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Gauge Theory Formulation of Hyperbolic Gravity
Frank Ferrari
We formulate the most general gravitational models with constant negative curvature ("hyperbolic gravity") on an arbitrary orientable two-dimensional surface of genus with …
On the large expansion of Hermitian multi-matrix models
Sylvain Carrozza, Frank Ferrari, Adrian Tanasa +1
We investigate the existence and properties of a double asymptotic expansion in and in invariant Hermitian multi-matrix mo…
Phases Of Melonic Quantum Mechanics
Frank Ferrari, Fidel I. Schaposnik Massolo
We explore in detail the properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large limit, or a…
More on the New Large Limit of Matrix Models
Tatsuo Azeyanagi, Frank Ferrari, Paolo Gregori +2
In this paper, we extend the recent analysis of the new large limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as t…
A New Large N Expansion for General Matrix-Tensor Models
Frank Ferrari, Vincent Rivasseau, Guillaume Valette
We define a new large limit for general or invariant tensor models, based on an enhanced large scaling of the coupling constants. The re…
Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
Tatsuo Azeyanagi, Frank Ferrari, Fidel I. Schaposnik Massolo
We compute the phase diagram of a invariant fermionic planar matrix quantum mechanics [equivalently tensor or complex Sachdev-Ye-Kitaev (SYK) mod…
The Large D Limit of Planar Diagrams
Frank Ferrari
We show that in invariant matrix theories containing a large number of complex or Hermitian matrices, one can define a limit for which the su…
Gravity and On-Shell Probe Actions
Frank Ferrari, Antonin Rovai
In any gravitational theory and in a wide class of background space-times, we argue that there exists a simple, yet profound, relation between the on-shell Euclidean gravitational…
Black Hole Horizons and Bose-Einstein Condensation
Frank Ferrari
Consider a particle sitting at a fixed position outside of a stable black hole. If the system is heated up, the black hole horizon grows and there should exist a critical temperatu…
Holography, Probe Branes and Isoperimetric Inequalities
Frank Ferrari, Antonin Rovai
In many instances of holographic correspondences between a d dimensional boundary theory and a d+1 dimensional bulk, a direct argument in the boundary theory implies that there mus…
FQHE on curved backgrounds, free fields and large N
Frank Ferrari, Semyon Klevtsov
We study the free energy of the Laughlin state on curved backgrounds, starting from the free field representation. A simple argument, based on the computation of the gravitational…
D-Brane Probes in the Matrix Model
Frank Ferrari
Recently, a new approach to large N gauge theories, based on a generalization of the concept of D-brane probes to any gauge field theory, was proposed. In the present note, we comp…
2D Quantum Gravity at One Loop with Liouville and Mabuchi Actions
Adel Bilal, Frank Ferrari, Semyon Klevtsov
We study a new two-dimensional quantum gravity theory, based on a gravitational action containing both the familiar Liouville term and the Mabuchi functional, which has been shown…
Gauge Theories, D-Branes and Holography
Frank Ferrari
Based on a generalization of the string theoretic concept of D-brane probe, we propose a new approach to large N gauge theories which makes the holographic properties manifest. For…
Partial Gauge Fixing and Equivariant Cohomology
Frank Ferrari
Given a gauge theory with gauge group G, it is sometimes useful to find an equivalent formulation in terms of a non-trivial gauge subgroup H of G. This amounts to fixing the gauge…
Multi-Loop Zeta Function Regularization and Spectral Cutoff in Curved Spacetime
Adel Bilal, Frank Ferrari
We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically soun…
Emergent D5-brane Background from D-strings
Frank Ferrari, Antonin Rovai
We solve the worldsheet theory describing the near-horizon dynamics of a D-string in the presence of a very large number N of D5-branes. The model is pre-geometric in the sense tha…
On Matrix Geometry and Effective Actions
Frank Ferrari
We provide an elementary systematic discussion of single-trace matrix actions and of the group of matrix reparameterization that acts on them. The action of this group yields a gen…
Emergent D4-Brane Background from D-Particles
Frank Ferrari, Micha Moskovic
We show that the solution of a pre-geometric strongly coupled quantum mechanical model describing K D-particles in the presence of N D4-branes in type IIA string theory, at fixed K…
Examples of Emergent Type IIB Backgrounds from Matrices
Frank Ferrari, Micha Moskovic, Antonin Rovai
We study models of emergent space associated with the Coulomb branch, non-commutative and beta deformations of the N=4 super Yang-Mills theory, extending a previous work on the und…
Emergent Space and the Example of AdS_5XS^5
Frank Ferrari
We explain how to build field theoretic observables from which the geometrical properties of a dual holographic formulation can be read off straightforwardly. In some cases this co…
Gravitational Actions in Two Dimensions and the Mabuchi Functional
Frank Ferrari, Semyon Klevtsov, Steve Zelditch
The Mabuchi energy is an interesting geometric functional on the space of Kähler metrics that plays a crucial rôle in the study of the geometry of Kähler manifolds. We show that th…
Random Geometry, Quantum Gravity and the Kähler Potential
Frank Ferrari, Semyon Klevtsov, Steve Zelditch
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible…
Random Kähler Metrics
Frank Ferrari, Semyon Klevtsov, Steve Zelditch
The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a Kähler manifold. The main idea is to use finite dimensional spaces o…