Frontiers of Quantum Black Holes

A black hole is a theoretical prediction of Einstein’s general theory of relativity, differently from Newtonian gravity, which is a non-relativistic gravity. In recent few years, its direct detection via gravitational waves and other multi-messenger observations have made it possible to test the prediction and hence its associated general relativity. From purely theoretical points of view, general relativity cannot be a complete description due to its not being compatible with quantum mechanics, which is a successful description of microscopic objects. In this article, we introduce the conceptional development of quantum-gravity theories and give brief sketches of fundamental problems in quantum black holes. As an interesting model of quantum black holes, we consider a collapsing shell of matter to form a Hayward black hole and investigate semiclassically quantum radiation from the shell. By using the Israel’s formulation and the functional Schrödinger formulation for massless quantum radiation, we find that the Hawking temperature can be deduced from the occupation number of excited states when the shell approaches its own horizon.

Building bases of loop integrands

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of ‘power-counting’ for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all ‘leading-(transcendental-)weight’ contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory — for generic helicities and arbitrary multiplicity.

Conformal Field Theory

Chapter 10 introduces the notion of conformal transformations and the important topic of the massless quantum field theories associated to the critical points of the statistical models. The chapter establishes the important conceptual result that the classification of all possible critical phenomena in two dimensions consists of finding out all possible irreducible representations of the Virasoro algebra. It covers the algebra of local fields, conformal invariance, Polyakov's theorem, quasi-primary fields, Ward identity, primary fields, the Schwartz derivative, the representation theory, radial quantization, the Hilbert space of conformal states, the use of the Cauchy formula, orthogonality of conformal families and structure constants of descendant fields.

Fermionic Casimir effect in Horava–Lifshitz theories

In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava–Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.

Note on soft photons and Faddeev–Jackiw symplectic reduction of quantum electrodynamics in the eikonal limit

In this note, we go over the recent soft photon model and Faddeev–Jackiw quantization of the massless quantum electrodynamics in the eikonal limit to some extent. Throughout our readdressing, we observe that the gauge potentials in both approaches become pure gauges and the associated eikonal Faddeev–Jackiw quantum bracket matches with the soft quantum bracket. These observations and the fact that the gauge fields in two cases localize in two-dimensional plane (even if it is spatial in soft photon case and (1[Formula: see text]+[Formula: see text]1)-dimensional Minkowski in the eikonal case) imply that there might be an interesting relation between these two distinct perspectives.

Generalized Dirac structure beyond the linear regime in graphene

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a fundamental minimal length (here graphene lattice spacing) and Lorentz violation (here the particle/hole asymmetry, the trigonal warping, etc.) is naturally obtained. We then show that the corresponding emergent field theory is a table-top realization of such scenarios, by explicitly computing the third-order Hamiltonian, and giving the general recipe for any order. Remarkably, our results imply that going beyond the low-energy approximation does not spoil the well-known correspondence with analog massless quantum electrodynamics phenomena (as usually believed), but rather it is a way to obtain experimental signatures of quantum-gravity-like corrections to such phenomena.