arXiv subjects

Emil Mottola

Publications and source records attributed to Emil Mottola.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational Vacuum Polarization: Decoupling and the Conformal Anomaly

A compact form of the stress tensor $\langle T^{ab}T^{cd}\rangle$ correlation function of a quantum scalar field of arbitrary mass $m$ and curvature coupling $\xi$ is presented, with particular emphasis on decoupling in the $m\to\infty$ limit and infrared origin of the conformal anomaly as $m \to 0$. The Ward Identity (WI) of covariant conservation is verified for the full second order metric variation of the one-loop effective action, of which $\langle T^{ab}T^{cd}\rangle$ is part, including local contact terms. This WI is satisfied by two tensors, one spin-2 (traceless) and the second spin-0 (traceful), each multiplied by a Lorentz invariant form factor computed in $n$-dimensional regularization. Minimal subtraction of pole terms at $n =4$ produces form factors that fail to satisfy decoupling for general $\xi \neq 1/6$, but can be simply amended to do so. Particular interest attaches to the $\xi=1/6$ case, in which the spin-0 form factor at $n =4$ is completely finite, requires no UV regularization or subtractions, and satisfies decoupling directly. Its imaginary part defines a spectral function that obeys a UV finite sum rule for any $m$, while its real part unambiguously determines the $\square R$ in the massless limit. Its $m^2$ dependence describes a Wilsonian renormalization group flow to an effective field theory limit at large distances. At $m= 0$ the spin-0 spectral function becomes a Dirac $\delta$-function at zero energy, demonstrating the existence of a massless scalar Goldstone collective excitation due to the conformal anomaly in the low energy effective theory of gravity.

hep-th↗

arXiv2025

Gravitational Vacuum Condensate Stars in the Effective Theory of Gravity

The low energy effective theory of gravity comprises two elements of quantum theory joined to classical general relativity. The first is the quantum conformal anomaly, which is responsible for macroscopic correlations on light cones and a stress tensor that can strongly modify the classical geometry at black hole horizons. The second is the formulation of vacuum energy as $\Lambda_{\rm eff}\!\propto\! F^2$ in terms of an exact $4$-form abelian gauge field strength $F\!=\!dA$. When $A$ is identified with the Chern-Simons $3$-form of the Euler class, defined in terms of the spin connection, a $J\cdot A$ interaction is generated by the conformal anomaly of massless fermions. Due to the extreme blueshifting of local frequencies in the near-horizon region of a `black hole,' the lightest fermions of the Standard Model can be treated as massless there, contributing to the anomaly and providing a $3$-current source $J$ for the `Maxwell' equation $d\ast F = \ast J$. In this phase boundary region, torsion is activated, and $F$ can change rapidly. The Schwarzschild black hole horizon is thereby replaced by a surface, with a positive surface tension and $\mathbb{R}\otimes \mathbb{S}^2$ worldtube topology, separating regions of differing vacuum energy. The result is a gravitational vacuum condensate star, a cold, compact, horizonless object with a $p_{_V}\!=\! - \rho_{_V}$ zero entropy, non-singular de Sitter interior and thin quantum phase boundary layer at the Schwarzschild radius $2GM/c^2$.

gr-qc↗

arXiv2023

Axions and Superfluidity in Weyl Semimetals

An effective field theory (EFT) for dynamical axions in Weyl semimetals (WSMs) is presented. A pseudoscalar axion excitation is predicted in WSMs at sufficiently low temperatures, independently of the strength of the Weyl fermion self-coupling. For strong fermion self-coupling the axion is the gapless Goldstone boson of chiral $U(1)^{\text{ch}}$ spontaneous symmetry breaking. For weak fermion self-coupling an axion is also generated at non-zero chiral density for Weyl nodes displaced in energy, as a gapless collective mode of correlated fermion pair excitations of the Fermi surface. This is an explicit example of the extension of Goldstone's theorem to symmetry breaking by the axial anomaly itself. In both cases the axion is a chiral density wave or phason mode of the superfluid state of the WSM, and the Weyl fermions form a chiral condensate $\langle\bar{\psi}\psi\rangle$ at low temperatures. In the presence of an applied magnetic field the axion mode becomes gapped, in analogy to the Anderson-Higgs mechanism in a superconductor. 't Hooft anomaly matching from ultraviolet to infrared scales is directly verified in the EFT approach. WSMs thus provide an interesting quantum system in which superfluid, non-Fermi liquid behavior, and a dynamical axion are predicted to follow directly from the axial anomaly in a consistent EFT that may be tested experimentally.

hep-th↗

arXiv2023

Quantum Effects of the Conformal Anomaly in a 2D Model of Gravitational Collapse

The macroscopic effects of the quantum conformal anomaly are evaluated in a simplified two-dimensional model of gravitational collapse. The effective action and stress tensor of the anomaly can be expressed in a local quadratic form by the introduction of a scalar conformalon field which satisfies a linear wave equation. A wide class of non-vacuum initial state conditions is generated by different solutions of this equation. An interesting subclass of solutions corresponds to initial states that give rise to an arbitrarily large semi-classical stress tensor on the future horizon of the black hole formed in classical collapse. These lead to modification and suppression of Hawking radiation at late times after the collapse, and potentially large backreaction effects on the horizon scale due to the conformal anomaly. The probability of non-vacuum initial conditions large enough to produce these effects is estimated from the Gaussian vacuum wave functional in the Schrodinger representation and shown to be of order 1. These results indicate that quantum effects of the conformal anomaly in non-vacuum states are relevant for gravitational collapse in the effective theory of gravity in four dimensions as well.

gr-qc↗

arXiv2023

Quantum Information Science and Technology for Nuclear Physics. Input into U.S. Long-Range Planning, 2023

In preparation for the 2023 NSAC Long Range Plan (LRP), members of the Nuclear Science community gathered to discuss the current state of, and plans for further leveraging opportunities in, QIST in NP research at the Quantum Information Science for U.S. Nuclear Physics Long Range Planning workshop, held in Santa Fe, New Mexico on January 31 - February 1, 2023. The workshop included 45 in-person participants and 53 remote attendees. The outcome of the workshop identified strategic plans and requirements for the next 5-10 years to advance quantum sensing and quantum simulations within NP, and to develop a diverse quantum-ready workforce. The plans include resolutions endorsed by the participants to address the compelling scientific opportunities at the intersections of NP and QIST. These endorsements are aligned with similar affirmations by the LRP Computational Nuclear Physics and AI/ML Workshop, the Nuclear Structure, Reactions, and Astrophysics LRP Town Hall, and the Fundamental Symmetries, Neutrons, and Neutrinos LRP Town Hall communities.

nucl-ex↗

arXiv2023

Gravitational Vacuum Condensate Stars

Gravitational vacuum condensate stars, proposed as the endpoint of gravitational collapse consistent with quantum theory, are reviewed. Gravastars are cold, low entropy, maximally compact objects characterized by a surface boundary layer and physical surface tension instead of an event horizon. Within this thin boundary layer the effective vacuum energy changes rapidly, such that the interior of a non-rotating gravastar is a non-singular static patch of de Sitter space with eq. of state p=-rho. Remarkably, essentially this same result is obtained by extrapolating Schwarzschild's 1916 constant density interior solution to its compact limit, showing how the black hole singularity theorems and the Buchdahl compactness bound are evaded. The surface stress tensor on the horizon is determined by a modification of the Lanczos-Israel junction conditions for null hypersurfaces, which is applied to rotating gravastar solutions as well. The fundamental basis for the quantum phase transition at the horizon is the stress tensor of the conformal anomaly, depending upon a new light scalar field in the low energy effective action for gravity. This scalar conformalon field allows the effective value of the vacuum energy described as a condensate of an exact 4-form abelian gauge field to change at the horizon. The resulting effective theory thus replaces the fixed constant Lambda of classical general relativity, and its apparently unnaturally large sensitivity to UV physics, with a dynamical condensate whose ground state value in empty flat space is zero identically. This provides both a solution to the cosmological constant problem and an effective Lagrangian dynamical framework for the boundary layer and interior of gravitational condensate stars. The status of present observational constraints and prospects for detection of gravastars through their gravitational wave and echo signatures are discussed.

gr-qc↗

arXiv2023

Gravitational Condensate Stars: An Alternative to Black Holes

A new solution for the endpoint of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, compact object with an interior de Sitter condensate phase and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These are separated by a phase boundary with a small but finite thickness of fluid with eq. of state p= +rho, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, instead of the Bekenstein-Hawking entropy. Unlike black holes, a collapsed star of this kind is thermodynamically stable and has no information paradox.

gr-qc↗

arXiv2022

The Effective Theory of Gravity and Dynamical Vacuum Energy

Gravity and general relativity are considered as an Effective Field Theory at low energies and macroscopic distances. The effective action of the conformal anomaly of light or massless quantum fields has significant effects on macroscopic scales, due to associated light cone singularities that are not captured by an expansion in local curvature invariants. A compact local form for the WZ effective action of the conformal anomaly and stress tensor is given, requiring the introduction of a new light scalar field, which it is argued should be included in the low energy effective action for gravity. The scalar conformalon couples to the conformal part of the spacetime metric and allows the effective value of the vacuum energy, described as a condensate of a 4-form abelian gauge field strength F=dA, to change in space and time. This is achieved by the identification of the torsion dependent part of the Chern-Simons 3-form of the Euler class with the gauge potential A, which enters the effective action of the conformal anomaly as a J.A interaction analogous to electromagnetism. The conserved 3-current J describes the worldtube of 2-surfaces that separate regions of differing vacuum energy. The resulting EFT thus replaces the fixed constant Lambda of classical gravity, and its apparently unnaturally large sensitivity to UV physics, with a dynamical condensate whose ground state value in empty flat space is Lambda = 0 identically. By allowing Lambda to vary rapidly near the 2-surface of a black hole horizon, the proposed EFT of dynamical vacuum energy provides an effective Lagrangian for gravitational condensate stars, as the final state of complete gravitational collapse consistent with quantum theory. The possible consequences of dynamical vacuum dark energy for cosmology, the cosmic coincidence problem, and the role of conformal invariance for other fine tuning issues in the SM are discussed.

hep-th↗

arXiv2022

Report of the Topical Group on Cosmic Probes of Fundamental Physics for for Snowmass 2021

Cosmic Probes of Fundamental Physics take two primary forms: Very high energy particles (cosmic rays, neutrinos, and gamma rays) and gravitational waves. Already today, these probes give access to fundamental physics not available by any other means, helping elucidate the underlying theory that completes the Standard Model. The last decade has witnessed a revolution of exciting discoveries such as the detection of high-energy neutrinos and gravitational waves. The scope for major developments in the next decades is dramatic, as we detail in this report.

hep-ph↗

arXiv2022

Beyond Einstein's Horizon: Gravitational Condensates and Black Hole Interiors in the Effective Theory of Gravity

Two of the most fundamental problems at the nexus of Einstein's classical General Relativity (GR) and Quantum Field Theory (QFT) are: (1) complete gravitational collapse, presumed in classical GR to lead to a Black Hole (BH) horizon and interior singularity, which generate a number of paradoxes for quantum theory; and (2) the origin and magnitude of the cosmological dark energy driving the accelerated expansion of the Universe. In this Snowmass white paper it is proposed that these twin puzzles on disparate scales are related, and that their resolution depends upon taking full account of the conformal anomaly of quantum matter in gravitational fields. The topological term in the anomaly leads naturally to the introduction of an abelian $3$-form gauge field, whose field strength can account for a variable gravitational condensate with the vacuum dark energy equation of state $p=-ρ$, the magnitude of which depends upon macroscopic boundary conditions rather than ultraviolet cutoffs. The resulting Effective Field Theory (EFT) of low energy quantum gravity results in a non-singular `BH' interior and physical surface replacing the classical event horizon, which is a gravitational condensate star free of any information paradox. The development and predictions of this EFT can be tested by gravitational waves and observational cosmology in the coming decade.

gr-qc↗

arXiv2022

Snowmass2021 Cosmic Frontier White Paper: Fundamental Physics and Beyond the Standard Model

Gravitational wave detectors are formidable tools to explore strong-field gravity, especially black holes and neutron stars. These compact objects are extraordinarily efficient at producing electromagnetic and gravitational radiation. As such, they are ideal laboratories for fundamental physics and have an immense discovery potential. The detection of black hole binaries by third-generation Earth-based detectors, space-based detectors and pulsar timing arrays will provide exquisite tests of general relativity. Loud "golden" events and extreme mass-ratio inspirals can strengthen the observational evidence for horizons by mapping the exterior spacetime geometry, inform us on possible near-horizon modifications, and perhaps reveal a breakdown of Einstein's gravity. Measurements of the black-hole spin distribution and continuous gravitational-wave searches can turn black holes into efficient detectors of ultralight bosons across ten or more orders of magnitude in mass. A precise monitoring of the phase of inspiralling binaries can constrain the existence of additional propagating fields and characterize the environment in which the binaries live, bounding the local dark matter density and properties. Gravitational waves from compact binaries will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address fundamental issues in our current understanding of the cosmos.

hep-ph↗

arXiv2022

Slowly rotating gravastars

We solve Einstein's equations for slowly-rotating gravitational condensate stars (gravastars) up to second order in the rotation by expanding about the spherically symmetric gravastar with de Sitter interior and Schwarzschild exterior matched at their common horizon. Requiring that the perturbations are finite on the null surface reduces the exterior geometry to that of a Kerr black hole, implying that a slowly rotating gravastar cannot be distinguished from a Kerr black hole by any measurement or observation restricted to the macroscopic spacetime exterior to the horizon. We determine the interior solution, the surface stress tensor, and the Komar mass and angular momentum localized on the slowly rotating horizon surface. With the interior equation of state fixed at $p=-ρ$, finite junction conditions on the null horizon surface necessarily lead to an interior solution with a singular core, where the perturbative expansion breaks down. Comparison to other models and implications for more rapidly rotating gravastars are briefly discussed.

gr-qc↗

arXiv2022

Surface Stress Tensor and Junction Conditions on a Rotating Null Horizon

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Although the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac $δ$-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities $[κ]$ and $[\cal J]$ of the surface gravity $κ$ and angular momentum density $\cal J$. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of $[κ]$ and $[\cal J]$. Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal $\boldsymbol n$ to the surface is allowed to tend continuously to a null vector. The relation to Israel's original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating `black hole' exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrabès-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

gr-qc↗

arXiv2021

TTT in CFT: Trace Identities and the Conformal Anomaly Effective Action

Stress-energy correlation functions in a general Conformal Field Theory (CFT) in four dimensions are described in a fully covariant approach, as metric variations of the quantum effective action in an arbitrary curved space background field. All Conservation, Trace and Conformal Ward Identities (CWIs), including contact terms, are completely fixed in this covariant approach. The Trace and CWIs are anomalous. Their anomalous contributions may be computed unambiguously by metric variation of the exact 1PI quantum effective action determined by the conformal anomaly of $\left\langle T^{μν}\right\rangle$ in $d = 4$ curved space. This action implies the existence of massless propagator poles in three and higher point correlators of $T^{μν}$ . The metric variations of the anomaly effective action in its local form in terms of a scalar conformalon field are carried out explicitly for the case of the correlator of three CFT stress-energy tensors, and the result is shown to coincide with the algebraic reconstruction of $\left\langle TTT\right\rangle$ from its transverse, tracefree parts, determined independently by the solution of the CWIs in d dimensional flat space in the momentum representation. This demonstrates that the specific analytic structure and massless poles predicted by the general curved space anomaly effective action are in fact a necessary feature of the exact solution of the anomalous CWIs in any $d = 4$ CFT.

hep-th↗

arXiv2021

Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly

We show that as a result of the axial anomaly, massless fermions at zero temperature define a relativistic quantum superfluid. The anomaly pole implies the existence of a gapless Chiral Density Wave (CDW), i.e. an axion-like acoustic mode of an irrotational and dissipationless Hamiltonian perfect fluid, that is a correlated fermion/anti-fermion pair excitation of the Fermi-Dirac sea. In $D\!=\!2$ dimensions the chiral superfluid effective action coincides with that of the Schwinger model as $e\rightarrow 0$, and the CDW acoustic mode is precisely the Schwinger boson. Since this identity holds also at zero chiral chemical potential, the Dirac vacuum itself may be viewed as a quantum superfluid state. The CDW collective boson is a $U(1)$ chiral phase field, which is gapless as a result of a novel, non-linear realization of Goldstone's theorem, extended to this case of symmetry breaking by an anomaly. A new local form of the axial anomaly bosonic effective action in any $D$ even spacetime is given, consistent with superfluidity, and its quantization is shown to be required by the anomalous Schwinger terms in fermion current commutators. In QED$_4$ this collective Goldstone mode appears as a massless pole in the axial anomaly triangle diagram, and is responsible for the macroscopic non-dissipative currents of the Chiral Magnetic and Chiral Separation Effects, as well as the Anomalous Hall Effect. In a constant uniform magnetic field an exact dimensional reduction from $D\!=\!4$ to $D\!=\!2$ occurs and the collective $e^+e^-$ CDW chiral pair excitation propagating along the magnetic field direction is a Chiral Magnetic Wave, which acquires a mass gap $M^2\!=\! e^{3}B/2π^{2}$. Possible realizations and tests of the theory of collective bosonic excitations due to the anomaly in Dirac/Weyl materials are briefly discussed.

hep-th↗

arXiv2019

Dislocation drag from phonon wind in an isotropic crystal at large velocities

The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force $v B(v, T, ρ)$ on the dislocation. In early studies the drag coefficient $B$ was computed and experimentally determined only for dislocation velocities $v$ much less than transverse sound speed, $c_t$. In this paper we derive analytic expressions for the velocity dependence of $B$ up to $c_t$ in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to $B$ in the range 1%-90% $c_t$ for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as $v \rightarrow c_t$, whereas $B$ is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.

cond-mat.mtrl-sci↗

arXiv2018

Scalar Gravitational Waves in the Effective Theory of Gravity

As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective action associated with the trace anomaly is expressed in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Linearized around flat spacetime, this semi-classical EFT admits scalar gravitational wave solutions in addition to the transversely polarized tensor waves of the classical Einstein theory. The amplitude of the scalar wave modes, as well as their energy and energy flux which are positive and contain a monopole moment, are computed. Astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals.

gr-qc↗

arXiv2017

Decay of the de Sitter Vacuum

The decay rate of the Bunch-Davies state of a massive scalar field in the expanding flat spatial sections of de Sitter space is determined by an analysis of the particle pair creation process in real time. The Feynman definition of particle and antiparticle Fourier mode solutions of the scalar wave equation, and their adiabatic phase analytically continued to the complexified time domain, show conclusively that the Bunch-Davies state is not the vacuum state at late times. The closely analogous creation of charged particle pairs in a uniform electric field is reviewed and Schwinger's result for the vacuum decay rate is recovered by the real time analysis. The vacuum decay rate in each case is also calculated by switching the background field on adiabatically, allowing it to act for a very long time, and then adiabatically switching it off again. In both the uniform electric field and de Sitter cases the particles created while the field is switched on are verified to be real, in the sense that they persist in the final asymptotic flat zero-field region. In the de Sitter case there is an interesting residual dependence of the rate on how the de Sitter phase is ended, indicating a greater sensitivity to spatial boundary conditions. The electric current of the created particles in the E-field case and their energy density and pressure in the de Sitter case are also computed, and the magnitude of their backreaction effects on the background field estimated. Possible consequences of the Hubble scale instability of the de Sitter vacuum for cosmology, vacuum dark energy, and the cosmological `constant' problem are discussed.

gr-qc↗