Nontrivial Vacuum 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.

Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and F(R,T,Q,Tm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(R,T,Q,T_{m})$$\\end{document} gravity

We extend the anholonomic frame and connection deformation method, AFCDM, for constructing exact and parametric solutions in general relativity, GR, to geometric flow models and modified gravity theories, MGTs, with nontrivial torsion and nonmetricity fields. Following abstract geometric or variational methods, we can derive corresponding systems of nonmetric gravitational and matter field equations which consist of very sophisticate systems of coupled nonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and applying the AFCDM, we prove that such systems of PDEs can be decoupled and integrated in general forms for generic off-diagonal metric structures and generalized affine connections. We generate new classes of quasi-stationary solutions (which do not depend on time like coordinates) and study the physical properties of some physically important examples. Such exact or parametric solutions are determined by nonmetric solitonic distributions and/or ellipsoidal deformations of wormhole hole configurations. It is not possible to describe the thermodynamic properties of such solutions in the framework of the Bekenstein–Hawking paradigm because such metrics do not involve, in general, certain horizons, duality, or holographic configurations. Nevertheless, we can always elaborate on associated Grigori Perelman thermodynamic models elaborated for nonmetric geometric flows. In explicit form, applying the AFCDM, we construct and study the physical implications of new classes of traversable wormhole solutions describing solitonic deformation and dissipation of non-Riemannian geometric objects. Such models with nontrivial gravitational off-diagonal vacuum are important for elaborating models of dark energy and dark matter involving wormhole configurations and solitonic-type structure formation.

Mean-Field Phase Transitions in Tensorial Group Field Theory Quantum Gravity.

Controlling the continuum limit and extracting effective gravitational physics are shared challenges for quantum gravity approaches based on quantum discrete structures. The description of quantum gravity in terms of tensorial group field theory (TGFT) has recently led to much progress in its application to phenomenology, in particular, cosmology. This application relies on the assumption of a phase transition to a nontrivial vacuum (condensate) state describable by mean-field theory, an assumption that is difficult to corroborate by a full RG flow analysis due to the complexity of the relevant TGFT models. Here, we demonstrate that this assumption is justified due to the specific ingredients of realistic quantum geometric TGFT models: combinatorially nonlocal interactions, matter degrees of freedom, and Lorentz group data, together with the encoding of microcausality. This greatly strengthens the evidence for the existence of a meaningful continuum gravitational regime in group-field and spin-foam quantum gravity, the phenomenology of which is amenable to explicit computations in a mean-field approximation.

Gravitational Coleman-Weinberg mechanism

The Coleman-Weinberg mechanism provides a procedure by which a scalar field, which initially has no mass parameters, acquires a mass due to the anomalous nature of scale symmetry. Loop corrections trigger a spontaneous symmetry breaking and the appearance of a non-trivial vacuum. We first review the basic example of the Coleman-Weinberg mechanism, scalar Quantum Electrodynamics, in a perturbative regime where the scalar particle becomes massive through photon loops. We then present the main results of this article, what we name the gravitational Coleman-Weinberg mechanism: we analyse the same effect in a gravitational theory without explicit energy scales at tree-level. Finally, we also study the mechanism for two scalar fields in the mentioned gravitational theory. We will derive the gravitational Coleman-Weinberg potentials, analyse the parameter space where we have a symmetry breaking, and obtain the value of the corresponding scalar masses.

Wave correlations and quantum noise in cosmology

Wave noise is correlated. While it may look random in space, correlations appear in space–time, because the noise is carried by wave propagation. These correlations of wave noise give rise to fluctuation forces such as the Casimir force, they are responsible for the particle creation in the dynamical Casimir effect and in the expanding Universe. This paper considers the noise correlations for light waves in non-exponentially expanding flat space. The paper determines the high-frequency asymptotics of the correlation spectrum in the conformal vacuum. These noise correlations give rise to a nontrivial vacuum energy that may appear as the cosmological constant.

A comment on loop corrections to the celestial stress tensor

In this note we show how the 1-loop exact correction to the subleading soft graviton theorem arising from IR divergences of scattering amplitudes matches onto the quadratic corrections to the soft charges computed from the BMS flux algebra. In the process, we examine how the BMS flux construction extends the celestial diamond framework to non-linear order and non-trivial vacua, and provides the natural symmetry generators for Celestial CFT.

Vacua by derivative corrections in mathcal {N} = 1 supergravity with matter multiplets

We study the vacuum structures of four-dimen-sional mathcal {N} = 1 old minimal supergravity with higher derivative corrections. We find that mathcal {N} = 1 supergravity with Riemann curvature square corrections and higher derivative matter chiral multiplets induces a non-trivial de Sitter vacuum, even in the absence of superpotentials. This vacuum generically breaks supersymmetry. We show that the auxiliary fields in the gravity and the chiral multiples play important roles to generate a potential in supersymmetric higher derivative theories.

Nonlinear [formula omitted] supersymmetry and 3D supersymmetric Born-Infeld theory

Dp-branes acquire effective nonlinear descriptions whose bosonic part is related to the Born-Infeld action. This nonlinearity has been proven to be a consequence of the partial N=2→N=1 supersymmetry breaking, originating from the solitonic nature of the branes. In this work, we focus on the effective descriptions of D2-branes. Using the Goldstone multiplet interpretation of the action and the method of nilpotent N=2 superfields, we construct the 3D, N=1 superspace effective action which makes the first supersymmetry manifest and realizes the second, spontaneously broken, supersymmetry nonlinearly. We show that there are two such supersymmetric extensions of the 3D Born-Infeld action which correspond to the dynamics of the 3D Maxwell-Goldstone multiplet and the 3D projection of the Tensor-Goldstone multiplet respectively. Moreover, we demonstrate that these results are derived by applying the constrained superfield approach on the N=2,D=3 vector and chiral multiplets after expanding them around a nontrivial vacuum. We find that these two descriptions are related by a duality transformation which results in the inversion of a dimensionless parameter. For both descriptions we derive the explicit bosonic and fermionic parts of the 3D super Born-Infeld action. Finally, consider the deformation of the Maxwell-Goldstone superspace action by the characteristic Chern-Simons-like, gauge invariant, mass term.

Tadpoles and vacuum bubbles in light-front quantization

We develop a method by which vacuum transitions may be included in light-front calculations. This allows tadpole contributions which are important for symmetry-breaking effects and yet are missing from standard light-front calculations. These transitions also dictate a nontrivial vacuum and contributions from vacuum bubbles to physical states. In nonperturbative calculations these separate classes of contributions (tadpoles and bubbles) cannot be filtered; instead, we regulate the bubbles and subtract the vacuum energy from the eigenenergy of physical states. The key is replacement of momentum-conserving delta functions with model functions of finite width; the width becomes the regulator and is removed after subtractions. The approach is illustrated in free scalar theory, in quenched scalar Yukawa theory, and in a limited Fock-space truncation of ${\ensuremath{\phi}}^{4}$ theory.

Centre vortex structure of QCD-vacuum fields and confinement

The non-trivial ground-state vacuum fields of QCD form the foundation of matter. Using modern visualisation techniques, this presentation examines the microscopic structure of these fields. Of particular interest are the centre vortices identified within the ground-state fields of lattice QCD. Our current focus is on understanding the manner in which dynamical fermions in the QCD vacuum alter the centre-vortex structure. The impact of dynamical fermions is significant and provides new insights into the role of centre vortices in underpinning both confinement and dynamical chiral symmetry breaking in QCD.

Gauge-Higgs models from nilmanifolds

We consider the compactification of a Yang-Mills theory on a three-dimensional nilmanifold. The compactification generates a Yang-Mills theory in four space-time dimensions, coupled to a specific scalar sector. The compactification geometry gives rise to masses for the zero-modes, proportional to the twist parameter of the nilmanifold. We study the simple example of an SU(3) model broken by a non-trivial vacuum of the scalar potential which generates three mass scales, two being at tree level, and the third one at loop level. We point out the relevance of general twisted geometries for model building and in particular for gauge-Higgs type models, as the twist generates tree-level mass hierarchies useful for grand unification and for the Higgs sector in electroweak symmetry breaking.

Gauge hierarchy from electroweak vacuum metastability

We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. This perspective is motivated by the early-time framework for eternal inflation put forth recently, which favors vacua that are relatively short-lived, but applies more generally to any theoretical approach predicting that our vacuum should be metastable. We find that the metastability of the electroweak vacuum, together with the requirement that such a non-trivial vacuum exists, requires the Higgs mass to be smaller than the instability scale by around one order of magnitude. While this bound is quite weak in the Standard Model (SM), as the instability scale is $\sim 10^{11}$ GeV, simple and well-motivated extensions of the SM - concretely, the $\nu$MSM with an approximate $B-\tilde{L}$ symmetry and the minimal SU(4)/Sp(4) composite Higgs model - can significantly tighten the bound by lowering the instability scale. We find that the bound can be brought down to $\simeq 10$ TeV where our perturbative treatment of the decay rate becomes unreliable. Our results imply that, assuming the SM symmetry breaking pattern, small running Higgs masses are a universal property of theories giving rise to metastability, suggesting a common origin of the two underlying fine-tunings and providing a strong constraint on any attempt to explain metastability.

GRAVITATIONAL CASIMIR EFFECT IN INSPIRALLING NEUTRON STAR BINARY

Currently, the discussions and investigations for the vacuum energy are drawing great both theoretical and experimental attention. The vacuum states of variety of fields, subject to special boundary conditions, may contribute to non-trivial macroscopic vacuum energy, i.e., the Casimir effect, which become an interdisciplinary subject and plays an important role in a variety of fields of physics. We adopt Schwingers source theory and study the quantization of gravitation contributions to the Casimir effect, i.e., the gravitational Casimir effect, in inspiraling neutron star binaries with wide separation of 109 m. By considering gravitoelectromagnetism (GEM) arising from the spiral-in orbital motion and evaluating the gravitoelectromagnetic contributions to the vacuum energy of gravitons radiated during the orbital decay, we demonstrate that, when the radial separation of the system decay a distance L, the GEM results in a small Casimir correction to the gravitational vacuum energy, which contributes to an attractive gravitational Casimir force to the binary, in addition to the gravitational force. We also discuss the possible detections for such gravitational Casimir effect from both the future space-based gravitational wave observatories and cosmological observations.

GRAVITATIONAL CASIMIR EFFECT IN INSPIRALLING NEUTRON STAR BINARY

Currently, the discussions and investigations for the vacuum energy is drawing great both theoretical and experimental attention. The vacuum states of variety of fields, subject to special boundary conditions, may contribute to non-trivial macroscopic vacuum energy, i.e. the Casimir effect, which become an interdisciplinary subject and plays an important role in a variety of fields of physics. We adopt Schwinger's source theory and study the Casimir effect due to the quantization of gravitation, i.e. the gravitational Casimir effect (GCE), in inspiraling neutron star (NS) binaries with wide separation of $10^9 \rm m$. By considering gravitoelectromagnetism (GEM) arising from the spiral-in orbital motion and evaluating the contributions of GEM to the vacuum energy of gravitons radiated during the orbital decay, we demonstrate that, when the orbital separation of the binary decay a distance of $L$ in radial direction, the GEM results in a small Casimir correction to the gravitational vacuum energy, which contributes to an attractive gravitational Casimir force to the binary, in addition the gravitational force. The gravitational waves (GWs), emitted from wide inspiraling NS binaries, locate in the low-frequency band of $10^{-4}-1$ Hz. For a characteristic GW frequency of $10^{-3}$ Hz, the gravitational Casimir correction to the signals is estimated as of the order of $\sim10^{-24}$, which corresponds to a force of $10^{-20}$ N. By considering that the sensitivity of space-based gravitational wave observatory, LISA/eLISA and Taiji, can be reduced to $10^{-24}$, we would expect that LISA/eLISA and Taiji with sensitivity improvements give the powerful tool to detect GCE in the near future.

Higgs Boson-Induced Reheating and Dark Matter Production

We discuss a perturbative and non-instantaneous reheating model, adopting a generic post-inflationary scenario with an equation of state w. In particular, we explore the Higgs boson-induced reheating, assuming that it is achieved through a cubic inflaton-Higgs coupling ϕ|H|2. In the presence of such coupling, the Higgs doublet acquires a ϕ-dependent mass and a non-trivial vacuum–expectation–value that oscillates in time and breaks the Standard Model gauge symmetry. Furthermore, we demonstrate that the non-standard cosmologies and the inflaton-induced mass of the Higgs field modify the radiation production during the reheating period.This, in turn, affects the evolution of a thermal bath temperature, which has remarkable consequences for the ultraviolet freeze-in dark matter production.

Correlations and commuting transfer matrices in integrable unitary circuits

We consider a unitary circuit where the underlying gates are chosen to be \check{R}Ř-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.

Dynamical fermions, centre vortices, and emergent phenomena

The non-trivial ground-state vacuum fields of QCD form the foundation of matter. Here we examine the centre vortices identified within the ground-state fields of lattice QCD. We aim to understand the manner in which dynamical fermions in the QCD vacuum alter the centre-vortex structure. Using modern visualisation techniques, the centre-vortex structure of pure-gauge and dynamical-fermion fields is quantified and compared. We then explore the impact this modified structure has on measures of confinement and dynamical mass generation. The string tension of the static quark potential, positivityviolation in the gluon propagator, and dynamical mass generation in the overlap quark propagator are of particular interest. The impact of dynamical fermions is significant and provides new insights into the role of centre vortices in underpinning both confinement and dynamical chiral symmetry breaking in QCD.

Kalb–Ramond scalar QED multiple vacua

We study a model of interacting vector and Kalb–Ramond gauge fields in a non-trivial Higgs vacuum generated by a charged and a neutral scalar field. The system admits different vacua for different v.e.v. of the two Higgs fields. Our primary interest in this paper regards the ‘mixed phase’ where both the photon and the Kalb–Ramond acquire a mass. In this phase we compute the interaction potential energy between static test charges. It turns out that the limit in which the photon becomes massless, while the Kalb–Ramond remains massive, leads to a Cornell confining potential between test charges.

Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island

The island rule for the entanglement entropy is applied to an eternal Reissner–Nordström black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.

Analytic nonintegrability and S -matrix factorization

We formulate an equivalence between the 2-dim $\ensuremath{\sigma}$-model spectrum expanded on a nontrivial massive vacuum and a classical particle Hamiltonian with variable mass and potential. By considering methods of analytic Galoisian nonintegrability on the appropriate geodesics of the Hamiltonian system we algebraically constrain the particle masses at fixed time, such that integrability is allowed. Through our equivalence, this explicitly constrains the masses of the excited spectrum of the dual 2-dim theory in such a way to imply the $S$-matrix factorization and no particle production. In particular, the integrability of the classical particle system implies the factorization of the $S$-matrix in the dual quantum 2-dim theory. Our proposal provides also nontrivial evidence on the connection between integrability and $S$-matrix factorization for large class of theories with interactions that break Lorentz invariance.