Vacuum Expectation Value Research Articles

Critical lumpy black holes in AdSp\xd7Sq

In this paper we study lumpy black holes with AdSp × Sq asymptotics, where the isometry group coming from the sphere factor is broken down to SO(q). Depending on the values of p and q, these are solutions to a certain Supergravity theory with a particular gauge field. We have considered the values (p, q) = (5, 5) and (p, q) = (4, 7), corresponding to type IIB supergravity in ten dimensions and eleven-dimensional supergravity respectively. These theories presumably contain an infinite spectrum of families of lumpy black holes, labeled by a harmonic number ℓ, whose endpoints in solution space merge with another type of black holes with different horizon topology. We have numerically constructed the first four families of lumpy solutions, corresponding to ℓ = 1, 2+, 2− and 3. We show that the geometry of the horizon near the merger is well-described by a cone over a triple product of spheres, thus extending Kol’s local model to the present asymptotics. Interestingly, the presence of non-trivial fluxes in the internal sphere implies that the cone is no longer Ricci flat. This conical manifold accounts for the geometry and the behavior of the physical quantities of the solutions sufficiently close to the critical point. Additionally, we show that the vacuum expectation values of the dual scalar operators approach their critical values with a power law whose exponents are dictated by the local cone geometry in the bulk.

Probing thermal fluctuations through scalar test particles

The fundamental vacuum state of quantum fields, related to Minkowski space, produces divergent fluctuations that must be suppressed in order to bring reality to the description of physical systems. As a consequence, negative vacuum expectation values of classically positive-defined quantities can appear. This has been addressed in the literature as subvacuum phenomenon. Here it is investigated how a scalar charged test particle is affected by the vacuum fluctuations of a massive scalar field in D + 1 spacetime when the background evolves from empty space to a thermal bath, and also when a perfectly reflecting boundary is included. It is shown that when the particle is brought into a thermal bath it gains an amount of energy by means of positive dispersions of its velocity components. The magnitude of this effect is dependent on the temperature and also on the field mass. However, when a reflecting wall is inserted, dispersions can be positive or negative, showing that subvacuum effect happens even in a finite temperature environment. Furthermore, a remarkable result is that temperature can even improve negative velocity fluctuations. The magnitude of the residual effects depends on the switching interval of time the system takes to evolve between two states.

Operator product expansion of the non-local gluon condensate

We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study [1], we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.

U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap

We generalise the form factor bootstrap approach to integrable field theories with U(1) symmetry to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are solved for the free massive Dirac and complex boson theories, which are the simplest theories with U(1) symmetry. We present the exact and complete solution for the bootstrap, including vacuum expectation values and form factors involving any type and arbitrarily number of particles. The non-trivial solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. An alternative and compact determination of the novel form factors is also presented. Based on the form factors of the U(1) composite branch-point twist fields, we re-derive earlier results showing entanglement equipartition for an interval in the ground state of the two models.

Modular invariant A4 models for quarks and leptons with generalized CP symmetry

We perform a systematical analysis of the A4 modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus τ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply A4 modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.

Thermodynamics of a Two-Step Electroweak Phase Transition.

New field content beyond that of the standard model of particle physics can alter the thermal history of electroweak symmetry breaking in the early Universe. In particular, the symmetry breaking may have occurred through a sequence of successive phase transitions. We study the thermodynamics of such a scenario in a real triplet extension of the standard model, using nonperturbative lattice simulations. Two-step electroweak phase transition is found to occur in a narrow region of allowed parameter space with the second transition always being first order. The first transition into the phase of nonvanishing triplet vacuum expectation value is first order in a non-negligible portion of the two-step parameter space. A comparison with two-loop perturbative calculation is provided and significant discrepancies with the nonperturbative results are identified.

Black hole evolution in a quantum-gravitational framework

Abstract We investigated black hole evolution on a quantum-gravitational scattering framework with the aim of tackling the black hole information paradox. With this setup, various pieces of system information are explicit from the start and unitary evolution is manifest throughout. The scattering amplitudes factorize into a perturbative part and a non-perturbative part. The non-perturbative part is dominated by an instanton-type contribution, i.e. a black hole analogue of the Coleman–De Luccia bounce solution, and we propose that the Hawking radiation be identified with the particles generated by the vacuum decay. Our results indicate that the black hole degrees of freedom are entangled not only with the Hawking modes but also with the pre-Hawking modes. The Wald’s entropy charge measures their entanglement. The full quantum-gravitational entropy is defined as the vacuum expectation value of the Wald entropy charge. With this definition, a shifted Page-like curve is generically generated and its quantum extension is readily defined.

Polynomial KP and BKP $$\tau $$-Functions and Correlators

Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations of Jacobi's bialternant formula for Schur functions and Nimmo's Pfaffian ratio formula for Schur $Q$-functions. These are obtained by applying Wick's theorem to fermionic vacuum expectation value representations in which the infinite group element acting on the lattice of basis states stabilizes the vacuum.

Electron-Positron Vacuum Instability in Strong Electric Fields. Relativistic Semiclassical Approach

The instability of electron-positron vacuum in strong electric fields is studied. First, falling to the Coulomb center is discussed at Z>137/2 for a spinless boson and at Z>137 for electron. Subsequently, focus is concentrated on description of deep electron levels and spontaneous positron production in the field of a finite-size nucleus with the charge Z>Zcr≃170. Next, these effects are studied in application to the low-energy heavy-ion collisions. Subsequently, we consider phenomenon of “electron condensation” on levels of upper continuum crossed the boundary of the lower continuum ϵ=−m in the field of a supercharged nucleus with Z≫Zcr. Finally, attention is focused on many-particle problems of polarization of the quantum electrodynamics (QED) vacuum and electron condensation at ultra-short distances from a source of charge. We argue for a principal difference of cases, when the size of the source is larger than the pole size rpole, at which the dielectric permittivity of the vacuum reaches zero and smaller rpole. Some arguments are presented in favor of the logical consistency of QED. All of the problems are considered within the same relativistic semiclassical approach.

Vacuum expectation value renormalization in the standard model and beyond

We show how the renormalization constant of the Higgs vacuum expectation value, fixed by a tadpole condition, is responsible for gauge dependences in various definitions of parameters in the $R_{\xi}$-gauge. Then we show the relationship of this renormalization constant to the Fleischer-Jegerlehner (FJ) scheme, which is used to avoid these gauge dependences. In this way, we also present a viewpoint on the FJ-scheme complementary to the ones already existing in the literature. Additionally, we compare and discuss different approaches to the renormalization of tadpoles by identifying the similarities and relations between them. The relationship to the Higgs background field renormalization is also discussed.

Electric charge quantization in SU(3)c ⊗ SU(n)L ⊗ U(1)Y gauge models

We prove that the Cotăescu general method of solving SU(3)c ⊗ SU(n)L ⊗ U(1)Y gauge models exactly predicts the observed electric charge quantization, as the theory remains renormalizable, both in its strong and electroweak sectors, while all the fermions get their masses—by means of Yukawa terms—the spontaneous symmetry breakdown (SSB) successively. The latter is achieved by a scalar sector consisting of n Higgs multiplets, each acquiring its own vacuum expectation value (VEV).

Background-independent composite gravity

We explore a background-independent model of composite gravity. In a mean-field approximation, the vacuum expectation value of the composite metric satisfies Einstein’s equations (with corrections) as a consistency condition. A gravitational interaction then emerges in vacuum correlation functions. The action remains diffeomorphism invariant even as perturbation theory is organized about the dynamically selected vacuum spacetime. We discuss the role of nonphysical clock and rod fields in the analysis, the identification of physical observables, and the generalization to other theories including the standard model.

Common origin of radiative neutrino mass, dark matter and leptogenesis in scotogenic Georgi-Machacek model

We explore the phenomenology of the Georgi-Machacek model extended with two Higgs doublets and vector fermion doublets invariant under SU(2)L×U(1)Y×Z4×Z2. The Z4 symmetry is broken spontaneously while the imposed Z2 symmetry forbids triplet fields to generate any vacuum expectation value and leading to an inert dark sector providing a viable candidate for dark matter and generate neutrino mass radiatively. Another interesting feature of the model is leptogenesis arising from decay of vector-like fermions. A detailed study of the model is pursued in search for available parameter space consistent with the theoretical and experimental observations for dark matter, neutrino physics, flavor physics, matter-antimatter asymmetry in the Universe.

Seesaw neutrino dark matter by freeze-out

We investigate whether right-handed neutrinos can play the role of the dark matter of the Universe and be generated by the freeze-out production mechanism. In the standard picture, the requirement of a long lifetime of the right-handed neutrinos implies a small neutrino Yukawa coupling. As a consequence, they never reach thermal equilibrium, thus prohibiting production by freeze-out. We note that this limitation is alleviated if the neutrino Yukawa coupling is large enough in the early Universe to thermalize the sterile neutrinos, and then becomes tiny at a certain moment, which makes them drop out of equilibrium. As a concrete example realization of this framework, we consider a Froggatt-Nielsen model supplemented by an additional scalar field which obeys a global symmetry (not the flavour symmetry). Initially, the vacuum expectation value of the flavon is such, that the effective neutrino Yukawa coupling is large and unsuppressed, keeping them in thermal equilibrium. At some point the new scalar also gets a vacuum expectation value that breaks the symmetry. This may occur in such a way that the vev of the flavon is shifted to a new (smaller) value. In that case, the Yukawa coupling is reduced such that the sterile neutrinos are rendered stable on cosmological time scales. We show that this mechanism works for a wide range of sterile neutrino masses.

Bumblebee gravity with a Kerr\u2013Sen like solution and its Shadow

We have considered the bumblebee gravity model where lorentz-violating (LV) scenario gets involved through a bumblebee field vector field B_mu . A spontaneous symmetry breaking allows the field to acquires a vacuum expectation value that generates LV into the system. A Kerr–Sen-like solution has been found out starting from the generalized form of a radiating stationery axially symmetric black hole metric. We compute the effective potential offered by the null geodesics in the bumblebee rotating black hole spacetime. The shadow has been sketched for different variations of the parameters involved in the system. A careful investigation has been carried out to study how the shadow gets affected when Lorentz violation enters into the picture. The emission rate of radiation has also been studied and how it varies with the LV parameter ell is studied scrupulously.

Palatini double-well and Coleman-Weinberg potentials with non-minimal coupling

We present the impact of non-minimal coupling ξϕ2 R on the inflationary parameters by taking into account the models of single-field inflation with the inflaton that has a non-zero vacuum expectation value (v) after the period of inflation in Palatini gravity. We discuss the well-known symmetry-breaking type potentials, namely the double-well potential and Coleman-Weinberg potential. We show that the inflationary predictions, n s and r, of these potentials for both ϕ > v and ϕ < v inflation are compatible with the recent measurements within the regions of the v-ξ plane. Finally, we take into account the inflationary predictions of Coleman-Weinberg potential for selected ξ values as a function of v in the Palatini formalism.

Minimal scoto-seesaw mechanism with spontaneous CP violation

We propose simple scoto-seesaw models to account for dark matter and neutrino masses with spontaneous CP violation. This is achieved with a single horizontal {mathcal{Z}}_8 discrete symmetry, broken to a residual {mathcal{Z}}_2 subgroup responsible for stabilizing dark matter. CP is broken spontaneously via the complex vacuum expectation value of a scalar singlet, inducing leptonic CP-violating effects. We find that the imposed {mathcal{Z}}_8 symmetry pushes the values of the Dirac CP phase and the lightest neutrino mass to ranges already probed by ongoing experiments, so that normal-ordered neutrino masses can be cornered by cosmological observations and neutrinoless double beta decay experiments.

Extra equation of gravity induced by spontaneous local Lorentz symmetry breakdown

A model of spontaneous Lorentz violation in four dimension is given, which seems to provide a Lorentz invariant effective theory. An SU(2) Yang-Mills gauge field and an auxiliary U(1) vector field generate gravity and other interactions when they have vacuum expectation values. The emergent gravity is equivalent to conventional general relativity up to the third order terms in the Lagrangian. The coupling to matter, including spin-1/2 fermions, is also given correctly to this level. It remains to be seen whether this formalism reproduces the properties of black holes and other consequences obtained from Einstein's theory.

Electroweak restoration at the LHC and beyond: The Vh channel

The LHC is exploring electroweak (EW) physics at the scale EW symmetry is broken. As the LHC and new high energy colliders push our understanding of the Standard Model to ever-higher energies, it will be possible to probe not only the breaking of but also the restoration of EW symmetry. We propose to observe EW restoration in double EW boson production via the convergence of the Goldstone boson equivalence theorem. This convergence is most easily measured in the vector boson plus Higgs production, $Vh$, which is dominated by the longitudinal polarizations. We define EW restoration by carefully taking the limit of zero Higgs vacuum expectation value (vev). EW restoration is then measured through the ratio of the $p_T^h$ distributions between $Vh$ production in the Standard Model and Goldstone boson plus Higgs production in the zero vev theory, where $p_T^h$ is the Higgs transverse momentum. As EW symmetry is restored, this ratio converges to one at high energy. We present a method to extract this ratio from collider data. With a full signal and background analysis, we demonstrate that the 14 TeV HL-LHC can confirm that this ratio converges to one to 40% precision while at the 27 TeV HE-LHC the precision will be 6%. We also investigate statistical tests to quantify the convergence at high energies. Our analysis provides a roadmap for how to stress test the Goldstone boson equivalence theorem and our understanding of spontaneously broken symmetries, in addition to confirming the restoration of EW symmetry.

Flavorgenesis in an SU(19) model

We present a model where all fermions are contained in a single irreducible representation of an SU(19) gauge symmetry group. If there is only one scalar field, Yukawa interactions are controlled by a single number rather than by one or more 3×3 matrices of couplings. The low-energy concept of flavor emerges entirely from the scalar-sector parameters; more specifically, entries of the Standard Model Yukawa matrices are controlled by several vacuum expectation values.