Nonperturbative Vacuum Research Articles

Compact objects in and beyond the standard model from nonperturbative vacuum scalarization

We consider a theory in which a real scalar field is Yukawa coupled to a fermion and has a potential with two nondegenerate vacua. If the coupling is sufficiently strong, a collection of N fermions deforms the true vacuum state, creating energetically favored false-vacuum pockets in which fermions are trapped. We embed this model within general relativity and prove that it admits self-gravitating compact objects where the scalar field acquires a nontrivial profile due to nonperturbative effects. We discuss some applications of this general mechanism: (i) “neutron soliton stars” in low-energy effective QCD, which naturally happen to have masses around 2M⊙ and radii around 10 km even without neutron interactions; (ii) “Higgs false-vacuum pockets” in and beyond the standard model; (iii) “dark soliton stars” in models with a dark sector. In the latter two examples, we find compelling solutions naturally describing centimeter-size compact objects with masses around 10−6M⊙, intriguingly in a range compatible with the Optical Gravitational Lensing Experiment (OGLE)+Hyper Suprime-Cam (HSC) microlensing anomaly. In addition to these interesting examples, the mechanism of nonperturbative vacuum scalarization may play a role in various contexts in and beyond the standard model, providing a support mechanism for new compact objects that can form in the early Universe, can collapse into primordial black holes through accretion past their maximum mass, and serve as dark matter candidates. Published by the American Physical Society 2024

Lorentz invariance violation and the CPT -odd electromagnetic response of a tilted anisotropic Weyl semimetal

We derive the electromagnetic response of a particular fermionic sector in the minimal QED contribution to the Standard Model Extension (SME), which can be physically realized in terms of a model describing a tilted and anisotropic Weyl semimetal (WSM). The contact is made through the identification of the Dirac-like Hamiltonian resulting from the SME with that corresponding to the WSM in the linearized tight-binding approximation. We first calculate the effective action by computing the nonperturbative vacuum polarization tensor using thermal field theory techniques, focusing upon the corrections at finite chemical potential and zero temperature. Next, we confirm our results by a direct calculation of the anomalous Hall current within a chiral kinetic theory approach. In an ideal Dirac cone picture of the WSM (isotropic and nontilted) such response is known to be governed by axion electrodynamics, with the space-time dependent axion angle Θ(r,t)=2(b·r−b0t), being 2b and 2b0 the separation of the Weyl nodes in momentum and energy, respectively. In this paper we demonstrate that the node tilting and the anisotropies induce novel corrections at a finite density which however preserve the structure of the axionic field theory. We apply our results to the ideal Weyl semimetal EuCd2As2 and to the highly anisotropic and tilted monopnictide TaAs. Published by the American Physical Society 2024

Wilsonian effective potentials and closed string field theory

We investigate Wilsonian effective field theory as a model for the construction of the tachyon potential and nonperturbative vacua in closed string field theory. In a number of cases we are able to find the effective potential exactly, and observe what appear to be universal features. We find that the effective field theory contains the same nonperturbative vacuum structure as the bare Lagrangian, though this information is encoded less efficiently as the distance scale of the effective field theory is increased. The implication is that closed string field theory plausibly contains information about the nonperturbative vacuum structure of string theory, in spite of its similarities to effective field theory. We also truncate the effective potential at a fixed power of the field and investigate how the global structure of the effective potential may be approximated via Padé resummation. Qualitative comparisons suggest that computation of the eighth to sixteenth order closed string vertex should be enough to obtain reliable results for the closed string field theory action evaluated on the tachyon field.

Can We Observe Nonperturbative Vacuum Shifts in Cavity QED?

We address the fundamental question of whether or not it is possible to achieve conditions under which the coupling of a single dipole to a strongly confined electromagnetic vacuum can result in nonperturbative corrections to the dipole's ground state. To do so we consider two simplified, but otherwise rather generic cavity QED setups, which allow us to derive analytic expressions for the total ground-state energy and to distinguish explicitly between purely electrostatic and genuine vacuum-induced contributions. Importantly, this derivation takes the full electromagnetic spectrum into account while avoiding any ambiguities arising from an adhoc mode truncation. Our findings show that while the effect of confinement perse is not enough to result in substantial vacuum-induced corrections, the presence of high-impedance modes, such as plasmons or engineered LC resonances, can drastically increase these effects. Therefore, we conclude that with appropriately designed experiments it is at least in principle possible to access a regime where light-matter interactions become nonperturbative.

Strange quark mass (m s ) dependent model of anisotropic strange quark star* *A fellowship has been provided to A. Hakim by Government of West Bengal (G.O. No. 52-Edn(B)/5B-15/2017 dated June 7, 2017, read with 65-Edn(B)/5-15/2017 dated July 11, 2017) and to K.B. Goswami by Council of Scientific and Industrial Research, India (vide no. 09/1219 (0004)/2019-EMR-I)

This article presents the configuration of strange quark stars in hydrostatic equilibrium considering the Vaidya-Tikekar metric ansatz. The interior of such stars comprises strange quark matter (henceforth SQM), whose equation of state () is described by the MIT EoS , where B is the difference between perturbative and non-perturbative vacuum. We have included the mass of the strange quark into the EoS and studied its effect on the overall properties of the strange quark star in this work. It is observed that the maximum mass reaches its highest value when . We have evaluated the range of the maximum mass of the strange quark star by solving the TOV equation for necessary for stable strange quark matter at a zero external pressure condition with respect to neutrons. Maximum mass lies within the range of to when B ranges from to and . It is noted that the maximum mass decreases with an increase in . Our model is found suitable for describing the mass of pulsars such as PSR J1614-2230 and Vela X-1 and the secondary objects in the GW170817 event. The model is also useful in predicting the radius of the recently observed pulsars PSR J0030+0451, PSR J0740+6620, and PSR J0952-0607 and the secondary objects in the GW170817 and GW190814 events. Our model is found to be stable with respect to all stability criteria of the stellar configurations and is also stable with respect to small perturbations.

Analytic continuation and physical content of the gluon propagator

The analytic continuation of the gluon propagator is revised in the light of recent findings on the possible existence of complex conjugated poles. The contribution of the anomalous pole must be added when Wick rotating, leading to an effective Minkowskian propagator which is not given by the trivial analytic continuation of the Euclidean function. The effective propagator has an integral representation in terms of a spectral function which is naturally related to a set of elementary (complex) eigenvalues of the Hamiltonian, thus generalizing the usual K\"all\'en-Lehmann description. A simple toy model shows how the elementary eigenvalues might be related to actual physical quasiparticles of the nonperturbative vacuum.

Dipole-like Field Configurations in Nonperturbative Vacuum

A model of nonperturbative vacuum in SU(2) Yang–Mills theory coupled to a nonlinear spinor field is suggested. By analogy with Abelian magnetic monopole dominance in quantum chromodynamics, it is assumed that the dominant contribution to such a vacuum comes from dipole-like field configurations existing in this theory. Using an assumption of the behavior of the number density of dipole-like field configurations whose energy approaches infinity, we derive an approximate expression for the energy density of such nonperturbative vacuum symmetrical under translation that turns out to be finite, unlike the infinite energy density of perturbative vacuum. Using characteristic values of the parameters appearing in the expression for the nonperturbative energy density, it is shown that this density may be of the order of the energy density associated with Einstein’s cosmological constant. The physical interpretation of the spinor field self-coupling constant as a characteristic distance between dipole-like field configurations is suggested. The questions of experimental verification of the nonperturbative vacuum model under consideration and of determining its pressure are briefly discussed.

Dual QCD thermodynamics at finite temperature and chemical potential

A Dual QCD formulation for [Formula: see text] color gauge has been developed in terms of dual gauge potentials, building on our previously published study for the [Formula: see text] case with zero bario-chemical potential [H. C. Chandola, G. Punetha and H. Dehnen, Nucl. Phys. A 945, 226 (2016).] and taking into account the local as well as topological structure of the color gauge group into its dynamics. For the purpose of examining the nonperturbative characteristics of QCD, the dynamical configuration of the resulting dual QCD vacuum and its flux tube configuration have been examined. The thermal behavior of the nonperturbative QCD vacuum has been investigated for exploring the dynamics of quark-hadron phase transition at finite chemical potential. Related thermodynamic quantities and equation of state (EoS) to characterize quark matter have also been discussed within the framework of dual QCD-based hadronic bag which guarantees the critical parameters and the associated critical points for quark-hadron phase transition. These thermodynamic quantities are expected to play important roles in understanding the order of quark-hadron phase transition and are likely to predict the features of a first-order quark-hadron phase transition for finite chemical potential. Moreover, we have investigated the bulk properties of quark matter by constructing the free energy change and the associated surface tension for quark-hadron phase transition. For consistency and compatibility check, we have also compared our results with state-of-the-art three-loop Hard Thermal Loop perturbative results and available lattice QCD results and in the process found reasonable agreements.

London model of dual color superconductor

The Meissner effect for the chromoelectric field E⃗a is a property of the non-perturbative QCD vacuum medium assumed to explain the observed confinement of color. The color dielectric function ϵ of such a medium should vanish. By Lorentz invariance ϵμ = 1 i.e., its color magnetic permeability μ should diverge. The assumption based on analogy is well motivated: Ordinary superconductor is the physical medium with μ = 0, confining the opposite magnetic charges (would they exist). For the first successful phenomenological description of both the Meissner effect and superconductivity within Maxwell equations Fritz London guessed two equations for the superconductivity current. We adapt his arguments to QCD and come with two analogous manifestly non-Abelian London-like equations. One equation describes the dual Meissner effect. The analogy is, however, not perfect: We can only speculate that there is some sort of chromo-magnetic superfluidity in QCD phenomena to which the second equation might be ascribed. Moreover, from more advanced Ginzburg-Landau (GL) theory of superconductivity it follows that the Meissner effect is a consequence of spontaneous breaking of the underlying global U(1) symmetry. This is certainly not the case of the dual Meissner effect. Fortunately, the derived London-like equations suggest a strongly color-paramagnetic behavior. We interpret it as a guide to the phenomenological Ginzburg-Landau-like manifestly gauge-invariant low-momentum QCD with the confining vacuum which behaves as a perfect color paramagnet (μ = +∞).

An effective three-dimensional de Sitter cosmology in string theory

Motivated by the lack of consensus on whether or not de Sitter (dS) lies in the Swampland, we use a recently developed braneworld construction and known Anti-de Sitter (AdS) vacua to compute an explicit effective dS cosmology in three dimensions. We consider a non-perturbative AdS4 vacuum decaying to another lower AdS4 vacuum via bubble-nucleation. We also consider the more speculative case where a dS4 decay to a Minkowski4. The Israel junction conditions are solved across the bubble and we obtain the Friedmann equations from which the cosmological constants can be read off, in the respective cases. The cosmological constants are computed in a flux background yielding small positive values admitting a dS cosmology. However, we find that an energetically viable model in the AdS to AdS case requires more fine-tuning.

Quantum phase transitions within a nuclear cluster model and an effective model of QCD

The catastrophe theory is applied to a nuclear cluster model and an effective model for QCD at low energy. The study of quantum phase transitions in the cluster model was considered in an earlier publication, but restricted to spherical clusters and on a semi-classical level. In the present contribution, we include the case of deformed clusters and determine the spectrum numerically as a function of an interaction parameter, where signatures of a quantum phase transition can be seen. It is shown that in this more complicated case, with deformation of the clusters, the catastrophe theory can be applied with some interesting consequences. A further example of a many-body problem is considered, namely an effective model of QCD, which is able to describe the low energy hadron spectrum and, when temperature is introduced, even ratios of particle-antiparticle productions. The catastrophe theory is able to provide useful information on the phase transition from a perturbative to a non-perturbative vacuum. These contributions show the universal usefulness of catastrophe theory, while more examples of applications to different fields are mentioned in the Introduction.

Holographic naturalness and topological phase transitions

We show that our Universe lives in a topological and non-perturbative vacuum state full of a large amount of hidden quantum hairs, the hairons. We will discuss and elaborate on theoretical evidences that the quantum hairs are related to the gravitational topological winding number in vacuo. Thus, hairons are originated from topological degrees of freedom, holographically stored in the de Sitter area. The hierarchy of the Planck scale over the Cosmological Constant (CC) is understood as an effect of a Topological Memory intrinsically stored in the space-time geometry. Any UV quantum destabilizations of the CC are re-interpreted as Topological Phase Transitions, related to the disappearance of a large ensamble of topological hairs. This process is entropically suppressed, as a tunneling probability from the [Formula: see text]- to the 0-states. Therefore, the tiny CC in our Universe is a manifestation of the rich topological structure of the space-time. In this portrait, a tiny neutrino mass can be generated by quantum gravity anomalies and accommodated into a large [Formula: see text]-vacuum state. We will re-interpret the CC stabilization from the point of view of Topological Quantum Computing. An exponential degeneracy of topological hairs non-locally protects the space-time memory from quantum fluctuations as in Topological Quantum Computers.

Quark and Gluon Condensates at a Finite Isospin Chemical Potential

The nonperturbative vacuum of quantum chromodynamics at a finite isospin chemical potential has been studied. Low-energy relations for the quark and gluon condensates have been derived ab initio. Analytical expressions for the quark and gluon condensates in the pion-condensate phase have been obtained at the tree level of the chiral perturbation theory. It has been shown that the quark condensate decreases with increasing μI, whereas the gluon condensate increases.

Relativistic self-energy decomposition of nuclear symmetry energy and equation of state of neutron matter within QCD sum rules

Properties of the relativistic nucleon self-energy decomposition of the symmetry energy as well as the equation of state (EOS) of pure neutron matter (PNM) are explored systematically within the QCD sum rules (QCDSR). Our main conclusions are as follows: (1) The five self-energy decomposition terms of the symmetry energy according to the nucleon Lorentz structure are carefully studied, leading to the conclusion that the symmetry energy increases as the nucleon sigma term ${\ensuremath{\sigma}}_{\mathrm{N}}$ increases and the contributions to the symmetry energy due to the momentum dependence of the self-energies in symmetric nuclear matter (SNM) are very small compared with those from other decomposition terms. (2) A smaller strange quark mass is found to generate a larger symmetry energy, and this correlation is useful for understanding the origins of the uncertainties on the (nucleonic matter) symmetry energy from quark level. (3) The EOS of PNM at low densities can be effectively approximated by ${E}_{\mathrm{n}}(\ensuremath{\rho})\ensuremath{\approx}{E}_{\mathrm{n}}^{\mathrm{FFG}}(\ensuremath{\rho})+(M\ensuremath{\rho}/2{\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}}_{\mathrm{vac}})[(1\ensuremath{-}\ensuremath{\xi})({\ensuremath{\sigma}}_{\mathrm{N}}/2{m}_{\mathrm{q}})\ensuremath{-}5]$ which depends only on several physical quantities such as ${m}_{\mathrm{q}},{\ensuremath{\sigma}}_{\mathrm{N}}$ and ${\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}}_{\mathrm{vac}}$, and this formula already has predictive power and the results are found to be consistent with those from other celebrated microscopic many-body theories at low densities. (4) The higher order density terms in quark condensates are shown to be important to describe the empirical EOS of PNM in the density region around and above nuclear saturation density, and these higher order density terms are also found to hinder the appearance of chiral symmetry restoration in PNM at high densities. (5) The symmetry energy is shown to depend strongly on the five-dimensional condensate ${\ensuremath{\langle}{g}_{\mathrm{s}}{q}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\sigma}\mathcal{G}q\ensuremath{\rangle}}_{\ensuremath{\rho},\ensuremath{\delta}}$, providing a useful approach to explore the symmetry energy through knowledge on the condensates which can be extracted from hadronic physics. (6) The twist-4 four-quark condensates are shown to have significant effects on the EOS of both SNM and PNM but have minor effects on the symmetry energy, and combined with the analyses on the effects of the higher order density terms in the chiral condensates, three parameter sets of QCDSR are constructed and they are shown to be able to describe the EOS of PNM and the symmetry energy within a wide range of densities. Our results in the present work demonstrate that the QCDSR approach can provide a useful way to understand the properties of dense nucleonic matter from nonperturbative QCD vacuum.

Transitions of orbifold vacua

We study the global structure of vacua of heterotic strings compactified on orbifolds T4/ℤN (N = 2, 3) in the presence of heterotic 5-branes. Gauge symmetry breaking associated with orbifold is described by instantons in the field theory. There is phase transition between small (zero size limit) instantons and heterotic 5-branes. This mechanism provides top-down, stringy account to the spectrum and modular invariance condition of non-perturbative vacua with 5-branes. Also it takes us from one vacuum to another by emitting and absorbing instantons. This means that many vacua with different gauge theories are in fact connected and are inherited from perturbative vacua. It follows that there is also transition of twisted instantons at the fixed points. Thus we can understand transitions among perturbative vacua as well.

Phenomenological theory of Superconductivity in the frameworks of QCD and RCD

Carrying out the study of phenomenological theory of superconductivity at microscopic level in the framework of QCD and restricted chromodynamics, we have investigated the topology of dyons in magnetic gauge space and showed that RCD vavuum containing plasma of dyons and anti-dyons behave like a chromomagnetic superconductor within which the chromomagnetic gluons propagate in the non-perturbative vacuum. Study of the superconductivity, dual superconductivity and color superconductivity have shown to automatically incorporate the condensation of monopoles or dyons ultimately leading to superconducting confining phases of the QCD vacuum.

Phenomenological theory of Superconductivity in the frameworks of QCD and RCD

Carrying out the study of phenomenological theory of superconductivity at microscopic level in the framework of QCD and restricted chromodynamics, we have investigated the topology of dyons in magnetic gauge space and showed that RCD vavuum containing plasma of dyons and anti-dyons behave like a chromomagnetic superconductor within which the chromomagnetic gluons propagate in the non-perturbative vacuum. Study of the superconductivity, dual superconductivity and color superconductivity have shown to automatically incorporate the condensation of monopoles or dyons ultimately leading to superconducting confining phases of the QCD vacuum.

Quarkonium Phenomenology from a Generalised Gauss Law

We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum potential with a weak-coupling description of the QCD medium. The resulting Gauss-law parametrisation is able to reproduce full lattice QCD data by using only a single temperature dependent parameter, the Debye mass m D . Using this parametrisation we model the in-medium potential at finite baryo-chemical potential, which allows us to estimate the Ψ ′ / J / Ψ ratio in heavy-ion collisions at different beam energies.

A Non-perturbative Hamiltonian Approach to the Cosmological Constant Problem

It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the non-perturbative vacuum energy density as a function of the cosmological constant with multiple choices of time. We also include a spatial curvature of the universe and generalize this calculation beyond cosmology at a classical level. We show that vacuum energy density depends on the choice of time, and in almost all time gauges, is a non-linear function of the cosmological constant. This non-linear relation is a calculation for the vacuum energy density given some arbitrary value of the cosmological constant. Hence, in this non-perturbative framework, certain conventional aspects of the cosmological constant problem do not arise. We also discuss why the conventional cosmological constant problem is not well-posed, and formulate and answer the question: “Does vacuum gravitate?”

Essentially Nonperturbative Vacuum Polarization Effects in a Two-Dimensional Dirac-Coulomb System for Z > Zcr: Vacuum Polarization Effects

For a planar Dirac-Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge Z > Zcr,1and radius R0, we consider essentially nonperturbative vacuum polarization effects in the overcritical region. Using results obtained in our preceding paper for the induced charge density \({\rho _{{\rm{VP}}}}(\vec r)\), we thoroughly consider the calculation of the vacuum energy eVPbased on the renormalization, the convergence of the partial expansion for \({\rho _{{\rm{VP}}}}(\vec r)\), and the behavior of the integral induced charge QVPin the overcritical region. In particular, we show that the renormalization using the fermionic loop with two external lines turns out to be a universal technique, which eliminates the divergence of the theory in the purely perturbative and essentially nonperturbative modes for \({\rho _{{\rm{VP}}}}(\vec r)\) and eVP. The most significant result is that for Z ≫ Zcr,1in such a system, the vacuum energy becomes a rapidly decreasing function of the source charge Z reaching large negative values; its behavior is estimated from below (in absolute value) as ∼ −|ηeffZ3|/R0. We also study the dependence of the effect of the decrease in eVPon the cutoff of the Coulomb asymptotics of the external field at different scales R1 gt; R0and R1 ≫ R0.