International Journal of Modern Physics A

In 1978, Salam and Strathdee suggested on the basis of Froissart boundedness that curvature-squared terms should be included in the gravitational Lagrangian. Despite the presence of ghosts in such theories, the subject has remained a persistent topic in approaches to quantum gravity and cosmology. In this article, the space of spherically symmetric solutions to such theories is explored, highlighting horizonless solutions, wormholes and non-Schwarzschild black holes.

By way of paying tribute to Abdus Salam, I first recall the ideas of higher unification which the two of us introduced in 1972–73 to remove certain shortcomings in the status of particle physics prevailing then, and then present their current role in theory as well as experiments. These attempts initiated the idea of grand unification and provided the core symmetry-structure $G(2,2,4)=SU{(2)}_L\times SU{(2)}_R\times SU(4)$-color towards such a unification. Embodied with quark-lepton unification and left-right symmetry, the symmetry $G(2,2,4)$ is uniquely chosen as being the minimal one that permits members of a family to belong to a single multiplet. The minimal extension of $G(2,2,4)$ to a simple group is given by the attractive SO(10)-symmetry that was suggested a year later. The new concepts, and the many advantages introduced by this core symmetry (which are, of course, retained by SO(10) as well) are noted. These include explanations of the observed: (i) (rather weird) electroweak and color quantum numbers of the members of a family; (ii) quantization of electric charge; (iii) electron-proton charge-ratio being $-1$; (iv) the co-existence of quarks and leptons; (v) likewise that of the three basic forces — the weak, electromagnetic and strong; (vi) the non-trivial cancelation of the triangle anomalies within each family; and opening the door for (vii) the appealing concept of parity being an exact symmetry of nature at the fundamental level.

In addition, as a distinguishing feature, both because of SU(4)-color and independently because of $\mathrm{\text{SU}}{(2)}_{\mathrm{\text{R}}}$ as well, the symmetry $G(2,2,4)$ introduced, to my knowledge, for the first time in the literature: (viii) a new kind of matter — the right-handed (RH) neutrino $({\nu }_R)$ — as a compelling member of each family, and together with it; (ix) (B-L) as a local symmetry. The RH neutrions — contrary to prejudices held in the 1970’s against neutrinos being massive and thereby against the existence of ${\nu }_R$’s as well — have in fact turned out to be an asset. They are needed to (a) understand naturally the tiny mass-scales observed in neutrino oscillations by combining the seesaw mechanism together with the unification ideas based on the symmetry SU(4)-color, and also (b) to implement the attractive mechanism of baryogenesis via leptogenesis. The quantitative success of the attempts as regards understanding both (a) and (b) are discussed in Sec. 6. These provide a clear support simultaneously for the following three features: (i) the seesaw mechanism, (ii) the SU(4)-color route to higher unification based on a symmetry like SO(10) or a string-derived $G(2,2,4)$ symmetry in 4D, as opposed to alternative symmetries like SU(5) or even [SU(3)]³, and (iii) the (B-L)-breaking scale being close to the unification scale $\sim 2\times 10^{16}$ GeV.

The observed dramatic meeting of the three gauge couplings in the context of low-energy supersymmetry, at a scale ${\mathrm{\text{M}}}_{\mathrm{\text{U}}}\sim 2\times 10^{16}$ GeV, providing strong evidence in favor of the ideas of both grand unification and supersymmetry, is discussed in Sec. 3. The implications of such a meeting in the context of string-unification are briefly mentioned. Weighing the possibility of a stringy origin of gauge coupling unification versus the familiar problem of doublet-triplet splitting in supersymmetric SO(10) (or SU(5)), I discuss the common advantages as well as relative merits and demerits of an effective SO(10) versus a string-derived $G(2,2,4)$ symmetry in 4D.

In Sec. 7, I discuss the hallmark prediction of grand unification, viz. proton decay, which is a generic feature of most models of grand unification. I present results of works carried out in collaboration with Babu and Wilczek and most recently with Babu and Tavartkiladze on expectations for decay modes and lifetimes for proton decay, including upper limits for such lifetimes, in the context of a well-motivated class of supersymmetric SO(10)-models. In view of such expectations, I stress the pressing need for having the next-generation large underground detectors — like DUNE and HyperKamiokande — coupled to long-baseline neutrino beams to search simultaneously with high sensitivity for (a) proton decay, (b) neutrino oscillations and (c) supernova neutrinos. It is remarked that the potential for major discoveries through these searches would be high.

Some concluding remarks on the invaluable roles of neutrinos and especially of proton decay in probing physics at the highest energy scales are made in the last section. The remarkable success of a class of supersymmetric grand unification models (discussed here) in explaining a large set of distinct phenomena is summarized. Noticing such a success and yet its limitations in addressing some fundamental issues within its premises, such as an understanding of the origin of the three families, and most importantly, the realization of a well-understood unified quantum theory of gravity describing reality, some wishes are expressed on the possible emergence and the desirable role of a string-derived grand-unified bridge between string/M-theory in higher dimensions and the world of phenomena at low energies.

If one modifies the Dirac equation in momentum space to $[{\gamma }^{\mu }{p}_{\mu }-m-\mathrm{\Delta }m(𝜃(p_0)-𝜃(-p_0))𝜃(p_{\mu }^2)]\psi (p)=0$, the symmetry of positive and negative energy eigenvalues is lifted by $m\pm \mathrm{\Delta }m$ for a small $\mathrm{\Delta }m$. The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations $𝜃(\pm p_0)𝜃(p_{\mu }^2)$ with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but nonlocal at the distance scale of the Planck length. The application of this Lorentz invariant CPT breaking mechanism to the possible mass splitting of the neutrino and antineutrino in the Standard Model is briefly discussed.

The charge given to me by the organisers of the memorial meeting for Prof. Abdus Salam’s 90th birthday is to recall my personal impressions of him and review an aspect of the standard model (SM) physics related to my work. Salam was, first and foremost, a brilliant theoretical physicist whose work is still very much en vogue, currently being tested precisely by the experiments at the Large Hadron Collider (LHC). Salam was, however, equally effective as a scientific advisor to many institutions, such as IAEA and CERN, but also to the government of Pakistan as the chief scientific strategist. He was also an untiring advocate of scientific research and higher education in developing countries, which took a concrete form in the International Centre for Theoretical Physics (ICTP) in Trieste. I discuss these aspects of his scientific life seen from my perspective in the first part. In the second part of my talk, which may appear as a disjoint piece to the first, I summarise some selected topics in rare B-decays — the current flavour physics frontier. Experiments carried out over several decades are largely in agreement with the SM, thanks also to dedicated theoretical effort in their interpretation. However, this field is undergoing an anomalous phase in a number of key measurements, in particular reported by LHCb, triggering a very lively debate and model building. These anomalies, which I review here, are too numerous to be ignored, but none is individually significant enough to announce a breakdown of the SM.

For all its brilliant success stories, theoretical physics is actually in a lamentable state. The best way to highlight the situation and at the same time point out that it is not difficult to do better — using action principles — is to present several examples.

At the beginning of last century we witnessed the emergence of new physics, quantum theory and gravitational theory, which gave us correct understanding of the world of atoms and deep insight into the structure of universe we live in. Towards the end of the century, string theory emerged as the most promising candidate to unify these two theories.

In this talk, I would like to assert that the understanding of the origin of physical constants, $\hslash$ (Planck constant) for quantum theory, and G (Newton’s gravitational constant) for gravitational theory within the framework of string theory is the key to understanding string theory.

Then, I will shift to experimental high energy physics and discuss the necessity of world-wide collaboration in the area of superconducting technology which is essential in constructing the 100 TeV hadron collider.

In recent years, studies of long-range interacting (LRI) systems have taken center stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In the first, introductory, Section 1, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. In Section 2, we discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers. In Section 3, we discuss the general scenario of dynamical evolution of generic LRI systems. In Section 4, we discuss an illustrative example of LRI systems, the Kardar–Nagel spin system, which involves discrete degrees of freedom, while in Section 5, we discuss a paradigmatic example involving continuous degrees of freedom, the so-called Hamiltonian mean-field (HMF) model. For the former, we demonstrate the effects of ensemble inequivalence and slow relaxation, while for the HMF model, we emphasize in particular the occurrence of the so-called quasistationary states (QSSs) during relaxation towards the Boltzmann–Gibbs equilibrium state. The QSSs are non-equilibrium states with lifetimes that diverge with the system size, so that in the thermodynamic limit, the systems remain trapped in the QSSs, thereby making the latter the effective stationary states. In Section 5, we also discuss an experimental system involving atoms trapped in optical cavities, which may be modelled by the HMF system. In Section 6, we address the issue of ubiquity of the quasistationary behavior by considering a variety of models and dynamics, discussing in each case the conditions to observe QSSs. In Section 7, we investigate the issue of what happens when a long-range system is driven out of thermal equilibrium. Conclusions are drawn in Section 8.