 F-theory: parity projection reduces the Type II coset SL(5)/SO(3,2) to the Type I coset SO(3,3)/SO(2,1)2 = SL(4)/SO(2,2).

Unification of massless field equations solutions for any spin

A unification in terms of exact solutions for massless Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, Einstein, and bosonic and fermionic fields of any spin is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre-potential functions, which satisfy the d'Alembert equation. The coupled equations satisfied by the pre-potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre-potentials that satisfy the usual wave equation which may be used to construct exact non-trivial solutions to Klein-Gordon, Dirac, Maxwell, Rarita-Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field equations, thus giving rise to a unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre-potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

Supersymmetry, T-duality and heterotic \u03b1\u2032-corrections

Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional mathcal{N} = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

Massless higher spin cubic vertices in flat four dimensional space

In this paper we construct a number of cubic interaction vertices for massless bosonic and fermionic higher spin fields in flat four dimensional space. First of all, we construct these cubic vertices in AdS4 space using a so-called Fradkin-Vasiliev approach, which works only for the non-zero cosmological constant. Then we consider a flat limit taking care on all the higher derivative terms which FV-approach generates. We restrict ourselves with the four dimensions because this allows us to use the frame-like multispinor formalism which greatly simplifies all calculations and provides a description for bosons and fermions on equal footing.

Scattering of massless bosonic fields by Kerr black holes: On-axis incidence

We study the scattering of monochromatic bosonic plane waves impinging upon a rotating black hole, in the special case that the direction of incidence is aligned with the spin axis. We present accurate numerical results for electromagnetic Kerr scattering cross sections for the first time, and give a unified picture of the Kerr scattering for all massless bosonic fields.

Vertex Constraints in 3D Higher Spin Theories.

We analyze the constraints imposed by gauge invariance on higher-order interactions between massless bosonic fields in three-dimensional higher-spin gravities. Focusing on the transverse-traceless part, we show that vertices of quartic and higher order that are independent of the cubic ones can only involve scalars and Maxwell fields. As a consequence, the full nonlinear interactions of massless higher-spin fields are completely fixed by the cubic vertex.

Lagrangian description of the partially massless higher spin N = 1 supermultiplets in AdS4 space

In the recent paper [1] the classification of non-unitary representations of the three dimensional superconformal group has been constructed. From AdS/CFT they must correspond to N = 1 supermultiplets containing partially massless fields in AdS4. Moreover, the simplest example of such supermultiplets which contains a partially massless spin-2 was explicitly constructed. In this paper we extend this result and develop explicit Lagrangian construction of general N = 1 supermultiplets containing partially massless fields with arbitrary superspin. We use the frame-like gauge invariant description of partially massless higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two partially massless bosonic and two partially massless fermionic fields we derive the supertransformations leaving the sum of their free Lagrangians invariant such that the AdS4 superalgebra is closed on-shell.

Lagrangian formulation for the infinite spin N = 1 supermultiplets in d = 4

We provide an explicit Lagrangian construction for the massless infinite spin N=1 supermultiplet in four dimensional Minkowski space. Such a supermultiplet contains a pair of massless bosonic and a pair of massless fermionic infinite spin fields with properly adjusted dimensionful parameters. We begin with the gauge invariant Lagrangians for such massless infinite spin bosonic and fermionic fields and derive the supertransformations which leave the sum of their Lagrangians invariant. It is shown that the algebra of these supertransformations is closed on-shell.

Cubic interactions of massless bosonic fields in three dimensions. II. Parity-odd and Chern-Simons vertices

This work completes the classification of the cubic vertices for arbitrary spin massless bosons in three dimensions started in a previous companion paper by constructing parity-odd vertices. Similarly to the parity-even case, there is a unique parity-odd vertex for any given triple $s_1\geq s_2\geq s_3\geq 2$ of massless bosons if the triangle inequalities are satisfied ($s_1<s_2+s_3$) and none otherwise. These vertices involve two (three) derivatives for odd (even) values of the sum $s_1+s_2+s_3$. A non-trivial relation between parity-even and parity-odd vertices is found. Similarly to the parity-even case, the scalar and Maxwell matter can couple to higher spins through current couplings with higher derivatives. We comment on possible lessons for 2d CFT. We also derive both parity-even and parity-odd vertices with Chern-Simons fields and comment on the analogous classification in two dimensions.

Cubic Interactions of Massless Bosonic Fields in Three Dimensions.

In this Letter, we take the first step towards construction of nontrivial Lagrangian theories of higher-spin gravity in a metriclike formulation in three dimensions. The crucial feature of a metriclike formulation is that it is known how to incorporate matter interactions into the description. We derive a complete classification of cubic interactions for arbitrary triples s_{1}, s_{2}, s_{3} of massless fields, which are the building blocks of any interacting theory with massless higher spins. We find that there is, at most, one vertex for any given triple of spins in 3D (with one exception, s_{1}=s_{2}=s_{3}=1, which allows for two vertices). Remarkably, there are no vertices for spin values that do not respect strict triangle inequalities and contain at least two spins greater than one. This translates into selection rules for three-point functions of higher-spin conserved currents in two dimensional conformal field theory. Furthermore, universal coupling to gravity for any spin is derived. Last, we argue that this classification persists in arbitrary Einstein backgrounds.

Continuous spin fields of mixed-symmetry type

We propose a description of continuous spin massless fields of mixed-symmetry type in Minkowski space at the level of equations of motion. It is based on the appropriately modified version of the constrained system originally used to describe massless bosonic fields of mixed-symmetry type. The description is shown to produce generalized versions of triplet, metric-like, and light-cone formulations. In particular, for scalar continuous spin fields we reproduce the Bekaert-Mourad formulation and the Schuster-Toro formulation. Because a continuous spin system inevitably involves infinite number of fields, specification of the allowed class of field configurations becomes a part of its definition. We show that the naive choice leads to an empty system and propose a suitable class resulting in the correct degrees of freedom. We also demonstrate that the gauge symmetries present in the formulation are all Stueckelberg-like so that the continuous spin system is not a genuine gauge theory.

Emergence of Supersymmetric Quantum Electrodynamics.

Supersymmetric (SUSY) gauge theories such as the minimal supersymmetric standard model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator hosting three Dirac cones, such as the topological Kondo insulator SmB_{6}. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric XYZ model, which is dual by mirror symmetry to N=2 supersymmetric quantum electrodynamics in 2+1 dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point exactly, which may be measured in future experiments.

Relative entanglement entropies in 1 + 1-dimensional conformal field theories

We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(ρ1∥ρ0) between two given reduced density matrices ρ1 and ρ0 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(ρ1ρ0n − 1) and define a set of Rényi relative entropies Sn(ρ1∥ρ0). We compute these quantities for integer values of the parameter n and derive via the replica limit the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i∂ϕ, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement.

Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

One of the fundamental principles of statistical physics is that only partial information about a system's state is required for its macroscopic description. This is not only true for thermal ensembles, but also for the unconventional ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to describe the relaxation of integrable systems after a quantum quench. By analytically studying the quench dynamics in a prototypical one-dimensional critical model, the massless free bosonic field theory, we find evidence of a novel type of equilibration characterized by the preservation of an enormous amount of memory of the initial state that is accessible by local measurements. In particular, we show that the equilibration retains memory of non-Gaussian initial correlations, in contrast to the case of massive free evolution which erases all such memory. The GGE in its standard form, being a Gaussian ensemble, fails to predict correctly the equilibrium values of local observables, unless the initial state is Gaussian itself. Our findings show that the equilibration of a broad class of quenches whose evolution is described by Luttinger liquid theory with an initial state that is non-Gaussian in terms of the bosonic field, is not correctly captured by the corresponding bosonic GGE, raising doubts about the validity of the latter in general one-dimensional gapless integrable systems such as the Lieb-Liniger model. We also propose that the same experiment by which the GGE was recently observed [Langen et al., Science 348 (2015) 207-211] can also be used to observe its failure, simply by starting from a non-Gaussian initial state.

3d N = 1 $$ \mathcal{N}=1 $$ effective supergravity and F-theory from M-theory on fourfolds

We consider 3d N=1 M-theory compactifications on Calabi-Yau fourfolds, and the effective 3d theory of light modes obtained by reduction from eleven dimensions. We study in detail the mass spectrum at the vacuum and, by decoupling the massive multiplets, we derive the effective 3d N=1 theory in the large-volume limit up to quartic fermion terms. We show that in general it is an ungauged N=1 supergravity of the form expected from 3d supersymmetry. In particular the massless bosonic fields consist of the volume modulus and the axions originating from the eleven-dimensional three-form, while the moduli-space metric is locally isometric to hyperbolic space. We consider the F-theory interpretation of the 3d N=1 M-theory vacua in the light of the F-theory effective action approach. We show that these vacua generally have F-theory duals with circle fluxes, thus breaking 4d Poincar\'e invariance.

Nonequilibrium transport through quantum-wire junctions and boundary defects for free massless bosonic fields

We consider a model of quantum-wire junctions where the latter are described by conformal-invariant boundary conditions of the simplest type in the multicomponent compactified massless scalar free field theory representing the bosonized Luttinger liquids in the bulk of wires. The boundary conditions result in the scattering of charges across the junction with nontrivial reflection and transmission amplitudes. The equilibrium state of such a system, corresponding to inverse temperature β and electric potential V, is explicitly constructed both for finite and for semi-infinite wires. In the latter case, a stationary nonequilibrium state describing the wires kept at different temperatures and potentials may be also constructed. The main result of the present paper is the calculation of the full counting statistics (FCS) of the charge and energy transfers through the junction in a nonequilibrium situation. Explicit expressions are worked out for the generating function of FCS and its large-deviations asymptotics. For the purely transmitting case they coincide with those obtained in the literature, but numerous cases of junctions with transmission and reflection are also covered. The large deviations rate function of FCS for charge and energy transfers is shown to satisfy the fluctuation relations and the expressions for FCS obtained here are compared with the Levitov–Lesovik formulae.

Travelling waves in expanding spatially homogeneous space–times

Some classes of the so-called ‘travelling wave’ solutions of Einstein and Einstein–Maxwell equations in general relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are presented. Similarly to the well known plane-fronted waves with parallel rays (pp-waves), these travelling wave solutions may depend on arbitrary functions of a null coordinate which determine the arbitrary profiles and polarizations of the waves. However, in contrast with pp-waves, these waves do not admit the null Killing vector fields and can exist in some curved (expanding and spatially homogeneous) background space–times, where these waves propagate in certain directions without any scattering. Mathematically, some of these classes of solutions arise as the fixed points of Kramer–Neugebauer transformations for hyperbolic integrable reductions of the above mentioned field equations or, in other cases, after imposing the ansatz that these waves do not change the part of the spatial metric transverse to the direction of wave propagation. It is worth noting that the strikingly simple forms of all the solutions presented prospectively make possible the consideration of the nonlinear interaction of these waves with the background curvature and singularities, as well as the collision of such wave pulses with solitons or with each other in the backgrounds where such travelling waves may exist.

Towards holographic higher-spin interactions: four-point functions and higher-spin exchange

Within holography, we calculate the contribution of an arbitrary spin-s gauge boson exchange in AdS d+1 to the four-point function with scalar operators on the boundary. As an important ingredient, we first compute the complete bulk-to-bulk propagators for massless bosonic higher-spin fields in the metric-like formulation, in any dimension and in various gauges. The split representation of the bulk-to-bulk propagators in terms of bulk-to-boundary propagators allows to present the higher-spin exchange diagram in the form of a conformal partial wave expansion. Our results provide a step towards the larger goal of the holographic reconstruction of bulk interactions, and of clarifying bulk locality.

Massless Asymptotic Fields and Haag–Ruelle Theory

We revisit the problem of the existence of asymptotic massless boson fields in quantum field theory. The well-known construction of such fields by Buchholz (Commun. Math. Phys. 52:147–173, 1977; Commun. Math. Phys. 85:49–71, 1982) is based on locality and the existence of vacuum vector, at least in regions spacelike to spacelike cones. Our analysis does not depend on these assumptions and supplies a more general framework for fields only very weakly decaying in spacelike directions. In this setting, the existence of appropriate null asymptotes of fields is linked with their spectral properties in the neighborhood of the lightcone. The main technical tool is one of the results of a recent analysis by one of us (Herdegen in Lett. Math. Phys. 104:1263–1280. doi: 10.1007/s11005-014-0710-5 , 2014), which allows application of the null asymptotic limit separately to creation/annihilation parts of a wide class of nonlocal fields. In vacuum representation the scheme allows application of the methods of the Haag–Ruelle theory closely analogous to those of the massive case. In local case this Haag–Ruelle procedure may be combined with the Buchholz method, which leads to significant simplification.