Week 16.03.2025 – 22.03.2025

Quantum Chromodynamics (QCD) has been a profound source of inspiration for theoretical physics, driving the development of key concepts such as string theory, effective field theories, instantons, anomalies, and lattice gauge theories. In these lectures, I will explore two distinct regimes of QCD - its infrared (IR) and ultraviolet (UV) limits - and the theoretical tools used to study them. In the IR regime, where perturbative techniques break down, Effective Field Theories (EFTs) provide a powerful framework. I will introduce the pion EFT as a tool to study non-linearly realized symmetries and soft theorems. In the UV regime, where QCD becomes amenable to perturbative analysis, I will discuss the Operator Product Expansion and renormalization group equations, focusing on their application to deep inelastic scattering, a cornerstone in the discovery of quarks and gluons. These two regimes illustrate the richness of QCD and its pivotal role in shaping our understanding of fundamental physics.

In this talk, we propose that topological order can replace sterile neutrinos as dark matter candidates to cancel the Standard Model global gravitational anomalies. Standard Model (SM) with 15 Weyl fermions per family (lacking the 16th, the sterile right-handed neutrino nuR) suffers from mixed gauge-gravitational anomalies tied to baryon number plus or minus lepton number B+(-)L symmetry. Including nuR per family can cancel these anomalies, but when B+(-)L symmetry is preserved as discrete finite subgroups rather than a continuous U(1), the perturbative local anomalies become nonperturbative global anomalies. We systematically enumerate these gauge-gravitational global anomalies involving discrete B+(-)L that are enhanced from the fermion parity ZF2 to ZF2N. The discreteness of B+(-)L is constrained by multi-fermion deformations beyond-the-SM and the family number Nf. Unlike the free quadratic nuR Majorana mass gap preserving the minimal ZF2, we explore novel scenarios canceling (B+(-)L)-gravitational anomalies while preserving the ZF2N discrete symmetries, featuring 4-dimensional interacting gapped topological orders or gapless sectors (e.g., conformal field theories). We propose symmetric anomalous sectors as quantum dark matter to cancel SM global anomalies. We find the uniqueness of the family number at Nf = 3, such that when the representation of ZF2N from the faithful B+L for baryons at both Nf and N equal to 3 is extended to the faithful Q + NcL for quarks at N = NcNf = 9, this symmetry extension ZNc=3 to ZNcNf =9 to ZNf =3 matches with the topological order dark matter construction. Key implications include: (1) a 5th force mediating between SM and dark matter via discrete B+(-)L gauge fields, (2) dark matter as topological order quantum matter with gapped anyon excitations at ends of extended defects, and (3) Ultra Unification and topological leptogenesis. [Based on arXiv:2502.21319, arXiv:2501.00607, arXiv:2411.05786, arXiv:2012.15860, arXiv:2112.14765, arXiv:2204.08393, arXiv:2302.14862, arXiv:2312.14928].

I will provide a rather lengthy introduction in oder to highlight interest in exploring QFts on AdS spaces (without dynamical gravity). The aspects involve the dyanmics of boundaries and interfaces in normal QFTs in flat space, the actual dynamics of confining gauge theories on AdS, the question of prximity in the pace of QFRTs, a more general notion of holography and its connection to S-matrices and finally Euclidean wormholes. All these issues will connect in the effort to describe holographic QFTs on AdS. We shall investigate in a concrete example how the related classical solutions explore the space of QFTs and we construct the general solutions that interpolate between the same or different CFTs with arbitrary couplings. The solution space contains many exotic RG flow solutions that realize unusual asymptotics, as boundaries of different regions in the space of solutions. We find phenomena like "walking" flows and the generation of extra boundaries via "flow fragmentation". We will then move on and describe an example of a holographic theory that confines on flat space, when we put it on AdS. We will find three types of regular solutions are found. Theories with two AdS boundaries provide interfaces between two confining theories. Theories with a single AdS boundary correspond to ground states of a single confining theory on AdS. We find solutions without a boundary, whose interpretation is probably as interfaces between topological theories. We analyze in detail the holographic dictionary for the one-boundary solutions and compute the free energy. No (quantum) phase transitions are found when we change the curvature. We find an infinite number of pure vev solutions, but no CFT solution without a vev. We also compute the free energy of the interface solutions. We find that the product saddle points have always lower free energy than the connected solutions. Finally we will comment on the spectrum of propa gating states of holographic theories on AdS and dS.