Consistent Quantum Theory Research Articles

Global flows of foliated gravity-matter systems

Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euclidean) time-direction in this framework. It equips spacetime with a foliation structure by encoding the gravitational degrees of freedom in a lapse function, shift vector, and a metric measuring distances on the spatial slices. We use the Wetterich equation to study the renormalization group flow of the graviton 2-point function extracted from the spatial metric. The flow is driven by the 3- and 4-point vertices generated by the foliated Einstein-Hilbert action supplemented by minimally coupled scalar and vector fields. We derive bounds on the number of matter fields cast by asymptotic safety. Moreover, we show that the phase diagram obtained in the pure gravity case is qualitatively stable within these bounds. An intriguing feature is the presence of an IR-fixed point for the graviton mass which prevents the squared mass taking negative values. This feature persists for any number of matter fields and, in particular, also in situations where there is no suitable interacting fixed point rendering the theory asymptotically safe. Our work complements earlier studies of the subject by taking contributions from the matter fields into account.

Carrollian conformal correlators and massless scattering amplitudes

The theory of particle scattering is concerned with transition amplitudes between states that belong to unitary representations of the Poincaré group. The latter acts as the isometry group of Minkowski spacetime \U0001d544, making natural the introduction of relativistic tensor fields encoding the particles of interest. Since the Poincaré group also acts as a group of conformal isometries of null infinity ℐ, massless particles can also be very naturally encoded into Carrollian conformal fields living on ℐ. In this work we classify the two- and three-point correlation functions such Carrollian conformal fields can have in any consistent quantum theory of massless particles and arbitrary dimension. We then show that bulk correlators of massless fields in \U0001d544 explicitly reduce to these Carrollian conformal correlators when evaluated on ℐ, although in the case of time-ordered bulk correlators this procedure appears singular at first sight. However we show that the Carrollian correlators of the descendant fields are perfectly regular and precisely carry the information about the corresponding S-matrix elements.

Saturating unitarity bounds at U-duality symmetric points

It has recently been shown that the leading Wilson coefficient in type II string theory can take (almost) all values allowed by unitarity, crossing symmetry and maximal supersymmetry in D = 10 and D = 9 dimensions. This suggests that string theory might define the unique consistent quantum theory of gravity with maximal supersymmetry. We study the minima of the leading Wilson coefficient in D = 6, 7 and 8 dimensions and find the global minimum at the point in moduli space with maximal symmetry. The minimum value turns out to always be negative for D ≤ 7.

Determining the normalization of the quantum field theory vacuum, with implications for quantum gravity

In a standard quantum field theory the norm of the vacuum state is taken to be finite. In this paper we provide a procedure, based on constructing an equivalent wave mechanics, for determining whether or not actually is finite. We provide an example based on a second-order plus fourth-order scalar field theory, a prototype for quantum gravity, in which it is not. In this example the Lorentzian path integral with a real measure diverges though the Euclidean path integral does not. Thus in this example contributions from the Wick rotation contour cannot be ignored. Since is not finite, use of the standard Feynman rules is not valid. And while these rules not only lead to states with negative norm, they in fact lead to states with infinite negative norm. However, if the fields in that theory are continued into the complex plane, we show that then there is a domain in the complex plane known as a Stokes wedge in which one can define an appropriate time-independent, positive and finite inner product, viz. the overlap of left-eigenstates and right-eigenstates of the Hamiltonian; with the vacuum state then being normalizable, and with there being no states with negative or infinite norm. In this Stokes wedge it is the Euclidean path integral that diverges while the Lorentzian path integral does not. The concerns that we raise in this paper only apply to bosons since the matrices associated with their creation and annihilation operators are infinite dimensional. Since the ones associated with fermions are finite dimensional, the fermion theory vacuum is automatically normalizable. We discuss some general implications of our results for quantum gravity studies, and show that they are relevant to the construction of a consistent, unitary and renormalizable quantum theory of gravity.

Composite Quantum Coriolis Forces

In a consistent quantum theory known as “non-Hermitian interaction picture” (NIP), the standard quantum Coriolis operator Σ(t) emerges whenever the observables of a unitary system are given in their quasi-Hermitian and non-stationary rather than “usual” representations. With Σ(t) needed, in NIP, in both the Schrödinger-like and Heisenberg-like dynamical evolution equations we show that another, amended and potentially simplified theory can be based on an auxiliary N−term factorization of the Dyson’s Hermitization map Ω(t). The knowledge of this factorization is shown to lead to a multiplet of alternative eligible Coriolis forces Σn(t) with n=0,1,…,N. The related formulae for the measurable predictions constitute a new formalism refered to as “factorization-based non-Hermitian interaction picture” (FNIP). The conventional NIP formalism (where N=1) becomes complemented by an (N−1)-plet of its innovative “hybrid” alternatives. Some of the respective ad hoc adaptations of observables may result in an optimal representation of quantum dynamics.

Introduction to Renormalization Theory and Chiral Gauge Theories in Dimensional Regularization with Non-Anticommuting γ5

This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for γ5. One goal was to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal was to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consistent quantum theories. Relevant topics include BPHZ renormalization, Slavnov–Taylor identities, the BRST formalism, and algebraic renormalization, as well as the theorems guaranteeing that dimensional regularization is a consistent regularization/renormalization scheme. All of these, including their proofs and interconnections, are explained and discussed in detail. Further, these theoretical concepts are illustrated in practical applications with the example of an Abelian and a non-Abelian chiral gauge theory. Not only the renormalization procedure for such chiral gauge theories is explained step by step, but also the results of all counterterms, including the symmetry-restoring ones, necessary for the consistent renormalization, are explicitly provided.

Group quantization of the black hole minisuperspace

The emergence of nontrivial symmetries for black holes minisuperspaces has been recently pointed out. These Noether symmetries possess non-null charges and hence map physical solutions to different ones. The symmetry group is isomorphic to the finite-dimensional Poincar\'e group $\mathrm{ISO}(2,1)$, whose irreducible representations are well known. This structure is used to build a consistent quantum theory of black hole minisuperspace. This has, among other consequences, the striking consequence of implying a continuous spectrum for the mass operator. Following loop quantum cosmology, we obtain a regularization scheme compatible with the symmetry structure. It is possible to study the evolution of coherent states following the classical trajectories in the low curvature regime. We show that this produces an effective metric where the singularity is replaced by a Killing horizon merging two asymptotically flat regions. The quantum correction comes from a fundamental discreteness of spacetime, and the uncertainty on the energy of the system. Remarkably, the effective evolution of semiclassical states is described by an effective Hamiltonian, related to the original one through a canonical transformation.

Swampland geometry and the gauge couplings

The purpose of this paper is two-fold. First we review in detail the geometric aspects of the swampland program for supersymmetric 4d effective theories using a new and unifying language we dub “domestic geometry”, the generalization of special Kähler geometry which does not require the underlying manifold to be Kähler or have a complex structure. All 4d SUGRAs are described by domestic geometry. As special Kähler geometries, domestic geometries carry formal brane amplitudes: when the domestic geometry describes the supersymmetric low-energy limit of a consistent quantum theory of gravity, its formal brane amplitudes have the right properties to be actual branes. The main datum of the domestic geometry of a 4d SUGRA is its gauge coupling, seen as a map from a manifold which satisfies the geometric Ooguri-Vafa conjectures to the Siegel variety; to understand the properties of the quantum-consistent gauge couplings we discuss several novel aspects of such “Ooguri-Vafa” manifolds, including their Liouville properties.Our second goal is to present some novel speculation on the extension of the swampland program to non-supersymmetric effective theories of gravity. The idea is that the domestic geometric description of the quantum-consistent effective theories extends, possibly with some qualifications, also to the non-supersymmetric case.

Noise and decoherence induced by gravitons

Behind the obvious goal of finding a consistent quantum theory of gravity lingers a question, namely if gravity is ``quantized'' at all. The authors work out in detail a recent proposal to detect quantum noise induced by gravitons in LIGO, and add another example, decoherence of massive particles induced by gravitons. Both concepts would prove the existence of quantum gravity and gravitons, the latter potentially in a tabletop experiment.

Quantum particles and the ergosphere of the Kerr metric

The existence of the ergosphere of the Kerr metric does not manifest itself in quantum equations for particles of different spins.To justify the Penrose process with energy extraction from the ergosphere, it is necessary to substantiate and prove its existence within the framework of the consistent quantum theory.

Trans-Planckian Censorship and the Swampland

In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. Applied to the case of scalar fields, it leads to conditions that are similar to the refined dS Swampland conjecture. For large field ranges, TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges. In particular for asymptotic regions of field space, TCC leads to a bound left|V^{prime}right|ge frac{2}{sqrt{left(d-1right)left(d-2right)}}V, which is consistent with all known cases in string theory. Like the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but it does allow sufficiently short-lived ones.

Radiation Reaction of a Jiggling Dipole in a Quantum Electromagnetic Field.

We show how to derive a consistent quantum theory of radiation reaction of a nonrelativistic point-dipole quantum oscillator by including the dynamical fluctuations of the position of the dipole. The proposed nonlinear theory displays neither runaway solutions nor acausal behavior without requiring additional assumptions. Furthermore, we show that quantum (zero-point) fluctuations of the electromagnetic field are necessary to satisfy the second law of thermodynamics. Our results are obtained by developing a nonperturbative technique involving a weak-coupling approximation at the level of the effective action.

Taming Hamiltonian systems with balanced loss and gain via Lorentz interaction: general results and a case study with Landau Hamiltonian

The kinetic energy term of Hamiltonian systems with balanced loss and gain is not semi-positive-definite, leading to instabilities at the classical as well quantum level. It is shown that an additional Lorentz interaction in the Hamiltonian allows the kinetic energy term to be semi-positive-definite and thereby, improving the stability properties of the system. Further, a consistent quantum theory admitting bound states may be obtained on the real line instead of Stoke wedges on the complex plane. The Landau Hamiltonian in presence of balanced loss and gain is considered for elucidating the general result. The kinetic energy term is semi-positive-definite provided the magnitude of the applied external magnetic field is greater than the magnitude of the ‘analogous magnetic field’ due to the loss-gain terms. It is shown that the classical particle moves on an elliptical orbit with a cyclotron frequency that is less than its value in absence of the loss-gain terms. The quantum system share the properties of the standard Landau Hamiltonian, but, with the modified cyclotron frequency. It is shown that the Hall current has non-vanishing components along the direction of the external uniform electric field and to its transverse direction. The Pauli equation in presence of balanced loss and gain is shown to be supersymmetric.

Exploring strong-field deviations from general relativity via gravitational waves

Two new observational windows have been opened to strong gravitational physics: gravitational waves, and very long baseline interferometry. This suggests observational searches for new phenomena in this regime, and in particular for those necessary to make black hole evolution consistent with quantum mechanics. We describe possible features of "compact quantum objects" that replace classical black holes in a consistent quantum theory, and approaches to observational tests for these using gravitational waves. This is an example of a more general problem of finding consistent descriptions of deviations from general relativity, which can be tested via gravitational wave detection. Simple models for compact modifications to classical black holes are described via an effective stress tensor, possibly with an effective equation of state. A general discussion is given of possible observational signatures, and of their dependence on properties of the colliding objects. The possibility that departures from classical behavior are restricted to the near-horizon regime raises the question of whether these will be obscured in gravitational wave signals, due to their mutual interaction in a binary coalescence being deep in the mutual gravitational well. Numerical simulation with such simple models will be useful to clarify the sensitivity of gravitational wave observation to such highly compact departures from classical black holes.

Swampland criteria in the slotheon field dark energy

We explore in this work whether Slotheon model of Dark Energy obeys the Swampland criteria of string theory. Since de Sitter vacuum is very difficult to construct in string theory the cosmological constant as an explanation of Dark Energy is almost ruled out in string theory since it involves a scalar potential $V$ with positive local minimum that ends up to a stable (or meta stable) de Sitter (ds) vacuum. In quintessence model however if the derivative of the scalar potential $V$ ($\nabla V$) is small and $\frac{|\nabla V|}{V} \sim {\cal {O}}(1)$ then in this situation the potential $V$ can be positive but the scalar field may not be at the minimum. For a consistent quantum theory of gravity the theory should not have any ds or meta stable ds vacua. In this regard the Swampland criterion is proposed which any low energy theory should obey to be consistent with quantum theory of gravity. This criterion is written as $|\nabla V|/V > c \sim {\cal {O}}(1)$. In this work we consider a scalar field model for Dark Energy namely the Slotheon Dark Energy model inspired by the theories of extra dimensions and show that this Dark Energy model agrees better with the Swampland criteria than the quintessence Dark Energy model.

Some Aspects of Complex Quantum Theories: A Brief Note

Theories with indefinite metric have a long and very rich history. Such theories are being used time to time in searching the solutions for many outstanding problems in physics over the several decades. However much attentions were not paid for these as they were not mathematically consistent with usual quantum theories. Towards the end of last century this field of research received huge boost, when attempts had been made to accommodate certain class of non-Hermitian theories in rigorous mathematical formulation. Subsequently it has been shown that certain specific types of non-Hermitian theories can lead to fully consistent quantum theories with complete real spectrum, unitary time evolution and probabilistic interpretation in a modified Hilbert space. Due to this important realisation, theories with complex Hamiltonian have become the topic of frontier research over last two decades and enormous applicationswere found in various branches of physics. In this brief note we try to review certain aspects of such theories where we have contributed. In particular, we discuss PT phase transition in non-relativistic, relativistic and quantum field theoretic systems and some new features of scattering in complex systems.

Some Aspects of Complex Quantum Theories: A Brief Note

Theories with indefinite metric have a long and very rich history. Such theories are being used time to time in searching the solutions for many outstanding problems in physics over the several decades. However much attentions were not paid for these as they were not mathematically consistent with usual quantum theories. Towards the end of last century this field of research received huge boost, when attempts had been made to accommodate certain class of non-Hermitian theories in rigorous mathematical formulation. Subsequently it has been shown that certain specific types of non-Hermitian theories can lead to fully consistent quantum theories with complete real spectrum, unitary time evolution and probabilistic interpretation in a modified Hilbert space. Due to this important realisation, theories with complex Hamiltonian have become the topic of frontier research over last two decades and enormous applicationswere found in various branches of physics. In this brief note we try to review certain aspects of such theories where we have contributed. In particular, we discuss PT phase transitionin non-relativistic, relativistic and quantum field theoretic systems and some new features of scattering in complex systems.

A holographic derivation of the weak gravity conjecture

The Weak Gravity Conjecture (WGC) demands the existence of superextremal particles in any consistent quantum theory of gravity. The standard lore is that these particles are introduced to ensure that extremal black holes are either unstable or marginally stable, but it is not clear what is wrong if this doesn’t happen. This note shows that, for a generic Einstein quantum theory of gravity in AdS, exactly stability of extremal black branes is in tension with rigorously proven quantum information theorems about entanglement entropy. Avoiding the contradiction leads to a nonperturbative version of the WGC, which reduces to the usual statement at weak coupling. The argument is general, and it does not rely on either supersymmetry or a particular UV completion, assuming only the validity of Einsteinian gravity, effective field theory, and holography. The pathology is related to the development of an infinite throat in the near-horizon region of the extremal solutions, which suggests a connection to the ER=EPR proposal.

The swampland, quintessence and the vacuum energy

It has recently been conjectured that string theory does not admit de Sitter vacua, and that quintessence explains the current epoch of accelerated cosmic expansion. A proposed, key prediction of this scenario is time-varying couplings in the dark sector, induced by the evolving quintessence field. We note that cosmological models with varying couplings suffer from severe problems with quantum corrections, beyond those shared by all quintessence models. The vacuum energy depends on the masses and couplings of the theory, and even small variations of parameters can lead to overwhelmingly large corrections to the effective potential. We find that quintessence models with varying parameters can be realised in consistent quantum theories by either: 1) enforcing exceptional levels of fine-tuning; 2) realising some unknown mechanism that cancels all undesirable contributions to the effective potential with unprecedented accuracy; or 3) ensuring that the quintessence field couples exclusively to very light states, and does not backreact on heavy fields.

Noncommutative geometry inspired rotating black string

Noncommutativity is an idea dating back to that early times of quantum mechanics and the string theory induced noncommutative (NC) geometry provided an effective framework to study the short distance spacetime dynamics. Also, string theory, a candidate for a consistent quantum theory of gravity, admits a variety of classical black hole solutions including black strings. In this paper, we study a NC geometry inspired rotating black string to cylindrical spacetime with a source given by a smeared distribution of mass. The resulting metric is a regular everywhere, i.e. curvature-singularity free rotating black string, that in large [Formula: see text] limit interpolates Lemos black string. Thermodynamical properties of the black strings are also investigated and exact expressions for the temperature, the entropy and the heat capacity are obtained. Owing to the NC correction in the solution, the thermodynamic quantities have also been modified and that the NC geometry inspired black string is always thermodynamically stable.