Conformal Scalar Field Research Articles

Cooling-heating properties of the FRW universe in gravity with a generalized conformal scalar field

In this paper, within the framework of modified gravity involving a conformal scalar field, we investigate the Joule-Thomson expansion of the Friedmann-Robertson-Walker (FRW) universe to identify cooling and heating regions. We observe a divergence in the Joule-Thomson coefficient (μ), precisely at the apparent horizon (RA=−2α) of the FRW universe, under conditions of negative gravitational coupling (α<0), which aligns with a thermodynamic singularity. Furthermore, we determine the inversion temperature and pressure for the FRW universe, and elucidate the salient features of inversion and isenthalpic curves in the temperature-pressure (T-P) plane. We compare these findings with results obtained under Einstein gravity, discussing the influence of the modification term on the cooling and heating properties of the FRW universe. This work presents insights into the formation of cooling and heating regions within the FRW universe, contributing to a deeper understanding of the physical mechanisms behind cosmic expansion history.

Nonlinearly charging the conformally dressed black holes preserving duality and conformal invariance

We start this paper by concisely rederiving ModMax, which is nothing but the unique nonlinear extension of Maxwell’s equations preserving conformal and duality invariance. The merit of this new derivation is its transparency and simplicity since it is based on an approach where the elusive duality invariance is manifest. In the second part, we couple the ModMax electrodynamics to Einstein gravity with a cosmological constant together with a standard conformal scalar field, and new stationary spacetimes with dyonic charges are found. These solutions are later used as seed configurations to generate nonlinearly charged (super-)renormalizably dressed spacetimes by means of a known generating method that we extend to include any nonlinear conformal electrodynamics. We end by addressing the issue of how to generalize some of these results to include the recently studied non-Noetherian conformal scalar fields, whose equation of motion still enjoys conformal symmetry even though its action does not. It turns out that the static non-Noetherian conformally dressed black holes also become amenable to being charged by ModMax. Published by the American Physical Society 2024

Heat capacity and quantum compressibility of dynamical spacetimes with thermal particle creation

This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, (1) placing what was studied in [] for thermal quantum fields in the context of early universe cosmology, and (2) extending the considerations of vacuum compressibility of dynamical spaces treated in [] to dynamical spacetimes with thermal quantum fields. We begin with a warning that thermal equilibrium condition is not guaranteed to exist or maintained in a dynamical setting and thus finite temperature quantum field theory in cosmological spacetimes needs more careful considerations than what is often described in textbooks. A full description requires nonequilibrium quantum field theory in dynamical spacetimes using “in-in” techniques. A more manageable subclass of dynamics is where thermal equilibrium conditions are established at both the beginning and the end of evolution, where the in-thermal state and the out-thermal state are both well defined. Particle creation in the full history can then be calculated in this in-out asymptotically-stationary setup via the S-matrix transition amplitudes. Here we shall assume an in-vacuum state. It has been shown that if the intervening dynamics has an initial period of exponential expansion, such as in inflationary cosmology, particles created from the parametric amplification of the vacuum fluctuations in the initial vacuum will have a thermal spectrum measured at the out-state. Under these conditions finite temperature field theory can be applied to calculate the quantum thermodynamic quantities. Here we consider a massive conformal scalar field in a closed four-dimensional Friedmann-Lemaître-Robertson-Walker universe based on the simple analytically solvable Bernard-Duncan model. We calculate the energy density of particles created from an in-vacuum and derive the partition function. From the free energy we then derive the heat capacity and the quantum compressibility of these spacetimes with thermal particle creation. We end with some discussions and suggestions for further work in this program of studies. Published by the American Physical Society 2024

Hairy black holes and naked singularities of quartic quasi-topological gravity within the framework of logarithmic electrodynamics

We establish a new family of hairy black hole solutions of quartic quasi-topological gravity sourced by logarithmic electrodynamics and conformal scalar field. Here, we derive the metric function defining black hole structures and investigate the effects of electric charge, scalar hair, and dimensionality parameters on the location of the event horizon. The corresponding hairy black hole solution of the quartic quasi-topological gravity sourced by Maxwell field is also deduced in this setup. In addition, we also compute thermodynamic quantities for these objects such as temperature, entropy and heat capacity, and check the first law of thermodynamics. Furthermore, the impacts of scalar hair and electric charge on the divergences of heat capacity and extreme black hole’s horizon radius are also investigated. Finally, we also analyze thermodynamic stability and critical behavior of the resultant hairy black holes at the event horizon.

Is the Coleman–de Luccia Action Minimum?: An AdS/CFT Approach

Abstract We use the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to find the least bounce action in an AdS false vacuum state, i.e. the most probable decay process of the metastable AdS vacuum within the Euclidean formalism by Callan and Coleman. It was shown that the O(4) symmetric bounce solution leads to the action minimum in the absence of gravity, but it is nontrivial in the presence of gravity. The AdS/CFT duality is used to evade the difficulties particular to a metastable gravitational system. To this end, we show that the Fubini bounce solution in CFT, corresponding to the Coleman–de Luccia (CdL) bounce in AdS, gives the least action among all finite bounce solutions in a conformal scalar field theory. Thus, we prove that the CdL action is the least action among all possible large and thin-wall configurations under certain conditions.

Thermodynamics and Phase Transitions of Dyonic AdS Black Holes in Gauss-Bonnet-Scalar Gravity

In this paper, by treating the cosmological constant as a thermodynamic pressure, we study the thermodynamics and phase transitions of the dyonic AdS black holes in Gauss-Bonnet-Scalar gravity, where the conformal scalar field is considered. In a more general extended phase space, we first verified the first law of black hole thermodynamics, and find that it is always true. Meanwhile, the corresponding Smarr relation is also obtained. Then, we found that this black hole exhibits interesting critical behaviors in six dimensions, i.e., two swallowtails can be observed simultaneously. Interestingly, in a specific parameter space, we observed the small/intermediate/large black hole phase transitions, with the triple point naturally appearing. Additionally, the small/large black hole phase transition, similar to the liquid/gas phase transition of the van der Waals fluids, can also be found in other parameter regions. Moreover, we note that the novel phase structure composed of two separate coexistence curves discovered in the dyonic AdS black holes in Einstein-Born-Infeld gravity disappears in Gauss-Bonnet-Scalar gravity. This suggests that this novel phase structure may be related to gravity theory, and importantly, it is generally observed that the triple point is a universal property of dyonic AdS black holes. On the other hand, we calculated the critical exponents near the critical points and found that they share the same values as in mean field theory. Finally, it is true that these results will provide some deep insights into the interesting thermodynamic properties of the dyonic AdS black holes in the background of conformal scalar fields.

Dimensionally continued black holes sourced by a conformally coupled scalar field and Chaplygin-like dark fluid

In this paper, we study the higher dimensional black holes of Lovelock gravity coupled with a conformal scalar field. The matter source of gravity is suggested to come from the Chaplygin-like dark fluid, i.e., the hybrid of a dark matter and dark energy. We primarily focus on dimensionally continued gravity where the coupling parameters are reduced into two independent parameters, i.e., the Newtonian and cosmological constants. In this specific case of Lovelock gravity, we derive the metric function that describes the hairy black holes surrounded by dark fluid. For these objects, the basic thermodynamic quantities are worked out. We discuss how the unified dark fluid affects both local and global thermodynamic stabilities. We also demonstrate that the radiation spectrum is proportional to the change in entropy of the hairy black holes. Lastly, the hairy black holes in the presence of Chaplygin-like dark fluid are briefly investigated within the context of generic Lovelock gravity.

Non-Noetherian conformal scalar fields

Recently, an extension of the standard four-dimensional scalar conformal action, yielding a second-order field equation that remains conformally invariant, was proposed. In spite of this, the corresponding action is not invariant under conformal transformations and this motivates us to define the notion of non-Noetherian conformal scalar field. In this article, we go further by determining the most general action in four dimensions that gives rise to a non-Noetherian conformal scalar field satisfying a second-order equation. This task is achieved by using the solution to the inverse problem of the calculus of variations. Surprisingly enough, the standard equation is shown to be extended by a non-Noetherian conformal piece involving a nonminimal coupling with a very particular combination of squared curvature terms, which is none other than the one defining the so-called Critical Gravity. We also prove that the most general second-order Euler–Lagrange equation for a conformal scalar field involves additional Noetherian conformal nonminimal couplings defined by an arbitrary function of the Weyl tensor. The recently proposed non-Noetherian conformal extension is recovered as a particular example of this function.

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.

Quasitopological electromagnetism, conformal scalar field and Lovelock black holes

In this work, we present the new higher dimensional dyonic black hole solutions of the Lovelock-scalar gravity coupled with quasitopological electromagnetism. First, we concentrate on the dimensionally continued gravity and construct the solution that describes the dyonic black holes with conformal scalar hair in diverse dimensions. We study the physical properties and discuss the effects of the quasitopological electromagnetism and conformal scalar field on the local thermodynamic stability of these dimensionally continued black holes. Next, we derive the solutions that describe the conformal hairy black holes of the Gauss–Bonnet and third order Lovelock gravities in the presence of quasitopological electromagnetism. The basic thermodynamic quantities of these black holes are calculated as well.

Black holes in a new gravitational theory with trace anomalies

In a new gravitational theory with the trace anomaly recently proposed by Gabadadze, we study the existence of hairy black hole solutions on a static and spherically symmetric background. In this theory, the effective 4-dimensional action contains a kinetic term of the conformal scalar field related to a new scale M¯ much below the Planck mass. This property can overcome a strong coupling problem known to be present in general relativity supplemented by the trace anomaly as well as in 4-dimensional Einstein-Gauss-Bonnet gravity. We find a new hairy black hole solution arising from the Gauss-Bonnet trace anomaly, which satisfies regular boundary conditions of the conformal scalar and metric on the horizon. Unlike unstable exact black hole solutions with a divergent derivative of the scalar on the horizon derived for some related theories in the literature, we show that our hairy black hole solution can be consistent with all the linear stability conditions of odd- and even-parity perturbations.

The Lamb shift in the BTZ spacetime

We study the Lamb shift of a two-level atom arising from its coupling to the conformal massless scalar field, which satisfies the Dirichlet boundary condition, in the Hartle-Hawking vacuum in the BTZ spacetime, and find that the Lamb shift in the BTZ spacetime is structurally similar to that of a uniformly accelerated atom near a perfectly reflecting boundary in (2+1)-dimensional flat spacetime. Our results show that the Lamb shift is suppressed in the BTZ spacetime as compared to that in the flat spacetime as long as the transition wavelength of the atom is much larger than AdS radius of the BTZ spacetime while it can be either suppressed or enhanced if the transition wavelength of the atom is much less than AdS radius, depending on the location of the atom. In contrast, the Lamb shift is always suppressed very close to the horizon of the BTZ spacetime and remarkably it reduces to that in the flat spacetime as the horizon is approached although the local temperature blows up there.

General light-cone gauge approach to conformal fields and applications to scalar and vector fields

Totally symmetric arbitrary spin conformal fields propagating in the flat space of even dimension greater than or equal to four are studied. For such fields, we develop a general ordinary-derivative light-cone gauge formalism and obtain restrictions imposed by the conformal algebra symmetries on interaction vertices. We apply our formalism for the detailed study of conformal scalar and vector fields. For such fields, all parity-even cubic interaction vertices are obtained. The cubic vertices obtained are presented in terms of dressing operators and undressed vertices. We show that the undressed vertices of the conformal scalar and vector fields are equal, up to overall factor, to the cubic vertices of massless scalar and vector fields. Various conjectures about interrelations between the cubic vertices for conformal fields in conformal invariant theories and the cubic vertices for massless fields in Poincaré invariant theories are proposed.

Critique of the use of geodesics in astrophysics and cosmology

Since particles obey wave equations, in general one is not free to postulate that particles move on the geodesics associated with test particles. Rather, for this to be the case one has to be able to derive such behavior starting from the equations of motion that the particles obey, and to do so one can employ the eikonal approximation. To see what kind of trajectories might occur we explore the domain of support of the propagators associated with the wave equations, and extend the results of some previous propagator studies that have appeared in the literature. For a minimally coupled massless scalar field the domain of support in curved space is not restricted to the light cone, while for a conformally coupled massless scalar field the curved space domain is only restricted to the light cone if the scalar field propagates in a conformal to flat background. Consequently, eikonalization does not in general lead to null geodesics for curved space massless rays even though it does lead to straight line trajectories in flat spacetime. Equal remarks apply to the conformal invariant Maxwell equations. However, for massive particles one does obtain standard geodesic behavior this way, since they do not propagate on the light cone to begin with. Thus depending on how big the curvature actually is, in principle, even if not necessarily in practice, the standard null-geodesic-based gravitational bending formula and the general behavior of propagating light rays are in need of modification in regions with high enough curvature. We show how to appropriately modify the geodesic equations in such situations. We show that relativistic eikonalization has an intrinsic light-front structure, and show that eikonalization in a theory with local conformal symmetry leads to trajectories that are only globally conformally symmetric. Propagation of massless particles off the light cone is a curved space reflection of the fact that when light travels through a refractive medium in flat spacetime its velocity is modified from its free flat spacetime value. In the presence of gravity spacetime itself acts as a medium, and this medium can then take light rays off the light cone. This is also manifest in a conformal invariant scalar field theory propagator in two spacetime dimensions. It takes support off the light cone, doing so in fact even if the geometry is conformal to flat. We show that it is possible to obtain eikonal trajectories that are exact without approximation, and show that normals to advancing wavefronts follow these exact eikonal trajectories, with these trajectories being the trajectories along which energy and momentum are transported. In general then, in going from flat space to curved space one does not generalize flat space geodesics to curved space geodesics. Rather, one generalizes flat space wavefront normals (normals that are geodesic in flat space) to curved space wavefront normals, and in curved space normals to wavefronts do not have to be geodesic.

Pseudo Entropy in U(1) gauge theory

We study the properties of pseudo entropy, a new generalization of entanglement entropy, in free Maxwell field theory in d = 4 dimension. We prepare excited states by the different components of the field strengths located at different Euclidean times acting on the vacuum. We compute the difference between the pseudo Rényi entropy and the Rényi entropy of the ground state and observe that the difference changes significantly near the boundary of the subsystems and vanishes far away from the boundary. Near the boundary of the subsystems, the difference between pseudo Rényi entropy and Rényi entropy of the ground state depends on the ratio of the two Euclidean times where the operators are kept. To begin with, we develop the method to evaluate pseudo entropy of conformal scalar field in d = 4 dimension. We prepare two states by two operators with fixed conformal weight acting on the vacuum and observe that the difference between pseudo Rényi entropy and ground state Rényi entropy changes only near the boundary of the subsystems. We also show that a suitable analytical continuation of pseudo Rényi entropy leads to the evaluation of real-time evolution of Rényi entropy during quenches.

Integrating three-loop modular graph functions and transcendentality of string amplitudes

Modular graph functions (MGFs) are SL(2, ℤ)-invariant functions on the Poincaré upper half-plane associated with Feynman graphs of a conformal scalar field on a torus. The low-energy expansion of genus-one superstring amplitudes involves suitably regularized integrals of MGFs over the fundamental domain for SL(2, ℤ). In earlier work, these integrals were evaluated for all MGFs up to two loops and for higher loops up to weight six. These results led to the conjectured uniform transcendentality of the genus-one four-graviton amplitude in Type II superstring theory. In this paper, we explicitly evaluate the integrals of several infinite families of three-loop MGFs and investigate their transcendental structure. Up to weight seven, the structure of the integral of each individual MGF is consistent with the uniform transcendentality of string amplitudes. Starting at weight eight, the transcendental weights obtained for the integrals of individual MGFs are no longer consistent with the uniform transcendentality of string amplitudes. However, in all the cases we examine, the violations of uniform transcendentality take on a special form given by the integrals of triple products of non-holomorphic Eisenstein series. If Type II superstring amplitudes do exhibit uniform transcendentality, then the special combinations of MGFs which enter the amplitudes must be such that these integrals of triple products of Eisenstein series precisely cancel one another. Whether this indeed is the case poses a novel challenge to the conjectured uniform transcendentality of genus-one string amplitudes.

Magnetized hairy black holes of dimensionally continued gravity coupled to double-logarithmic electrodynamics

A recently proposed model for nonlinear electrodynamics has been minimally coupled to dimensionally continued gravity, and the topological black holes in the presence of conformal scalar field were studied. In this set-up, the new magnetized hairy black hole solution has been found and its thermodynamic properties have also been analysed. The exact expressions for mass, entropy, Hawking temperature and heat capacity are derived, and local thermodynamic stability for the resulting black holes has been checked. In addition to this, the modified Smarr’s formula is constructed and the generalized first law has also been verified. Finally, the hairy magnetized black holes in general Lovelock-scalar gravity have also been studied.

Uniqueness of static spacetime with conformal scalar in higher dimensions

We discuss the uniqueness of asymptotically flat and static spacetimes in the $n$-dimensional Einstein-conformal scalar system. This theory potentially has a singular point in the field equations where the effective Newton constant diverges. We will show that the static spacetime with the conformal scalar field outside a certain surface $S_p$ associated with the singular point is unique.

Boundary conformal field theory at large charge

We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a |ϕ|6 interaction in three dimensions and the O(2) Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether’s theorem in perturbative theories.

Cauchy data space and multisymplectic formulation of conformal classical field theories

In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been added to account for field theories that are scale invariant, flat spaces, and because some conformal fields can be exactly solved or classified. In particular, we will solve the example of a conformal scalar field using the geometric Hamilton–Jacobi theory that is explicitly proposed for conformal fields on a multisymplectic manifold. To complete the geometric approach to study field theories, we propose the Hamilton–Jacobi theory for conformal fields in a Cauchy data space, in which space and time are split separately and the dynamics is depicted in an infinite-dimensional manifold.