Search Results (87)

We discuss a quantization of the Yang–Mills theory with an internal symmetry group $SO(1,n)$ treated as a unified theory of all interactions. In one-loop calculations, we show that Einstein gravity can be considered as an approximation to gauge theory. We discuss the role of the Chern–Simons wave functions in the quantization. Full article

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation, these factors eventually overwhelm the small loop-counting parameter of $G{H}^2$, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. Generalizing the technique to quantum gravity is a two-step process, the first of which is the determination of the gauge fixing condition that will allow this summation to be realized; this is the subject of this paper. Moreover, we briefly discuss the second step, which shall obtain the Langevin equation, in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field. Full article

In this work, we undertake a comprehensive study of the functional measure of gravitational path integrals within a general framework involving non-trivial configuration spaces. As in Riemannian geometry, the integration over non-trival configuration spaces requires a metric. We examine the interplay between the functional measure and the dynamics of spacetime for general configuration-space metrics. The functional measure gives an exact contribution to the effective action at the one-loop level. We discuss the implications and phenomenological consequences of this correction, shedding light on the role of the functional measure in quantum gravity theories. In particular, we describe a mechanism in which the graviton acquires a mass from the functional measure without violating the diffeomorphism symmetry nor including Stückelberg fields. Since gauge invariance is not violated, the number of degrees of freedom goes as in general relativity. For the same reason, Boulware–Deser ghosts and the vDVZ discontinuity do not show up. The graviton thus becomes massive at the quantum level while avoiding the usual issues of massive gravity. Full article

Quantum field theory (QFT) and general relativity (GR) are pillars of modern physics, each supported by extensive experimental evidence. QFT operates within Lorentzian spacetime, while GR ensures local Lorentzian geometry. Despite their successes, these frameworks diverge significantly in their estimations of vacuum energy density, leading to the cosmological constant problem—a discrepancy where QFT estimates exceed observed values by 123 orders of magnitude. This paper addresses this inconsistency by tracing the cooling evolution of the universe’s gauge symmetries—from $SU\left(3\right)\times SU\left(2\right)\times U\left(1\right)$ at high temperatures to $SU\left(3\right)$ alone near absolute zero—motivated by the experimental Meissner effect. This symmetry reduction posits that $SU\left(3\right)$ forms the fundamental “atoms” of vacuum energy. Our analysis demonstrates that the calculated number of $SU\left(3\right)$ vacuum atoms reconciles QFT’s predictions with empirical observations, effectively resolving the cosmological constant problem. The third law of thermodynamics, by preventing the attainment of absolute zero, ensures the stability of $SU\left(3\right)$ vacuum atoms, providing a thermodynamic foundation for quark confinement. This stability guarantees a strictly positive mass gap defined by the vacuum energy density and implies a Lorentzian quantum structure of spacetime. Moreover, it offers insights into the origins of both gravity/gauge duality and gravity/superconductor duality. Full article

Research at the intersection of quantum gravity and quantum information theory has seen significant success in describing the emergence of spacetime and gravity from quantum states whose entanglement entropy approximately obeys an area law. In a different direction, the Kaluza–Klein proposal aims to recover gauge symmetries by means of dimensional reduction in higher-dimensional gravitational theories. Integrating both of these, gravitational and gauge degrees of freedom in $3+1$ dimensions may be obtained upon dimensional reduction in higher-dimensional emergent gravity. To this end, we show that entangled systems of two and three qubits can be associated with $5+1$- and $9+1$-dimensional spacetimes, respectively, which are reduced to $3+1$ dimensions upon singling out a preferred complex direction. Depending on the interpretation of the residual symmetry, either the Standard Model gauge group, $SU\left(3\right)\times SU\left(2\right)\times U\left(1\right)/{\mathbb{Z}}_6$, or the symmetry of Minkowski spacetime together with the gauge symmetry of a right-handed ‘half-generation’ of fermions can be recovered. Thus, there seems to be a natural way to accommodate the chirality of the weak force in the given construction. This motivates a picture in which spacetime emerges from the area law contribution to the entanglement entropy, while gauge and matter degrees of freedom are obtained due to area-law-violating terms. Furthermore, we highlight the possibility of using this construction in quantum simulations of Standard Model fields. Full article

This paper presents a novel approach to solving the Yang–Mills existence and mass gap problem using quantum information theory. We develop a rigorous mathematical framework that reformulates the Yang–Mills theory in terms of quantum circuits and entanglement structures. Our method provides a concrete realization of the Yang–Mills theory that is manifestly gauge-invariant and satisfies the Wightman axioms. We demonstrate the existence of a mass gap by analyzing the entanglement spectrum of the vacuum state, establishing a direct connection between the mass gap and the minimum non-zero eigenvalue of the entanglement Hamiltonian. Our approach also offers new insights into non-perturbative phenomena such as confinement and asymptotic freedom. We introduce new mathematical tools, including entanglement renormalization for gauge theories and quantum circuit complexity measures for quantum fields. The implications of our work extend beyond the Yang–Mills theory, suggesting new approaches to quantum gravity, strongly coupled systems, and cosmological problems. This quantum information perspective on gauge theories opens up exciting new directions for research at the intersection of quantum field theory, quantum gravity, and quantum computation. Full article

This is a review/research paper on anomalies applied in a bottom–up approach to standard model and gravity. It is divided into two parts. The first consists of a proper review of anomalies in quantum field theories. Anomalies are analyzed according to three different methods: a perturbative one based on a Feynman diagram, a non-perturbative one relying on the Schwinger–DeWitt approach, and, third, one hinging on the Atiyah–Singer family’s index theorem. The three methods are applied both to chiral gauge anomalies and trace anomalies. The fundamental distinction, which our presentation leads to, is between obstructive (O) and non-obstructive (NO) anomalies. The former is tied to the non-existence of fermion propagators, which fatally maim the corresponding theory. In the second part, we apply this analysis to the SM and a variety of its extensions, which are immersed in a gravitational background, and we find that they are all plagued by a residual chiral trace anomaly. To completely eliminate all kinds of dangerous anomalies in SM-like theories, we propose a somewhat unconventional scheme and exemplify it by means of an explicit model. The latter is a left–right symmetric model. We embed it in a Weyl geometry to render it a conformal invariant. We then deal with some of its quantum aspects, particularly its even (NO) trace anomalies and the means to preserve its conformal invariance at the quantum level. We briefly review renormalization and unitarity in the framework of similar models discussed in the existing literature. Finally, we present a possible (conjectural) application of the model to describe the junction between cosmology and quantum field theory. Full article

In this work, we elaborate further on a (3+1)-dimensional cosmological Running-Vacuum-type-Model (RVM) of inflation based on string-inspired Chern-Simons(CS) gravity, involving axions coupled to gravitational-CS(gCS) anomalous terms. Inflation in such models is caused by primordial-gravitational-waves(GW)-induced condensation of the gCS terms, which leads to a linear-axion potential. We demonstrate that this inflationary phase may be metastable, due to the existence of imaginary parts of the gCS condensate. These are quantum effects, proportional to commutators of GW perturbations, hence vanishing in the classical theory. Their existence is quantum-ordering-scheme dependent. We argue in favor of a physical importance of such imaginary parts, which we compute to second order in the GW (tensor) perturbations in the framework of a gauge-fixed effective Lagrangian, within a (mean field) weak-quantum-gravity-path-integral approach. We thus provide estimates of the inflation lifetime. On matching our results with the inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the String-Mass-Scale-to-Planck-Mass ratio, consistent with previous estimates by the authors in the framework of a dynamical-system approach to linear-axion RVM inflation. Finally, we examine the role of periodic modulations in the axion potential induced by non-perturbative effects on the slow-roll inflationary parameters, and find compatibility with the cosmological data. Full article

Within the framework of noncommutative (NC) deformation of gauge field theory by the angular twist, we first rederive the NC scalar and gauge field model from our previous papers, and then generalize it to the second order in the Seiberg–Witten (SW) map. It turns out that SW expansion is finite and that it ceases at the second order in the deformation parameter, ultimately giving rise to the equation of motion for the scalar field in the Reissner–Nordström (RN) metric that is nonperturbative and exact at the same order. As a further step, we show that the effective metric put forth and constructed in our previous work satisfies the equations of Einstein–Maxwell gravity, but only within the first order of deformation and when the gauge field is fixed by the Coulomb potential of the charged black hole. Thus, the obtained NC deformation of the Reissner–Nordström (RN) metric appears to have an additional off-diagonal element which scales linearly with a deformation parameter. We analyze various properties of this metric. Full article

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers. Full article

The spin-torsion theory is a gauge theory approach to gravity that expands upon Einstein’s general relativity (GR) by incorporating the spin of microparticles. In this study, we further develop the spin-torsion theory to examine spherically symmetric and static gravitational systems that involve free-falling macroscopic particles. We posit that the quantum spin of macroscopic matter becomes noteworthy at cosmic scales. We further assume that the Dirac spinor and Dirac equation adequately capture all essential physical characteristics of the particles and their associated processes. A crucial aspect of our approach involves substituting the constant mass in the Dirac equation with a scale function, allowing us to establish a connection between quantum effects and the scale of gravitational systems. This mechanism ensures that the quantum effect of macroscopic matter is scale-dependent and diminishes locally, a phenomenon not observed in microparticles. For any given matter density distribution, our theory predicts an additional quantum term, the quantum potential energy (QPE), within the mass expression. The QPE induces time dilation and distance contraction, and thus mimics a gravitational well. When applied to cosmology, our theory yields a static cosmological model. The QPE serves as a counterpart to the cosmological constant introduced by Einstein to balance gravity in his static cosmological model. The QPE also offers a plausible explanation for the origin of Hubble redshift (traditionally attributed to the universe’s expansion). The predicted luminosity distance–redshift relation aligns remarkably well with SNe Ia data from the cosmological sample of SNe Ia. In the context of galaxies, the QPE functions as the equivalent of dark matter. The predicted circular velocities align well with rotation curve data from the SPARC (Spitzer Photometry and Accurate Rotation Curves database) sample. Importantly, our conclusions in this paper are reached through a conventional approach, with the sole assumption of the quantum effects of macroscopic matter at large scales, without the need for additional modifications or assumptions. Full article

We consider the decay of the inflaton in Starobinsky-like models arising from either an $R+R^2$ theory of gravity or $N=1$ no-scale supergravity models. If Standard Model matter is simply introduced to the $R+R^2$ theory, the inflaton (which appears when the theory is conformally transformed into the Einstein frame) couples to matter predominantly in Standard Model Higgs kinetic terms. This will typically lead to a reheating temperature of ∼3 × ${10}^9$ GeV. However, if the Standard Model Higgs is conformally coupled to curvature, the decay rate may be suppressed and vanishes for conformal coupling $\xi =1/6$. Nevertheless, the inflaton decays through the conformal anomaly, leading to a reheating temperature of the order of ${10}^8$ GeV. The Starobinsky potential may also arise in no-scale supergravity. In this case, the inflaton decays if there is a direct coupling of the inflaton to matter in the superpotential or to gauge fields through the gauge kinetic function. We also discuss the relation between the theories and demonstrate the correspondence between the no-scale models and the conformally coupled $R+R^2$ theory (with $\xi =1/6$). Full article

The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and its supercurvature components with the double covering of the general affine group $\overline{GA}(4,\mathbb{R})$. Then, by means of an appropriate decomposition of the metalinear double-covering group $\overline{SL}(5,\mathbb{R})$ with respect to the general linear double-covering group $\overline{GL}(4,\mathbb{R})$, one can easily obtain the enlargements of the fields while remaining consistent with the BRST algebra. This leads to the descent equations, allowing us to build the observables of the theory by means of the BRST algebra constructed using a $\overline{sa}(5,\mathbb{R})$ algebra-valued superconnection. In particular, we discuss the construction of topological invariants with torsion. Full article

We demonstrate the equivalence of two different conjectures in the literature for the holographic entanglement negativity in AdS₃/CFT₂, modulo certain constants. These proposals involve certain algebraic sums of bulk geodesics homologous to specific combinations of subsystems, and the entanglement wedge cross section (EWCS) backreacted by a cosmic brane for the conical defect geometry in the bulk gravitational path integral. It is observed that the former conjectures reproduce the field theory replica technique results in the large central charge limit whereas the latter involves constants related to the Markov gap. In this context, we establish an alternative construction for the EWCS of a single interval in a CFT₂ at a finite temperature to resolve an issue for the latter proposal involving thermal entropy elimination for holographic entanglement negativity. Our construction for the EWCS correctly reproduces the corresponding field theory results modulo the Markov gap constant in the large central charge limit. Full article

Entertaining the possibility of time travel will invariably challenge dearly-held concepts in fundamental physics. It becomes relatively easy to construct multiple logical contradictions using differing starting points from various well-established fields of physics. Sometimes, the interpretation is that only a full theory of quantum gravity will be able to settle these logical contradictions. Even then, it remains unclear if the multitude of problems could be overcome. Yet as definitive as this seems to the notion of time travel in physics, such recourse to quantum gravity comes with its own, long-standing challenge to most of these counter-arguments to time travel: These arguments rely on time, while quantum gravity is (in)famously stuck with the problem of time. One attempt to answer this problem within the canonical framework resulted in the Page–Wootters formalism, and its recent gauge-theoretic reinterpretation as an emergent notion of time. Herein, we will begin a program to study toy models implementing the Hamiltonian constraint in quantum theory, with an aim toward understanding what an emergent notion of time can tell us about the (im)possibility of time travel. Full article