Peter Suranyi 87th Birthday Festschrift

The following sections are included:

• Preface
• Contents

We investigate the hidden and visible symmetries in two-field cosmological models with hyperbolic field spaces. We find the most general solutions of the Noether symmetry conditions, when the field-space metric is that of an elementary hyperbolic surface. There are three types of such surfaces: the Poincaré disk, the hyperbolic punctured disk and the hyperbolic annuli. We recover all previously known symmetry generators for each of them. In addition, we find new hidden and visible symmetries in the punctured disk and annuli cases.

I describe a set of useful generalizations of the idea of a symmetry of a physical system that have been discovered over the last 30 years and indicate a few simple examples where they are realized in physical systems.

In this contribution to Peter Suranyi Festschrift, we study the Halliday–Suranyi perturbation method for calculating the energy eigenvalues of the quartic anharmonic oscillator.

In this chapter, I review the role of kaon physics in establishing some of the fundamental principles of the standard model and the role it is still playing in testing these principles.

Reggeon field theory (RFT), originally developed in the context of high-energy diffraction scattering, has a much wider applicability, describing, for example, the universal critical behavior of stochastic population models as well as probabilistic geometric problems, such as directed percolation. In 1975, Suranyi and others developed cut RFT (CRFT), which can incorporate the cutting rules of Abramovskii, Gribov and Kancheli for how each diagram contributes to inclusive cross-sections. In this chapter, we describe the corresponding probabilistic interpretations of CRFT: as a population model of two genotypes, which can reproduce both asexually and sexually, and as a kind of bicolor directed percolation problem. In both cases, the AGK rules correspond to simple limiting cases of these problems.

The following sections are included:

• Introduction
• Review of Matrix Model–String Theory Duality
• Quantum Quench in the Model
• Some Exact Solutions
• Emergent Spacetime
• Conclusions
• A Personal Note From S.R.D.
• Acknowledgments
• References

Lattice gauge theory simulations are our principal probe of the masses of the light quarks. Results from such computations are the primary evidence against the m_u = 0 solution to the strong CP problem. The large-N approximation offers an independent approach to light quarks. We extend the existing literature, noting that one can determine the parameters of the non-linear sigma model through second order in quark mass, rule out the m_u = 0 hypothesis and make predictions for outputs of lattice gauge theory and phenomenological fits. Crucial in this analysis is a Wilsonian effective action at scales above the η′ mass. One can test self-consistently the validity of aspects of this framework, and it may well be good for the part in three levels; we also note consistency with some phenomenological fits and existing lattice results.

We argue that deriving an effective field theory from string theory requires a Wilsonian perspective with a physical cutoff. Employing proper time regularization, we demonstrate the decoupling of states and contrast this with what happens in dimensional regularization. In particular, we point out that even if the cosmological constant (CC) calculated from some classical action at some ultra-violet scale is negative, this does not necessarily imply that the CC calculated at cosmological scales is also negative and discuss the possible criteria for achieving a positive CC starting with a CC at the string/KK scale which is negative. Obviously, this has implications for swampland claims.

In this chapter, we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra $F_4^{″}$ which is the split rank one form of the exceptional Lie algebra F₄. We classify the reducible Verma modules over F₄ which are compatible with this induction. Thus, we obtain the classification of the corresponding invariant differential operators.

The heat kernel expansion on even-dimensional hyperbolic spaces is asymptotic at both short and long times, with interestingly different Borel properties for these short- and long-time expansions. Resummations in terms of incomplete gamma functions provide accurate extrapolations and analytic continuations, relating the heat kernel to the Schrödinger kernel and the heat kernel on hyperbolic space to the heat kernel on spheres. For the diagonal heat kernel, there is also a duality between short and long times which mixes the scalar and spinor heat kernels.

Ultralight bosons are prime candidates for the identity of dark matter, and in many theories of their origin, it is natural for more than one flavor to be present. Such degrees of freedom can form gravitationally bound states known as boson stars during structure formation, and interactions (gravitational, self and mutual interactions) can modify the macroscopic properties of these objects. In this contribution to the Peter Suranyi Festschrift volume, we review the recent efforts at studying these boson stars formed from more than one flavor of ultralight bosons and their possible connection to outstanding astrophysical puzzles.

The following sections are included:

• Perturbation Theory — 1960s and 1970s
• The Halliday–Suranyi (H–S) Anharmonic Oscillator
• Lessons Learned
• Nostalgia
• References

I review the Thirring model in 2+1d dimensions, focusing in particular on possible strongly interacting UV-stable fixed points of the renormalization group corresponding to a continuous phase transition where a U(2N) global symmetry spontaneously breaks to U(N)⊗ U(N). Since there is no small parameter in play, a systematic non-perturbative approach, such as numerical simulation of lattice field theory, is mandated. I compare and contrast various formulations, paying particular attention to models formulated with either staggered or domain wall lattice fermions. Domain wall fermions, which faithfully capture U(2N) symmetry in the limit of wall separation L_s → ∞, predict a critical flavor number 1< N_c < 2.

This short synopsis outlines some recent work on near-conformal dilaton signatures of emergent light scalars in strongly interacting gauge theories close to the conformal window.

The Schwarzschild solution admits one parameter, the mass, which can be positive or negative. What is the meaning of the negative mass solution? Negative mass is an intriguing idea. Negative mass, to be physical, must satisfy the dominant energy condition. This condition asserts that locally, all matter density must be positive and must be seen by all time-like observers to be moving inside the future directed light cone. Indeed, stable configurations can be found that correspond to bubbles of negative mass [1–3], however crucially, in a background energy density. It seems that positive mass attracts while negative mass repels when acting on all masses, positive or negative, due to the equivalence principle [4]. However, a simple analysis of one graviton exchange implies that the potential between like mass particles should be negative, be they of positive or negative mass, implying naively attraction. We explain how this conclusion is eschewed and does not give rise to attraction for negative mass particles. We will see that the existence of the background is crucial.

This chapter is dedicated to Professor Peter Suranyi whom I know as a friend and collaborator. In this chapter, I examine the role of radiation and concomitant decoherence in the behavior of Unruh–deWitt particle detectors in the context of a simple solvable model.

Gravitational leptogenesis is an elegant way of explaining the matter–antimatter asymmetry in the universe. This chapter provides a review of the recently proposed mechanism of radiatively induced gravitational leptogenesis (RIGL), in which loop effects in QFT in curved spacetime automatically generate an asymmetry between leptons and antileptons in thermal quasi-equilibrium in the early universe. The mechanism is illustrated in a simple see-saw BSM model of neutrinos, where the lepton-number violating interactions required by the Sakharov conditions are mediated by right-handed neutrinos with Majorana masses of O(10¹⁰) GeV. The Boltzmann equations are extended to include new, loop-induced gravitational effects and solved to describe the evolution of the lepton-number asymmetry in the early universe. With natural choices of neutrino parameters, the RIGL mechanism is able to generate the observed baryon-to-photon ratio in the universe today.

Chiral anomalous effects in relativistic plasmas are reviewed. The essence of chiral separation and chiral magnetic effects is explained in simple terms. Qualitative differences between the two phenomena, both of which are triggered by background electromagnetic fields, are highlighted. It is shown how an interplay of the chiral separation and chiral magnetic effects could lead to a new collective plasma mode called the chiral magnetic wave. It is argued that the chiral magnetic wave is overdamped in weakly interacting plasmas. Its fate in a strongly interacting quark–gluon plasma is less clear, especially in the presence of a superstrong magnetic field. The observational signatures of the chiral anomalous effects are discussed briefly.

Dark Matter (DM) in the form of Bose–Einstein condensates (BECs) provides an attractive alternative to “cold” and “warm” dark matter. We consider a slowly rotating, self-gravitating BEC candidate for galactic halos employing the Gross–Pitaevskii–Poisson (GPP) equation and the non-relativistic, weak field Gravitoelectromagnetic (GEM) approximation of general relativity. Rather than taking a numerical approach to solving the GEM equations of motion, we use the variational method to examine the conditions under which rotating condensates, stable against gravitational collapse, may form in models with attractive and repulsive quartic interactions. We also describe the approximate dynamics of an imploding and rotating condensate by employing a collective coordinate description in terms of the condensate radius.

The following sections are included:

• Introduction
• Conservation of Energy
• The Space