Nontrivial Vacuum Structure Research Articles

Extraordinary Nature of the Nucleon Scalar Charge and Its Densities as a Signal of Nontrivial Vacuum Structure of QCD

It is widely known that the nucleon scalar charge is proportional to the pion–nucleon sigma term as one of the important low-energy observables of QCD. Especially interesting to us is the physics of the nucleon scalar charge densities. This comes from the fact that the corresponding operator has the same quantum number as the physical vacuum. It indicates unusual behavior of the nucleon scalar density as a function of the distance r from the nucleon center. Namely, it would not be reduced down to zero at the spatial infinity but rather approach some nonzero constant corresponding to the vacuum quark condensate. Naturally, this unique nature of the nucleon scalar density in the position space also affects the corresponding density in the momentum space, i.e., the corresponding parton distribution function (PDF) as a function of the Bjorken variable x. This PDF is known as the chiral-odd twist-3 PDF e(x). We argue that e(x) is likely to have a delta-function-type singularity at x=0 and that the appearance of this singularity can be interpreted as a signal of the nontrivial vacuum structure of QCD.

Interpolating ’t Hooft model between instant and front forms

The 't Hooft model, i.e., the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter $\ensuremath{\delta}$ between $\ensuremath{\delta}=0$ for the instant form dynamics (IFD) and $\ensuremath{\delta}=\ensuremath{\pi}/4$ for the light-front dynamics (LFD). With this parameter $\ensuremath{\delta}$, we formulate the interpolating mass gap equation which takes into account the nontrivial vacuum effect on the bare fermion mass to find the dressed fermion mass. Our interpolating mass gap solutions not only reproduce the previous IFD result at $\ensuremath{\delta}=0$ as well as the previous LFD result at $\ensuremath{\delta}=\ensuremath{\pi}/4$ but also link them together between the IFD and LFD results with the $\ensuremath{\delta}$ parameter. We find the interpolation angle independent characteristic energy function which satisfies the energy-momentum dispersion relation of the dressed fermion, identifying the renormalized fermion mass function and the wave function renormalization factor. The renormalized fermion condensate is also found independent of $\ensuremath{\delta}$, indicating the persistence of the nontrivial vacuum structure even in the LFD. Using the dressed fermion propagator interpolating between IFD and LFD, we derive the corresponding quark-antiquark bound-state equation in the interpolating formulation verifying its agreement with the previous bound-state equations in the IFD and LFD at $\ensuremath{\delta}=0$ and $\ensuremath{\delta}=\ensuremath{\pi}/4$, respectively. The mass spectra of mesons bearing the feature of the Regge trajectories are found independent of the $\ensuremath{\delta}$-parameter reproducing the previous results in LFD and IFD for the equal mass quark and antiquark bound states. The Gell-Mann-Oakes-Renner relation for the pionic ground-state in the zero fermion mass limit is confirmed indicating that the spontaneous breaking of the chiral symmetry occurs in the 't Hooft model regardless of the quantization for $0\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}\ensuremath{\pi}/4$. We obtain the corresponding bound-state wave functions and discuss their reference frame dependence with respect to the frame independent LFD result. Applying them for the computation of the so-called quasi-parton distribution functions now in the interpolating formulation between IFD and LFD, we note a possibility of utilizing not only the reference frame dependence but also the interpolation angle dependence to get an alternative effective approach to the LFD-like results.

The emergence of electroweak Skyrmions through Higgs bosons

Skyrmions are extended field configurations, initially proposed to describe baryons as topological solitons in an effective field theory of mesons. We investigate and confirm the existence of skyrmions within the electroweak sector of the Standard Model and study their properties. We find that the interplay of the electroweak sector with a dynamical Higgs field and the Skyrme term leads to a non-trivial vacuum structure with the skyrmion and perturbative vacuum sectors separated by a finite energy barrier. We identify dimension-8 operators that stabilise the electroweak skyrmion as a spatially localised soliton field configuration with finite size. Such operators are induced generically by a wide class of UV models. To calculate the skyrmion energy and radius we use a neural network method. Electroweak skyrmions are non-topological solitons but are exponentially long lived, and we find that the electroweak skyrmion is a viable dark matter candidate. While the skyrmion production cross section at collider experiments is suppressed, measuring the size of the Skyrme term in multi-Higgs-production processes at high-energy colliders is a promising avenue to probe the existence of electroweak skyrmions.

Transitioning from equal-time to light-front quantization in ϕ24 theory

We use the interpolating coordinates studied by Hornbostel to investigate a transition from equal-time quantization to light-front quantization, in the context of two-dimensional $\phi^4$ theory. A consistent treatment is found to require careful consideration of vacuum bubbles, in a nonperturbative extension of the analysis by Collins. Numerical calculations of the spectrum at fixed box size are shown to yield results equivalent to those of equal-time quantization, except when the interpolating coordinates are pressed toward the light-front limit. In that regime, a fixed box size is inconsistent with an accurate representation of vacuum-bubble contributions and causes a spurious divergence in the spectrum. The light-front limit instead requires the continuum momentum-space limit of infinite box size. The calculation of the vacuum energy density is then shown to be independent of the interpolation parameter, which implies that the light-front limit yields the same spectrum as an equal-time calculation. This emphasizes the importance of zero modes and near-zero modes in a light-front analysis of any theory with nontrivial vacuum structure.

Dark fermions and spontaneous CP violation in SU(2)-axion inflation

Remarkably, if CP was spontaneously broken in the physics of inflation, fermions would notice and remember it. Based on that, we present a new (non-thermal) mechanism for generating self-interacting dark Dirac fermions prior to the Hot Big Bang. The non-Abelian gauge fields and axions are well-motivated matter contents for the particle physics of inflation. In this background, we analytical study Dirac fermion doublets charged under the SU(2) gauge field and use point-splitting technique to regularize the currents. We show that the non-trivial CP-violating vacuum structure of SU(2)-axion models naturally leads to an efficient mechanism for generating massive fermions during inflation. The size of the fermionic backreaction and the density fraction of dark fermions put upper bounds on the fermion’s mass. For a GUT scale inflation, the generated dark fermions, only gravitationally coupled to the visible sector, can be as heavy as m ≲ 10 TeV.

Large effects from small QCD instantons: making soft bombs at hadron colliders

It is a common belief that the last missing piece of the Standard Model of particles physics was found with the discovery of the Higgs boson at the Large Hadron Collider. However, there remains a major prediction of quantum tunnelling processes mediated by instanton solutions in the Yang-Mills theory, that is still untested in the Standard Model. The direct experimental observation of instanton-induced processes, which are a consequence of the non-trivial vacuum structure of the Standard Model and of quantum tunnelling in QFT, would be a major breakthrough in modern particle physics. In this paper, we present for the first time a full calculation of QCD instanton-induced processes in proton-proton collisions accounting for quantum corrections due to both initial and final state gluon interactions, a first implementation in an MC event generator as well as a basic strategy how to observe these effects experimentally.

Thermal Simulations, Open Boundary Conditions and Switches

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

Generalized generating functional for mixed-representation Green's functions: A quantum-mechanical approach

When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we propose a generalized generating functional for Green's functions which allows to easily distinguish among a continuous set of vacua that are mutually connected via unitary canonical transformations. In order to keep our discussion as simple as possible, we limit ourselves to Quantum Mechanics where the generating functional of Green's functions is constructed by means of phase-space path integrals. The quantum-mechanical setting allows to accentuate the main logical steps involved without embarking on technical complications such as renormalization or inequivalent representations that should otherwise be addressed in the full-fledged Quantum Field Theory. We illustrate the inner workings of the generating functional obtained by discussing Green's functions among vacua that are mutually connected via translations and dilatations. Salient issues, including connection with Quantum Field Theory, vacuum-to-vacuum transition amplitudes and perturbation expansion in the vacuum parameter are also briefly discussed.

Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions

A few non-perturbative topics of quantum field theory in $$\hbox {D}=1+1$$ are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.

Worm algorithm for the [formula omitted] model

The CPN−1 model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D CPN−1 on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice CPN−1 model for N>2 has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice CPN−1 model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular CPN−1 lattice actions and exhibit marked differences in their approach to the continuum limit.

Towards an emergent model of solitonic particles from non-trivial vacuum structure

We motivate and introduce what we refer to as the principles of Lie-stability and Hopf-stability and see what the physical theories must look like. Lie-stability is needed on the classical side and Hopf-stability is needed on the quantum side. We implement these two principles together with Lie-deformations consistent with basic constraints on the classical kinematical variables to arrive at the form of a theory that identifies standard model fermions with quantum solitonic trefoil knotted flux tubes which emerge from a flux tube vacuum network. Moreover, twisted unknot fluxtubes form natural dark matter candidates

The pseudo chiral magnetic effect in QED3

Chiral magnetic effect (CME) has been suggested to take place during peripheral relativistic heavy ion collisions. However, signals of its realization are not yet independent of ambiguities and thus probing the non-trivial topological vacua of quantum chromodynamics (QCD) is still an open issue. Weyl materials, particularly graphene, on the other hand, are effectively described at low energies by the degrees of freedom of quantum electrodynamics in two spatial dimensions, QED3. This theory shares with QCD some interesting features, like confinement and chiral symmetry breaking and also possesses a non-trivial vacuum structure. In this regard, an analog of the CME is proposed to take place in graphene under the influence of an in-plane magnetic field in which the pseudo-spin or flavor label of charge carriers is participant of the effect, rather than the actual spin. In this contribution, we review the parallelisms and differences between the CME and the so-called pseudo chiral magnetic effect, PCME.

Three-charge black holes and quarter BPS states in Little String Theory

We show that the system of $k$ NS5-branes wrapping $\mathbb{T}^4\times S^1$ has non-trivial vacuum structure. Different vacua have different spectra of 1/4 BPS states that carry momentum and winding around the $S^1$. In one vacuum, such states are described by black holes; in another, they can be thought of as perturbative BPS states in Double Scaled Little String Theory. In general, both kinds of states are present. We compute the degeneracy of perturbative BPS states exactly, and show that it differs from that of the corresponding black holes. We comment on the implication of our results to the black hole microstate program, UV/IR mixing in Little String Theory, string thermodynamics, the string/black hole transition, and other issues.

Topology and Dark Energy: Testing Gravity in Voids

Modified gravity has garnered interest as a backstop against dark matter and dark energy (DE). As one possible modification, the graviton can become massive, which introduces a new scalar field--here with a Galileon-type symmetry. The field can lead to a nontrivial equation of state of DE which is density and scale dependent. Tension between type Ia supernovae and Planck could be reduced. In voids, the scalar field dramatically alters the equation of state of DE, induces a soon-observable gravitational slip between the two metric potentials, and develops a topological defect (domain wall) due to a nontrivial vacuum structure for the field.

CONNECTING THE NONSINGULAR ORIGIN OF THE UNIVERSE, THE VACUUM STRUCTURE AND THE COSMOLOGICAL CONSTANT PROBLEM

We consider a nonsingular origin for the universe starting from an Einstein static universe, the so-called "emergent universe" scenario, in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field ϕ are considered in the action. The first-order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (SSB) of scale invariance (SI). After SSB of SI, it is found that a nontrivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and ϕ → -∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities produce a nontrivial vacuum structure for the theory and are responsible for the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in ϕ → -∞, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. The nontrivial vacuum structure is crucial to ensure the smooth transition from the emerging phase, to an inflationary phase and finally to the slowly accelerated universe now. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

Building a nest at tree level: Classical metastability and nontrivial vacuum structure in supersymmetric field theories

It is becoming increasingly clear that metastable vacua may play a prominent role in supersymmetry breaking. To date, however, this idea has been realized only in models where nonperturbative dynamics complicates the analysis of metastability. In this paper, we present a simple construction in which metastable vacua occur classically, i.e., at tree level, and in which supersymmetry breaking is sourced by both $D$ terms and $F$ terms. All relevant dynamics is perturbative, and hence calculations of vacuum energies and lifetimes can be performed explicitly. Moreover, we find that our construction can even give rise to multiple nonsupersymmetric vacua which are degenerate. The nontrivial vacuum structure of such models therefore suggests that they can provide a rich arena for future studies of vacuum metastability in supersymmetric field theories. Our results may also have important consequences for ${Z}^{\ensuremath{'}}$ phenomenology and the string landscape.

Lorentz-invariant ensembles of vector backgrounds

We consider gauge field theories in the presence of ensembles of vector backgrounds. While Lorentz invariance is explicitly broken in the presence of any single background, here, the Lorentz invariance of the theory is restored by averaging over a Lorentz-invariant ensemble of backgrounds, i.e., a set of background vectors that is mapped onto itself under Lorentz transformations. This framework is used to study the effects of a non-trivial but Lorentz-invariant vacuum structure or mass dimension two vector condensates by identifying the background with a shift of the gauge field. Up to now, the ensembles used in the literature comprise configurations corresponding to non-zero field tensors together with such with vanishing field strength. We find that even when constraining the ensembles to pure gauge configurations, the usual high-energy degrees of freedom are removed from the spectrum of asymptotic states in the presence of said backgrounds in Euclidean and in Minkowski space. We establish this result not only for the propagators to all orders in the background and otherwise at tree level but for the full propagator.

Adjoint QCD1 + 1 in light-cone gauge, quantized at equal time

SU(2) gauge theory coupled to massless fermions in the adjoint representation is quantized in light-cone gauge by imposing the equal-time canonical algebra. The theory is defined on a space-time cylinder with “twisted” boundary conditions, periodic for one color component (the diagonal 3-component) and antiperiodic for the other two. The focus of the study is on the non-trivial vacuum structure and the fermion condensate. It is shown that the indefinite-metric quantization of free gauge bosons is not compatible with the residual gauge symmetry of the interacting theory. A suitable quantization of the unphysical modes of the gauge field is necessary in order to guarantee the consistency of the subsidiary condition and allow the quantum representation of the residual gauge symmetry of the classical Lagrangian: the 3-color component of the gauge field must be quantized in a space with an indefinite metric while the other two components require a positive-definite metric. The contribution of the latter to the free Hamiltonian becomes highly pathological in this representation, but a larger portion of the interacting Hamiltonian can be diagonalized, thus allowing perturbative calculations to be performed. The vacuum is evaluated through second order in perturbation theory and this result is used for an approximate determination of the fermion condensate.

Topology in the little Higgs models

We investigate the implications of the nontrivial vacuum structure of little Higgs models. In particular, focusing on the littlest Higgs model, we demonstrate the existence of three types of topological defects. One is a global cosmic string that is truly topological. The second is more subtle; a semilocal cosmic string, which may be stable due to dynamical effects. The final defect is a $Z_2$ monopole solution with an unusual structure. We briefly discuss the possible cosmological consequences of such nonperturbative structures, although we note that these depend crucially on the fermionic content of the models.

Nonperturbative origin of the delta-function singularity in the chirally odd twist-3 distribution functione(x)

We analytically prove that the existence of the delta-function singularity in the chirally-odd twist-3 distribution $e(x)$ of the nucleon is inseparably connected with the nonvanishing quark condensate as a signal of the spontaneous chiral symmetry breaking of the QCD vacuum. This singularity in $e(x)$, which would be observed as a sizable violation of the 1st moment sum rule, is then interpreted as giving a very rare case that the nontrivial vacuum structure of QCD manifests in an observable of a localized QCD excitation, i.e. the nucleon.