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.

We investigate emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor. We derive the general effective description of such dynamics, and apply it to the case where a hidden theory generates gravity that is coupled to the Standard Model. In the linearized description, generically, such gravity is massive with the presence of an extra scalar degree of freedom. The propagators of both the spin-two and spin-zero modes are positive and well defined. The associated emergent gravitational theory is a bi-gravity theory, as is (secretly) the case in holography. The background metric on which the QFTs are defined, plays the role of dark energy and the emergent theory has always as a solution the original background metric. In the case where the hidden theory is holographic, the overall description yields a higher-dimensional bulk theory coupled to a brane. The effective graviton on the brane has four-dimensional characteristics both in the UV and IR and is always massive. [please email a.held@imperial.ac.uk for zoom link or password]

Effective Holographic Theories are employed in order to classify and study the critical dynamics at low temperature of quantum field theoritec systems in 2 and 3 spacial dimensions at finite charge density. The relevant dynamics variables involve the energy momentum tensor, a scalar relevant or marginal operator and the charge density current. A wealth of scaling phases are found with interesting and sometimes counterintuitive properties.

Various holographic approaches to QCD in five dimensions are explored using input both from the perturbative five-dimensional non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure YM theory. A part of the effects of higher a'-corrections is resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS5 with logarithmic corrections reflecting the asymptotic freedom of QCD. The IR confining geometries are classified and analyzed. Near the singularity the 't Hooft coupling is driven to infinity. The glueball spectra are gapped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Meson dynamics is implemented via space filling D4-anti D4 brane pairs. The associated tachyon dynamics is analyzed and chiral symmetry breaking is shown. The dynamics of the RR axion is analyzed, and the non-perturbative running of the QCD theta-angle is obtained. It is shown to always vanish in the IR. The finite temperature structure is also analyzed and phase diagram is studied. Our preliminary results show a first order deconfining transition to a QGP phase with a transition temperature in agreement with lattice data.