Scalar Field Action Research Articles

Dynamics of Carrollian scalar fields

Abstract Adopting an intrinsic Carrollian viewpoint, we show that the generic Carrollian scalar field action is a combination of electric and magnetic actions, found in the literature by taking the Carrollian limit of the relativistic scalar field. This leads to non-trivial dynamics: even a single particle with non-vanishing energy can move in Carrollian physics.

Research on the Tunneling Radiation of Bosons from the Kerr-Sen-like Black Hole by Einstein-Bumblebee Gravitational Theory

Lorentz-breaking theory not only affects the curved space-time background, but also modifies the dynamic equations of bosons and fermions in curved space-time to some extent. Therefore, we need to make appropriate corrections for the quantum tunneling radiation of bosons and fermions in different black hole spacetimes. New expressions of black hole Hawking temperature and other physical quantities modified by Lorentz-breaking theory and their physical meanings are obtained. In this paper, according to the Kerr-Sen-like (KSL) black hole spacetime metric obtained from Einstein-Bumblebee gravitational theory, by introducing the correction term of the aether-like field vector into the scalar field action and the d'Alembert operator in curved spacetime, and applying the variational principle in curved spacetime, the Lorentzbreaking correction term in the spacetime metric and the new form of the dynamic equation of the bosons with zero spin in KSL spacetime are studied. By correctly selecting the aether-like field vector corresponding to the KSL spacetime metric and solving the modified bosons dynamic equation, the modified quantum tunneling rate is obtained. On this basis, the Hawking temperature and Bekenstein- Hawking entropy of the black hole with Lorentz-breaking correction term are studied. The effects of Lorentz-breaking theory on the distribution of positive and negative energy levels of bosons and the maximum crossing of energy levels are also studied, and then the conditions of quantum non-thermal radiation in the black hole space-time is studied. At the end of this paper, the physical significance of a series of results obtained in this paper is discussed in depth. The results show that the modified form of the bosons dynamic equation in curved spacetime, taking into account Lorentz-breaking theory, is shown in equation (26) and equation (27). The new expressions of the quantum tunneling rate, Bekenstein-Hawking entropy, Hawking temperature and quantum non-thermal radiation energy range of KSL black hole are obtained by applying equation (26) to KSL black hole space-time. These results are useful for studying the quantum tunneling radiation characteristics of black holes. It should be noted that the above research results are obtained under the WKB theory and the semiclassical case. If the effects of different powers of Planck are to be considered, the above research methods and related results need to be used for further modified research by using beyond the semi-classical theory.

Uniqueness of the Jackiw non-Noetherian conformal scalar field

Jackiw was undoubtedly the first to exhibit an example of a scalar field action which is not conformally invariant whereas its equation of motion is. This feature has recently been dubbed as a non-Noetherian conformal scalar field. The paradigmatic example of Jackiw was the generalization to curved spacetime of the two-dimensional Liouville action. Here, we prove that, up to second order, this is the unique example of a non-Noetherian conformal scalar field in two dimensions. We establish this result using an old and somewhat forgotten theorem which is none other than the solution to the inverse problem of the calculus of variations.

The inflated Chern-Simons number in spectator chromo-natural inflation

The chromo-natural inflation (CNI) scenario predicts a potentially detectable chiral gravitational wave signal, generated by a Chern-Simons coupling between a rolling scalar axion field and an SU(2) gauge field with an isotropy-preserving classical background during inflation. However, the generation of this signal requires a very large integer Chern-Simons level, which can be challenging to explain or embed in a UV-complete model. We show that this challenge persists in the phenomenologically viable spectator field CNI (S-CNI) model. Furthermore, we show that a clockwork scenario giving rise to a large integer as a product of small integers can never produce a Chern-Simons level large enough to have successful S-CNI phenomenology. We briefly discuss other constraints on the model, both in effective field theory based on partial-wave unitarity bounds and in quantum gravity based on the Weak Gravity Conjecture, which may be relevant for further explorations of alternative UV completions.

Covariant effective action for scalar-tensor theories of gravity

We develop the calculation of the divergent part of one-loop covariant effective action for scalar fields minimally and non-minimally coupled to gravity using the generalized Schwinger-DeWitt technique. We derive the field-space metric using Vilkovisky's prescription and obtain new terms in the one-loop corrections which are absent in past literature with trivial choices of field-space metric. We further calculate the covariant versions of past results, obtained using the standard approach, by applying Barvinsky and Vilkovisky's extension to the ordinary Schwinger-DeWitt approach. For completeness, we study the one-loop gravitational corrections for a dilaton-extended two-field Starobinsky model and compare with known results.

Nonlocal scalar field in an external potential: The WKB approximation

We consider a nonlocal theory of a scalar massive field in a flat spacetime background in the presence of an external potential and construct WKB solutions for this theory. We use a model in which the kinetic part of the scalar field action is modified by changing $\ensuremath{\square}$ to $\ensuremath{\square}f(\ensuremath{\square})$ operator. We discuss conditions when the corresponding form factor $f$ is chosen so that the theory does not contain new unphysical degrees of freedom. We applied the obtained WKB solutions for study energy levels of the field trapped by a one-dimensional potential and the probability of the barrier penetration. This allows us to illustrate how the effects of the nonlocality change the known results obtained for the local field theory.

Scalar field theory for warm dark matter

The warm dark matter (WDM) can be described by a simple and useful model called reduced relativistic gas (RRG). In this work, it is analytically constructed the scalar field actions minimally and non-minimally coupled to gravity, which are equivalent to RRG in the sense they produce the same cosmological solutions for the conformal factor of the metric. In particular, we construct the scalar theory which corresponds to the model of an ultra-relativistic ideal gas of spinless particles possessing conformal symmetry. Finally, the possibility of supplementing our scalar field model for WDM with dynamical dark energy in the form of a running cosmological constant is also considered.

The cosmological constant from conformal transformations: Möbius invariance and Schwarzian action

The homogeneous Friedman–Lemaî tre-Robertson–Walker (FLRW) cosmology of a free scalar field with vanishing cosmological constant was recently shown to be invariant under the one-dimensional conformal group acting as Möbius transformations on the proper time. Here we generalize this analysis to arbitrary transformations of the proper time, , which are not to be confused with reparameterizations of the time coordinate. First, we show that the FLRW cosmology with a non-vanishing cosmological constant Λ ≠ 0 is also invariant under a group of conformal transformations. The associated conformal Noether charges form a Lie algebra which encodes the cosmic evolution. Second, we show that a cosmological constant can be generated from the Λ = 0 case through particular conformal transformations, realizing a compactification or de-compactification of the proper time depending on the sign of Λ. Finally, we propose an extended FLRW cosmological action invariant under the full group of conformal transformations on the proper time, by promoting the cosmological constant to a gauge field for conformal transformations or by modifying the scalar field action to a Schwarzian action. Such a conformally-invariant cosmology leads to a renewed problem of time and to the necessity to re-think inflation in purely time-deparameterized terms.

Holographic RG and exact RG in O(N) model

In this paper an Exact Renormalization Group (ERG) equation is written for the critical O(N) model in D-dimensions (with D≈3) at the Wilson-Fisher fixed point perturbed by a scalar composite operator. The action is written in terms of an auxiliary scalar field and reproduces correlation functions of a scalar composite operator. The equation is derived starting from the Polchinski ERG equation for the fundamental scalar field. As described in Sathiapalan and Sonoda (2017) [1] an evolution operator for the Polchinski ERG equation can be written in the form of a functional integral, with a D+1 dimensional scalar field theory action. In the case of the fundamental scalar field this action only has a kinetic term and therefore looks quite different from Holographic RG where there are potential terms. But in the composite operator case discussed in this paper, the ERG equation and consequently the D+1 dimensional action contains higher order potential terms for the scalar field and is therefore very similar to the case of Holographic RG. Furthermore this action can be mapped to a scalar field action in AdSD+1 using the techniques of ([1]). The leading cubic term of the potential is computed in this paper for D≈3 and expectedly vanishes in D=3 in agreement with results in the AdS/CFT literature.

Neutron Stars in f(R)-Gravity and Its Extension with a Scalar Axion Field

We present a brief review of general results about non-rotating neutron stars in simple R 2 gravity and its extension with a scalar axion field. Modified Einstein equations are presented for metrics in isotropical coordinates. The mass–radius relation, mass profile and dependence of mass from central density on various equations of state are given in comparison to general relativity.

On restricting to one-loop order the radiative effects in quantum gravity

The dimensionful nature of the coupling in the Einstein–Hilbert action in four dimensions implies that the theory is non-renormalizable; explicit calculation shows that beginning at two loop order, divergences arise that cannot be removed by renormalization without introducing new terms in the classical action. It has been shown that, by use of a Lagrange multiplier field to ensure that the classical equation of motion is satisfied in the path integral, radiative effects can be restricted to one-loop order. We show that by use of such Lagrange multiplier fields, the Einstein–Hilbert action can be quantized without the occurrence of non-renormalizable divergences. We then apply this mechanism to a model in which there is in addition to the Einstein–Hilbert action, a fully covariant action for a self-interacting scalar field coupled to the metric. It proves possible to restrict loop diagrams involving internal lines involving the metric to one-loop order; diagrams in which the scalar field propagates occur at arbitrary high order in the loop expansion. This model also can be shown to be renormalizable. Incorporating spinor and vector fields in the same way as scalar fields is feasible, and so a fully covariant Standard Model with a dynamical metric field can also be shown to be renormalizable.

Dynamically Generated Inflationary ΛCDM

Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.

Galileon scalar electrodynamics

We construct a consistent model of Galileon scalar electrodynamics. The model satisfies three essential requirements: (1) The action contains higher-order derivative terms, and obey the Galilean symmetry, (2) Equations of motion also satisfy Galilean symmetry and contain only up to second-order derivative terms in the matter fields and, hence do not suffer from instability, and (3) local U(1) gauge invariance is preserved. We show that the non-minimal coupling terms in our model are different from that of the real scalar Galileon models; however, they match with the Galileon real scalar field action. We show that the model can lead to an accelerated expansion in the early Universe. We discuss the implications of the model for cosmological inflation.

Hidden conformal symmetry of smooth braneworld scenarios

In this paper, we generalize our previous model ( arXiv:1705.09331 ), on a hidden conformal symmetry of smooth braneworld scenarios, to the case with two real scalar fields non-minimally coupled to gravity. The gauge condition reduces the action of the system to the action where gravity minimally couples to one of the scalar fields, plus a cosmological constant. We show that, depending on the internal symmetry of the scalar fields, the two possibilities, SO(2) or SO(1, 1), emerge. In the SO(2) case, we get a ghost-like scalar field action, which can describe two models — Standing Wave and Sine-Gordon smooth braneworlds. For the SO(1, 1) case we get the standard sign for the kinetic part of the scalar field. By breaking the SO(1, 1) symmetry (but keeping the conformal one) we are able to get two Randall–Sundrum models, with a non-minimal coupling and with a scalar field having hyperbolic potential. We conclude that this method can be seen as a solution-generating technique and a natural way to introduce nontrivial scalar fields that can provide smooth braneworld models.

Holographic Wilson's RG

In an earlier paper (arXiv:1706.03371) a holographic form of the Exact Renormalization Group (ERG) evolution operator for a (perturbed) free scalar field (CFT) in D dimensions was formulated. It was shown to be equivalent, after a change of variables, to a free scalar field action in AdSD+1 spacetime. We attempt to extend this result to a theory where the scalar field has an anomalous dimension. Instead of the ERG evolution operator, we examine the generating functional with an infrared cutoff, and derive the prescription of alternative quantization by using the change of variables introduced in the previous paper. The anomalous dimension is thus related in the usual way to the mass of the bulk scalar field. Computation of higher point functions remains difficult in this theory, but should be tractable in the large N version.

First Law of Holographic Complexity.

We investigate the variation of holographic complexity for two nearby target states. Based on Nielsen's geometric approach, we find the variation only depends on the end point of the optimal trajectory, a result which we designate the first law of complexity. As an example, we examine the complexity=action conjecture when the anti-de Sitter vacuum is perturbed by a scalar field excitation, which corresponds to a coherent state. Remarkably, the gravitational contributions completely cancel and the final variation reduces to a boundary term coming entirely from the scalar field action. Hence, the null boundary of Wheeler-DeWitt patch appears to act like the "end of the quantum circuit".

Nonperturbative one-loop effective action for QED with Yukawa couplings

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full nonperturbative effective action to one loop in the constant background field approximation. Our result is nonperturbative in the external fields, and goes beyond existing results in the literature which treat only the first nontrivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler–Heisenberg effective action or the Coleman–Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.

Tunneling wave function of the universe

The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave function: (1) tunneling boundary conditions in superspace, (2) Lorentzian path integral, and (3) quantum tunneling from initial universe of a vanishing size. We show that the superspace approach requires Robin boundary conditions for the scalar field modes, the path integral approach requires adding an appropriate boundary term to the scalar field action, and the initial universe approach requires the initial quantum state of the scalar field to be Euclidean vacuum. We find that all three approaches yield identical wave functions and that scalar field fluctuations are well behaved, contrary to earlier claims in the literature.

Gravitational form factors and decoupling in 2D

We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to the second order in the curvature and confirmed using Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a generalized “running” form of the Polyakov action for a nonminimal scalar field and the usual Polyakov action in the conformally invariant cases. In the infrared (IR) we establish the gravitational decoupling theorem, which can be seen directly from the form factors or from the physical beta function for fields of any spin.

Holographic bulk reconstruction with α′ corrections

We outline a holographic recipe to reconstruct $\alpha'$ corrections to AdS (quantum) gravity from an underlying CFT in the strictly planar limit ($N\rightarrow\infty$). Assuming that the boundary CFT can be solved in principle to all orders of the 't Hooft coupling $\lambda$, for scalar primary operators, the $\lambda^{-1}$ expansion of the conformal dimensions can be mapped to higher curvature corrections of the dual bulk scalar field action. Furthermore, for the metric pertubations in the bulk, the AdS/CFT operator-field isomorphism forces these corrections to be of the Lovelock type. We demonstrate this by reconstructing the coefficient of the leading Lovelock correction, aka the Gauss-Bonnet term in a bulk AdS gravity action using the expression of stress-tensor two-point function up to sub-leading order in $\lambda^{-1}$.