arXiv subjects

Wen-Yuan Ai

Publications and source records attributed to Wen-Yuan Ai.

At least 37 records · Page 2Linked to original sources

arXiv2024

Double-well instantons in finite volume

Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green's functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.

hep-th↗

arXiv2024

Criterion for ultra-fast bubble walls: the impact of hydrodynamic obstruction

The Bödeker-Moore thermal friction is usually used to determine whether or not a bubble wall can run away. However, the friction on the wall is not necessarily a monotonous function of the wall velocity and could have a maximum before it reaches the Bödeker-Moore limit. In this paper, we compare the maximal hydrodynamic obstruction, a frictional force that exists in local thermal equilibrium, and the Bödeker-Moore thermal friction. We study the former in a fully analytical way, clarifying its physical origin and providing a simple expression for its corresponding critical phase transition strength above which the driving force cannot be balanced out by the maximal hydrodynamic obstruction. We find that for large parameter space, the maximal hydrodynamic obstruction is larger than the Bödeker-Moore thermal friction, indicating that the conventional criterion for the runaway behavior of the bubble wall may have to be modified. We also explain how to apply efficiently the modified criterion to particle physics models and discuss possible limitations of the analysis carried out in this paper.

hep-ph↗

arXiv2024

The QCD theta-parameter in canonical quantization

The role of the QCD theta-parameter is investigated in pure Yang-Mills theory in the spacetime given by the four-dimensional Euclidean torus. While in this setting the introduction of possibly unphysical boundary conditions is avoided, it must be specified how the sum over the topological sectors is to be carried out. To connect with observables in real time, we perceive the partition function as the trace over the canonical density matrix. The system then corresponds to one of a finite temperature on a spatial three-torus. Carrying out the trace operation requires canonical quantization and gauge fixing. Fixing the gauge and demanding that the Hermiticity of the Hamiltonian is maintained leads to a restriction of the Hilbert space of physical wave functionals that generalizes the constraints derived from imposing Gauss' law. Consequently, we find that the states in the Hilbert space are properly normalizable under an inner product that integrates over each physical configuration represented by the gauge potential one time and one time only. The observables derived from the constrained Hilbert space do not violate charge-parity symmetry. We note that an exact hidden symmetry of the theory that is present for arbitrary values of theta in the Hamiltonian is effectively promoted to parity conservation in this constrained space. These results, derived on a torus in order to avoid the introduction of boundary conditions, also carry over to Minkowski spacetime when taking account of all possible gauge transformations.

hep-th↗

arXiv2024

False vacuum decay rates, more precisely

We develop a method for accurately calculating vacuum decay rates beyond the thin-wall regime in a pure scalar field theory at the one-loop level of the effective action. It accounts for radiative effects resulting from quantum corrections to the classical bounce, including gradient effects stemming from the inhomogeneity of the bounce background. To achieve this, it is necessary to compute not only the functional determinant of the fluctuation operator in the background of the classical bounce but also its functional derivative evaluated at the classical bounce. The former is efficiently calculated using the Gel'fand-Yaglom method. We illustrate how the latter can also be calculated with the same method, combined with a computation of various Green's functions.

hep-ph↗

arXiv2023

Logarithmically divergent friction on ultrarelativistic bubble walls

We calculate the friction experienced by ultrarelativistic bubble walls resulting from the $1 \rightarrow 2$ light-to-heavy transition process, with finite-wall-width effects fully taken into account. In this process, the light particle is excited from the order-parameter scalar field, while the two heavy particles are excitations of a dark matter scalar field. Unlike earlier estimates suggesting a friction scaling as $γ_w^0$, where $γ_w$ represents the Lorentz factor of the wall velocity, our more precise numerical analysis reveals a logarithmic dependence of the friction on $γ_w$. We offer a numerical fit to capture this frictional pressure accurately. Our analysis verifies that the friction stemming from the $1 \rightarrow 2$ light-to-heavy transition is typically much smaller than the friction from the $1 \rightarrow 1$ transmission of the dark matter particles.

hep-ph↗

arXiv2023

Model-independent bubble wall velocities in local thermal equilibrium

Accurately determining bubble wall velocities in first-order phase transitions is of great importance for the prediction of gravitational wave signals and the matter-antimatter asymmetry. However, it is a challenging task which typically depends on the underlying particle physics model. Recently, it has been shown that assuming local thermal equilibrium can provide a good approximation when calculating the bubble wall velocity. In this paper, we provide a model-independent determination of bubble wall velocities in local thermal equilibrium. Our results show that, under the reasonable assumption that the sound speeds in the plasma are approximately uniform, the hydrodynamics can be fully characterized by four quantities: the phase strength $α_n$, the ratio of the enthalpies in the broken and symmetric phases, $Ψ_n$, and the sound speeds in both phases, $c_s$ and $c_b$. We provide a code snippet that allows for a determination of the wall velocity and energy fraction in local thermal equilibrium in any model. In addition, we present a fit function for the wall velocity in the case $c_s = c_b = 1/\sqrt 3$.

astro-ph.CO↗

arXiv2023

Instability of bubble expansion at zero temperature

In the context of false vacuum decay at zero temperature, it is well known that bubbles expand with uniform proper acceleration. We show that this uniformly accelerating expansion suffers from an instability related to the bubble size. This can be observed in Minkowski spacetime as a tachyonic mode in the spectrum of fluctuations for the energy functional in the reference frame in which the uniformly accelerating bubble wall appears static. In such a frame, arbitrary small perturbations cause an amplifying departure from the static wall solution. This implies that the nucleated bubble is not a critical point of the energy functional in the rest frame of nucleation but becomes one in the accelerating frame. The aforementioned instability for vacuum bubbles can be related to the well-known instability for the nucleated critical static bubbles during finite-temperature phase transitions in the rest frame of the plasma. It is therefore proposed that zero-temperature vacuum decays as seen from accelerating frames have a dual description in terms of finite-temperature phase transitions.

hep-th↗

arXiv2023

Wilsonian approach to the interaction $ϕ^2(iϕ)^\varepsilon$

We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $ϕ^2(iϕ)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\varepsilon$-expansion. Particular attention is therefore paid to the two interesting cases $\varepsilon=1,2$, and the one-loop beta functions for the coupling associated with the interaction $iϕ^3$ and $-ϕ^4$ are computed. It is found that the $-ϕ^4$ theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and $n$-point functions are also derived.

hep-th↗

arXiv2023

$\mathcal{P}\mathcal{T}$-symmetric $-gφ^4$ theory

The scalar field theory with potential $V(φ)=\textstyle{\frac{1}{2}} m^2φ^2-\textstyle{\frac{1}{4}} gφ^4$ ($g>0$) is ill defined as a Hermitian theory but in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric framework it is well defined, and it has a positive real energy spectrum for the case of spacetime dimension $D=1$. While the methods used in the literature do not easily generalize to quantum field theory, in this paper the path-integral representation of a $\mathcal{P}\mathcal{T}$-symmetric $-gφ^4$ theory is shown to provide a unified formulation for general $D$. A new conjectural relation between the Euclidean partition functions $Z^{\mathcal{P}\mathcal{T}}(g)$ of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric theory and $Z_{\rm Herm}(λ)$ of the $λφ^4$ ($λ>0$) Hermitian theory is proposed: $\log Z^{\mathcal{P}\mathcal{T}}(g)=\textstyle{\frac{1}{2}} \log Z_{\rm Herm}(-g+{\rm i} 0^+)+\textstyle{\frac{1}{2}}\log Z_{\rm Herm}(-g-{\rm i} 0^+)$. This relation ensures a real energy spectrum for the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric $-gφ^4$ field theory. A closely related relation is rigorously valid in $D=0$. For $D=1$, using a semiclassical evaluation of $Z^{\mathcal{P}\mathcal{T}}(g)$, this relation is verified by comparing the imaginary parts of the ground-state energy $E_0^{\mathcal{P}\mathcal{T}}(g)$ (before cancellation) and $E_{0,\rm Herm}(-g\pm {\rm i} 0^+)$.

hep-th↗

arXiv2022

Dissipation of oscillating scalar backgrounds in an FLRW universe

We study the dissipation of oscillating scalar backgrounds in a spatially flat Friedmann-Lemaître-Robertson-Walker universe using non-equilibrium quantum field theory. To be concrete, a $Z_2$-symmetric two-scalar model with quartic interactions is used. For quasi-harmonic oscillations, we adopt the multi-scale analysis to obtain analytical approximate expressions for the evolution of the scalar background in terms of the retarded self-energy and retarded proper four-vertex function. Different from the case in flat spacetime, we find that in an expanding universe the condensate decay in this model can be complete only if the imaginary part of the retarded self-energy is not negligibly small. The microphysical interpretation of the imaginary parts of the retarded self-energy and retarded proper four-vertex function in terms of particle production is also discussed.

hep-ph↗

arXiv2022

The limits of the strong $CP$ problem

While $CP$ violation has never been observed in the strong interactions, the QCD Lagrangian admits a $CP$-odd topological interaction proportional to the so called $θ$ angle, which weighs the contributions to the partition function from different topological sectors. The observational bounds are usually interpreted as demanding a severe tuning of $θ$ against the phases of the quark masses, which constitutes the strong $CP$ problem. Here we report on recent challenges to this view based on a careful treatment of boundary conditions in the path integral and of the limit of infinite spacetime volume, which leads to $θ$ dropping out of fermion correlation functions and becoming unobservable, implying that $CP$ is preserved in QCD.

hep-th↗

arXiv2022

Bubble wall velocities in local equilibrium

It is commonly expected that a friction force on the bubble wall in a first-order phase transition can only arise from a departure from thermal equilibrium in the plasma. Recently however, it was argued that an effective friction, scaling as $γ_w^2$ (with $γ_w$ being the Lorentz factor for the bubble wall velocity), persists in local equilibrium. This was derived assuming constant plasma temperature and velocity throughout the wall. On the other hand, it is known that, at the leading order in derivatives, the plasma in local equilibrium only contributes a correction to the zero-temperature potential in the equation of motion of the background scalar field. For a constant plasma temperature, the equation of motion is then completely analogous to the vacuum case, the only change being a modified potential, and thus no friction should appear. We resolve these apparent contradictions in the calculations and their interpretation and show that the recently proposed effective friction in local equilibrium originates from inhomogeneous temperature distributions, such that the $γ_w^2$-scaling of the effective force is violated. Further, we propose a new matching condition for the hydrodynamic quantities in the plasma valid in local equilibrium and tied to local entropy conservation. With this added constraint, bubble velocities in local equilibrium can be determined once the parameters in the equation of state are fixed, where we use the bag equation in order to illustrate this point. We find that there is a critical value of the transition strength $α_{\rm crit}$ such that bubble walls run away for $α>α_{\rm crit}$.

hep-ph↗

arXiv2021

Absence of $CP$ violation in the strong interactions

We derive correlation functions for massive fermions with a complex mass in the presence of a general vacuum angle. For this purpose, we first build the Green's functions in the one-instanton background and then sum over the configurations of background instantons. The quantization of topological sectors follows for saddle points of finite Euclidean action in an infinite spacetime volume and the fluctuations about these. For the resulting correlation functions, we therefore take the infinite-volume limit before summing over topological sectors. In contrast to the opposite order of limits, the chiral phases from the mass terms and from the instanton effects then are aligned so that, in absence of additional phases, these do not give rise to observables violating charge-parity symmetry. This result is confirmed when constraining the correlations at coincident points by using the index theorem instead of instanton calculus.

hep-th↗

arXiv2021

Nonsingular black hole in two-dimensional asymptotically flat spacetime

We study a special two-dimensional dilaton gravity with Lagrangian $\mathcal{L}=\frac{1}{2}\sqrt{-g}(ϕR+{λ^2}{\rm sech}^2ϕ)$ where $λ$ is a parameter of dimension mass. This theory describes two-dimensional spacetimes that are asymptotically flat. Very interestingly, it has an exact solution for the metric, $\d s^2=-(c+\tanh λx)\d t^2+ \d x^2/(c+\tanh λ x)$, parametrized by $c$. For $c\in(-1,1)$, the solution presents an event horizon but no singularity. Because of the kink profile for the metric components appearing in the solution, we refer to the spacetime described by the metric as a {\it gravitational domain wall} with the wall simply being the event horizon and separating two asymptotically Minkowskian spacetimes. The global causal structure for such an object is studied via coordinate extension and the thermodynamical quantities are computed. Only when $c\in(-1,0]$ are the entropy and energy non-negative.

hep-th↗

arXiv2021

Oscillating scalar dissipating in a medium

We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.

hep-ph↗

arXiv2020

Schwinger effect and false vacuum decay as quantum-mechanical tunneling of a relativistic particle

We present a simple and intuitive description of both, the Schwinger effect and false vacuum decay through bubble nucleation, as tunneling problems in one-dimensional relativistic quantum mechanics. Both problems can be described by an effective potential that depends on a single variable of dimension length, which measures the separation of the particles in the Schwinger pair, or the radius of a bubble for the vacuum decay. We show that both problems can be described as tunneling in one-dimensional quantum mechanics if one interprets this variable as the position of a relativistic particle with a suitably defined effective mass. The same bounce solution can be used to obtain reliable order of magnitude estimates for the rates of the Schwinger pair production and false vacuum decay.

hep-th↗

arXiv2020

Gradient effects on false vacuum decay in gauge theory

We study false vacuum decay for a gauged complex scalar field in a polynomial potential with nearly degenerate minima. Radiative corrections to the profile of the nucleated bubble as well as the full decay rate are computed in the planar thin-wall approximation using the effective action. This allows to account for the inhomogeneity of the bounce background and the radiative corrections in a self-consistent manner. In contrast to scalar or fermion loops, for gauge fields one must deal with a coupled system that mixes the Goldstone boson and the gauge fields, which considerably complicates the numerical calculation of Green's functions. In addition to the renormalization of couplings, we employ a covariant gradient expansion in order to systematically construct the counterterm for the wave-function renormalization. The result for the full decay rate however does not rely on such an expansion and accounts for all gradient corrections at the chosen truncation of the loop expansion. The ensuing gradient effects are shown to be of the same order of magnitude as non-derivative one-loop corrections.

hep-th↗

arXiv2020

A note on the novel 4D Einstein-Gauss-Bonnet gravity

Recently, a novel 4D Einstein-Gauss-Bonnet gravity has been proposed by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] by rescaling the coupling $α\rightarrow α/(D-4)$ and taking the limit $D\rightarrow 4$ at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit $D\rightarrow 4$ in the higher $D$-dimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with four-dimensional spacetime indices the contribution corresponding to the Gauss-Bonnet term vanishes identically in the equations of motion. A necessary condition (but may not be sufficient) for this procedure to work is that there is an embedding of the four-dimensional spacetime into the higher $D$-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with 2D Einstein gravity, we show several subtleties when applying the method used in [Phys. Rev. Lett. 124, 081301 (2020)].

gr-qc↗