Vacuum Expectation Value Research Articles

Gravitational Condensate Stars: An Alternative to Black Holes

A new final endpoint of complete gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a static, spherically symmetric solution to Einstein’s equations is obtained, characterized by an interior de Sitter region of p=−ρ gravitational vacuum condensate and an exterior Schwarzschild geometry of arbitrary total mass M. These are separated by a phase boundary with a small but finite thickness ℓ, replacing both the Schwarzschild and de Sitter classical horizons. The resulting collapsed cold, compact object has no singularities, no event horizons, and a globally defined Killing time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of order kBℓMc/ℏ, instead of the Bekenstein–Hawking entropy, SBH=4πkBGM2/ℏc. Unlike BHs, a collapsed star of this kind is consistent with quantum theory, thermodynamically stable, and suffers from no information paradox.

Infrared renormalons in supersymmetric theories

I argue that in large-$N$ supersymmetric QCD infrared renormalons are absent in the conformal window, there is no need in conspiracy, and vacuum expectation values of at least some gluon operators vanish. Basing on this conclusion I conjecture that in supersymmetric gluodynamics (supersymmetric Yang-Mills theory without matter) at least the leading renormalon ambiguity disappears which would be consistent with the fact that the gluon condensate vanishes in this theory, $\langle G_{\mu\nu}^a G^{\mu\nu\,a}\rangle =0$.

Analytics of type IIB flux vacua and their mass spectra

We analyze the tree-level potential of type IIB flux compactifications in warped Calabi-Yau orientifolds, in regions of weak coupling and moderately large complex structure. In this regime, one may approximate the flux-induced superpotential W by a polynomial on the axio-dilaton and complex structure fields, and a significant fraction of vacua corresponds to a quadratic W. In this quadratic case, we argue that vacua fall into three classes, for which one can push the analytic description of their features. In particular, we provide analytic expressions for the vacuum expectation values and flux-induced masses of the axio-dilaton and complex structure fields in a large subclass of vacua, independently of the Calabi-Yau and the number of moduli. We show that supersymmetric vacua always contain flat directions, at least at this level of approximation. Our findings allow to generate vast ensembles of flux vacua in specific Calabi-Yau geometries, as we illustrate in a particular example.

Axion-Higgs cosmology: Cosmic microwave background and cosmological tensions

Non-canonical cosmology with an uplifted Higgs vacuum expectation value (Higgs-VEV) in the early universe is believed to provide the solution for existing tensions within the $\Lambda$CDM regime. We recently proposed a theoretical model called axi-Higgs to explore this framework. The axi-Higgs model features an ultralight axion with mass $m_a \sim 10^{-29}$ eV, which couples to the Higgs field such that the Higgs-VEV is driven by the axion background evolution. Phenomenologically, the axi-Higgs model is equivalent to $\Lambda$CDM+$m_e$+$\omega_a$ which is defined as $\Lambda$CDM with electron mass variation and the presence of an ultralight axion. In this paper, we perform Markov Chain Monte Carlo analyses to investigate the parameter space of axi-Higgs and compare it with $\Lambda$CDM, $\Lambda$CDM+$m_e$ where only electron mass variation is allowed, and $\Lambda$CDM+$\omega_a$ where only an ultralight axion is present. Combining observational data from Cosmic Microwave Background, Baryon Acoustic Oscillations, weak-lensing cosmic shear survey we found $H_0 = 69.4 \pm 1.3$ km/s/Mpc, which reduces the Hubble tension to approximately $2.4\sigma$. Including data from supernovae Type IA and local Hubble measurement from SH0ES we found $H_0 = 71.34 \pm 0.96$ km/s/Mpc. The presence of this Higgs-VEV-driving axion may be tested by atomic clock and quasar spectral measurements in the near future.

On the Nekrasov partition function of gauged Argyres-Douglas theories

We study SU(2) gauge theories coupled to (A1, DN) theories with or without a fundamental hypermultiplet. For even N, a formula for the contribution of (A1, DN) to the Nekrasov partition function was recently obtained by us with Y. Sugawara and T. Uetoko. In this paper, we generalize it to the case of odd N in the classical limit, under the condition that the relevant couplings and vacuum expectation values of Coulomb branch operators of (A1, DN) are all turned off. We apply our formula to the (A2, A5) theory to find that its prepotential is related to that of the SU(2) gauge theory with four fundamental flavors by a simple change of variables.

Scalar-singlet assisted leptogenesis with CP violation from the vacuum

In the vanilla type-I seesaw leptogenesis scenario, CP violation required to generate the lepton asymmetries in the heavy Majorana neutrino decays stem from complex Dirac-type Yukawa couplings. In this paper we explore the case in which that CP violation originates from the vacuum expectation value of a complex scalar singlet at a very high scale. This non-trivial CP-violating phase can be successfully communicated to the low-energy neutrino sector via the heavy neutrino portal. The new scalar-singlet degrees of freedom generate new contributions to the CP asymmetries relevant for leptogenesis not only at the one-loop level but also through tree-level three-body decays. These are computed here for an arbitrary number of heavy neutrinos, Higgs doublets and scalar singlets. We also take into account the new decays and scattering processes that enter the unflavoured Boltzmann equations governing the heavy-neutrino particle densities and the (B – L)-asymmetry evolution. Having established the framework of interest, we present a simple model with two RH neutrinos, two Higgs doublets and a complex scalar singlet, supplemented with a Ƶ8 flavour symmetry. This symmetry minimises the number of free parameters without compromising the possibility of spontaneous CP violation and compatibility with neutrino data. In fact, the only viable Ƶ8 charge assignment shows a preference for a non-trivial spontaneous CP-violating phase, which in turn leads to a non-vanishing CP asymmetry due to the direct link between high- and low-energy CP violation. An interesting feature of this simple setup is that the usual wave and vertex type-I seesaw contributions to the CP asymmetry vanish due to the Ƶ8 symmetry. Thus, the observed baryon-to-photon ratio can be explained thanks to the new couplings among the heavy neutrinos and the new scalar degrees of freedom.

Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions

We study a quantum scalar field, with general mass and coupling to the scalar curvature, propagating on three-dimensional global anti-de Sitter space-time. We determine the vacuum and thermal expectation values of the square of the field, also known as the vacuum polarisation (VP). We consider values of the scalar field mass and coupling for which there is a choice of boundary conditions giving well-posed classical dynamics. We apply Dirichlet, Neumann and Robin (mixed) boundary conditions to the field at the space-time boundary. We find finite values of the VP when the parameter governing the Robin boundary conditions is below a certain critical value. For all couplings, the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximal symmetry of the background space-time. However, this is not the case for Robin boundary conditions, when both the vacuum and thermal expectation values depend on the space-time location. At the space-time boundary, we find that both the vacuum and thermal expectation values of the VP with Robin boundary conditions converge to the result when Neumann boundary conditions are applied, except in the case of Dirichlet boundary conditions.

The bumblebee field excitations in a cosmological braneworld

We investigate the effects of the spacetime curvature and extra dimensions on the excitations of the Lorentz violating bumblebee field B μ . By assuming the bumblebee field living in a five-dimensional AdS 5 bulk, we found an exponential suppression of the bumblebee self-interacting constant λ and of the bumblebee vacuum expectation value (VEV) b M along the fifth extra dimension. The fluctuations of the bumblebee field upon the VEV can be decomposed into transverse and longitudinal modes with respect to b M . For a spacelike b M along the extra dimension and assuming a thin FRW 3-brane embedded in the AdS 5, the transverse mode is localized on the brane. The bulk geometry leads to a propagating and unbound longitudinal mode along the extra dimension. On the brane, the cosmological expansion leads to the decay of the longitudinal mode in time, as Δt ≈ H −1.

Axiomatic de Sitter quantum Yang-Mills theory with color confinement and mass gap

The analyticity property of de Sitter's quantum Yang-Mills theory in the framework of Krein space quantization, including quantum metric fluctuation, is demonstrated. This property completes our previous work regarding quantum Yang-Mills theory in de Sitter's ambient space formalism, and we can construct an axiomatic quantum field theory similar to Wightman's axioms. The color confinement is proven for the general case, which was previously approved in the early universe. It is shown by using the interaction between gluon fields and the conformal sector of the gravitational field, which is a massless minimally coupled scalar gauge field. The gluon mass results from the interaction between the gluon fields and the massless minimally coupled scalar field as a conformal sector of the gravitational field and then the symmetry-breaking setting due to the vacuum expectation value of the scalar field.

SU(5) grand unification and W-boson mass

A realistic extension of the minimal SU(5) theory consisting of the addition of an adjoint fermion is known to predict light real fermion and scalar weak triplets, potentially accessible at the LHC. These particles, in addition to playing a key role in gauge coupling unification, have profound phenomenological implications. The fermion triplet, that through the seesaw mechanism offers a testable origin of neutrino mass, has been already extensively discussed. The scalar triplet develops a vacuum expectation value that modifies the W-boson mass. We show that its low-energy effective theory is remarkably predictive: in the leading approximation, all the relevant physical processes involving the scalar triplet depend only on its mass and the deviation from the Standard Model W-mass value.

Axionic Dirac seesaw mechanism and electroweak vacuum stability

We explore the connection between tree-level Dirac neutrino masses and axion physics in a scenario where the Peccei-Quinn (PQ) symmetry enforces lepton number conservation perturbatively. Requiring that the PQ scale ${f}_{a}$ is the only heavy scale to play a role in neutrino mass generation, we are led to the construction of a Kim--Shifman--Vainshtein--Zakharov-type model where Dirac neutrino masses are inversely proportional to ${f}_{a}$, provided a real scalar triplet (zero hypercharge) is added to the standard model scalar sector. We analyze this extended scalar sector, focusing on the stabilization of the electroweak vacuum. The contribution of the triplet vacuum expectation value to the $W$ mass may also be responsible for the recent hint of beyond-the-SM physics by the CDF collaboration.

Pseudo-Nambu-Goldstone dark matter from non-Abelian gauge symmetry

We propose a pseudo-Nambu-Goldstone boson (pNGB) dark matter (DM) model based on an additional non-Abelian gauge symmetry $SU(2{)}_{D}$. The gauge symmetry $SU(2{)}_{D}$ is spontaneously broken to a global custodial symmetry $U(1{)}_{V}$ via the nonvanishing vacuum expectation values of $SU(2{)}_{D}$ doublet and triplet scalar fields. Due to the exact global symmetry $U(1{)}_{V}$, the lightest $U(1{)}_{V}$ charged particle becomes stable. We assume that the lightest charged particle in the model is the charged complex pNGB, which we regard as DM. It avoids the strong constraints from current DM direct detection experiments due to the property of NGB. We find that the measured energy density of DM can be reproduced when the DM mass is larger than the half of the Higgs mass, where the lower limit generally comes from the constraint of DM invisible decay and the upper limit from DM direct detection experiments depends on the model parameters.

Holographic model with power-law Maxwell field for color superconductivity

Studying the color superconductivity (CSC) phase is important to understand the physics in the core of the neutron stars which is the only known context where the CSC phase might appear due to the gravitational force squeezing the matter to a sufficiently high density. We propose a simple holographic dual description of the CSC phase transition in the realistic Yang-Mills theory with the power-law Maxwell field. We find the CSC phase transition with the large color number in the deconfinement phase, which is not found in the case of the usual Maxwell field, if the power parameter characterizing for the power-law Maxwell field is sufficiently lower than one but above $1/2$ and the chemical potential is above a critical value. However, the power parameter is not arbitrary below one because when this parameter is sufficiently far away from one it leads to the occurrence of the CSC state in the confinement phase which is not compatible with a nonzero vacuum expectation value of the color nonsinglet operator.

Two-Real-Singlet-Model Benchmark Planes

In this manuscript, I briefly review the Benchmark Planes in the Two-Real-Singlet Model (TRSM), a model that enhances the Standard Model (SM) scalar sector by two real singlets that obey a Z2⊗Z2′ symmetry. In this model, all fields acquire a vacuum expectation value, such that the model contains in total three CP-even neutral scalars that can interact with each other. All interactions with SM-like particles are inherited from the SM-like doublet via mixing. I remind the readers of the previously proposed benchmark planes and briefly discuss possible production at future Higgs factories, as well as regions in a more generic scan of the model. For these, I also discuss the use of the W-boson mass as a precision observable to determine allowed/excluded regions in the models’ parameter space. This work is an extension of a white paper submitted to the Snowmass process.

Spontaneous conformal symmetry breaking and quantum quadratic gravity

We investigate several quantum phenomena related to quadratic gravity after rewriting the general fourth-order action in a more convenient form that is second order in derivatives and produces only first-class constraints in phase space. We find that a Higgs mechanism may occur in the conformally invariant subset of the general quadratic action if the theory is conformally coupled to a scalar field that acquires a nonzero vacuum expectation value and spontaneously breaks the conformal symmetry. Then, in the broken phase, the originally massless spin-2 ghost may absorb both the scalar and vector fields to become massive. We also perform a Becchi-Rouet-Stora-Tyutin quantization of second-order quadratic gravity in the covariant operator formalism and discuss conditions under which unitarity of the full interacting quantum theory may be established.

Stability of nontopological string in supersymmetric SU(2)×U(1) gauge theory

We construct a nontopological string solution for a supersymmetric gauge theory with [Formula: see text] gauge symmetry which is spontaneously broken to [Formula: see text] by developing the vacuum expectation value of two doublet Higgses. It is a supersymmetric extension of the electroweak string while supersymmetry is unbroken. We discuss the classical stability of the nontopological string by perturbations. We show that the classical stability is determined only by two parameters, and that the allowed region becomes essentially the same as in the electroweak string.

Unavoidable Higgs coupling deviations in the Z2 -symmetric Georgi-Machacek model

The $Z_{2}$-symmetric version of the Georgi-Machacek model does not possess a decoupling limit in which all the new particles can be made arbitrarily heavy, opening the possibility that the model can be entirely excluded if experiments reveal no deviations from the Standard Model. We explore this model, focusing on the part of parameter space in which the vacuum expectation value of the triplets, $\nu_\chi$, is small. In the small-$\nu_\chi$ limit, the second custodial-singlet scalar field $S$ necessarily becomes very light and can contribute to the total width of the 125 GeV Higgs boson $h$ via $h \to SS$. We show that this process, together with LHC measurements of the $h \to \gamma\gamma$ rate, entirely excludes masses $m_S < m_h/2$ and thereby severely constrains the parameter space, setting an experimental lower bound $\nu_\chi \gtrsim 12.5$ GeV on the vacuum expectation value of the triplets. This lower bound makes it impossible to avoid deviations from the Standard Model in the couplings of $h$ to fermion and vector boson pairs. We study the remaining parameter space after imposing constraints from direct searches for the additional Higgs bosons, and show that it is on the edge of being fully excluded at $95\%$ confidence level by LHC measurements of the 125 GeV Higgs boson's couplings. Measurements of these couplings at the future high-luminosity run of the LHC will have sufficient precision to entirely exclude the model at $5\sigma$ if no deviations from the Standard Model are observed.

Type II Dirac seesaw portal to the mirror sector: Connecting neutrino masses and a solution to the strong CP problem

We present a version of the Type II seesaw mechanism for parametrically small Dirac neutrino masses. Our model starts from an $\mathrm{SU}(2{)}_{\mathrm{L}}\ensuremath{\bigotimes}\mathrm{SU}(2{)}^{\ensuremath{'}}\ensuremath{\bigotimes}\mathrm{U}(1{)}_{\mathrm{X}}$ gauge extension of the Standard Model involving a sector of mirror fermions. A bidoublet scalar with a very small vacuum expectation value connects the SM leptons with their mirror counterparts, and we can identify the mirror neutrino with the right-handed neutrino. Similar to the conventional Type II seesaw, our particle spectrum features singly and doubly charged scalars. The strong $CP$ problem is solved by a discrete exchange symmetry between the two sectors that forces the contributions of quarks and mirror quarks to the strong $CP$ phase to cancel each other. We discuss the low-energy phenomenology, comment on the cosmological implications of this scenario, and indicate how to realize successful Dirac leptogenesis.

Scale-invariant 3-3-1-1 model with B−L symmetry

Motivated by a possible interplay between the mechanism of dynamical symmetry breaking and the seesaw mechanism for generating fermion masses, we present a scale-invariant model that extends the gauge symmetry of the Standard Model electroweak sector to SU(3)$_L\otimes$U(1)$_X\otimes$U(1)$_N$, with a built-in $B-L$ symmetry. The model is based on the symmetry structure of the known 3-3-1 models and, thus, it relates the number of the three observed fermion generations with the cancellation of gauge anomalies. Symmetry breaking is triggered via the Coleman-Weinberg mechanism taking into account a minimal set of scalar field multiplets. We establish the stability conditions for the tree-level scalar potential imposing the copositivity criteria and use the method of Gildener-Weinberg for computing the one-loop effective potential when one has multiple scalar fields. With the addition of vectorial fermions, getting their mass mainly through the vacuum expectation value of scalar singlets at $10^3$ TeV, the $B-L$ symmetry leads to textures for the fermion mass matrices, allowing seesaw mechanisms for neutrinos and quarks to take place. In particular, these mechanisms could partly explain the mass hierarchies of the quarks. Once the breakdown of the SU(3)$_L$ symmetry is supposed to occur around 10 TeV, the model also predicts new particles with TeV-scale masses, such as a neutral scalar, $H_{1}$, a charged scalar, $H^\pm$, and the gauge bosons $Z^{\prime}$, $W^{\prime\pm}$ and $Y^0$, that could be searched with the high-luminosity LHC.

Gravitational waves-tomography of Low-Scale-Leptogenesis

A long-lived scalar field (Φ) which couples weakly to the right-handed (RH) neutrinos (NRi), generates small RH neutrino masses (Mi) in Low-Scale-Leptogenesis (LSL) mechanisms, despite having a large vacuum expectation value vΦ. In this case, the correlation shared by the Mis and the duration of the non-standard cosmic history driven by the Φ provides an excellent opportunity to study LSL signatures on primordial gravitational waves (GWs). We find it engaging, specifically for the gravitational waves that originate due to the inflationary blue-tilted tensor power spectrum and propagate through the non-standard cosmic epoch. Depending on Mi, broadly, the scenario has two significant consequences. First, if LSL is at play, GWs with a sizeable blue tilt do not contradict the Big-Bang-Nucleosynthesis (BBN) bound even for the post-inflationary models with very high-scale reheating. Second, it opens up a possibility to probe LSLs via a low-frequency and a complementary high-frequency measurement of GW-spectral shapes which are typically double-peaked. For a case study, we consider the recent results on GWs from the Pulsar-Timing-Arrays (PTAs) as a ‘measurement’ at the low frequencies and forecast the signatures of LSL mechanisms at the higher frequencies.