Vittorio de Alfaro

Bio: Vittorio de Alfaro is an academic researcher. The author has contributed to research in topics: Primary field & Conformal symmetry. The author has an hindex of 1, co-authored 1 publications receiving 714 citations.

Conformal Invariance in Quantum Mechanics

Abstract: The properties of a field theory in one over-all time dimension, invariant under the full conformal group, are studied in detail. A compact operator, which is not the Hamiltonian, is diagonalized and used to solve the problem of motion, providing a discrete spectrum and normalizable eigenstates. The role of the physical parameters present in the model is discussed, mainly in connection with a semi-classical approximation.

Remarks on the Sachdev-Ye-Kitaev model

Abstract: The authors study in detail the quantum mechanical model of $N$ Majorana fermions with random interactions of a few fermions at a time (Sachdev-Ye-Kitaev model) in the large $N$ limit. At low energies, the system is strongly interacting and an emergent conformal symmetry develops. Performing technical calculations, the authors elucidate a number of properties of the model near the conformal point.

Comments on string theory backgrounds with non-relativistic conformal symmetry

Abstract: We consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories. If the field theory has a gravity dual, then the conformal quantum mechanical theory can have a gravity dual description in a suitable finite temperature and finite density regime. Using this we compute the thermodynamic properties of the system. We give an explicit example where we display both the conformal quantum mechanical theory as well as the gravity dual. We also discuss the string theory embedding of certain backgrounds with non-relativistic conformal symmetry that were recently discussed. Using this, we construct finite temperature and finite density solutions, with asymptotic non-relativistic conformal symmetry. In addition, we derive consistent Kaluza-Klein truncations of type IIB supergravity to a five dimensional theory with massive vector fields.

Liouville Field Theory — A decade after the revolution

Abstract: We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master’s thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004.

Local bulk operators in AdS/CFT correspondence : A boundary view of horizons and locality

Abstract: We develop the representation of local bulk fields in anti-de Sitter (AdS) space by nonlocal operators on the boundary, working in the semiclassical limit and using ${\mathrm{AdS}}_{2}$ as our main example. In global coordinates we show that the boundary operator has support only at points which are spacelike separated from the bulk point. We construct boundary operators that represent local bulk operators inserted behind the horizon of the Poincar\'e patch and inside the Rindler horizon of a two-dimensional black hole. We show that these operators respect bulk locality and comment on the generalization of our construction to higher dimensional AdS black holes.