AdS geometry: bulk and boundary; Isometry constraints on correlation functions; Bulk state / Boundary operator correspondence; Boundary operator product expansion.
I will talk about the black hole instabilities in AdS and the new hairy black hole configurations which we suggest to be the endpoints. Based on these findings, I will suggest better pictures on the spectral/entropic structures of the AdS quantum gravity.
We investigate large-N spin models that parallel the Sachdev–Ye–Kitaev construction and provide a controlled setting for studying manybody chaos. By implementing a Pandey–Mehta–type large-N crossover, we interpolate between distinct random-matrix universality classes and track how spectral correlations evolve with the crossover parameter. Using the adjacent-level spacing r-ratio and Krylov...
Vector field theories, dual to Higher Spin gravity are considered at Finite N. In the collective field representation a reduction of Hilbert space is discussed with implications on finiteness of the Trace and Entropy in this holographic representation.
It is shown how large N properties of multi-matrix systems can be obtained by minimization of a loop truncated effective Hamiltonian expressed directly in terms of gauge invariant operators. The large N loop space constraints are handled by the use of master variables. For two and three massless Yang-Mills coupled matrices, highly accurate results for large N planar correlators, as well as...
OPE decomposition of bulk 2 pt functions and boundary 4pt functions; Example of the free scalar; Example of the O(N) model: various phases and their boundary interpretation.
I will explain the cohomology program for the BPS black hole states in AdS/CFT. After explaining its general structures and examples, I will explain how to better understand the hairy BPS black hole states in this setup.
The mapping of the dilatation operator of planar N=4 SYM to an integrable spin chain has led to tremendous progress in understanding the spectrum of the theory, both perturbative and non-perturbative. Gauge theories will less supersymmetry have received less attention. In this talk I will review recent progress in understanding the spin chains for planar N=2 superconformal theories obtained by...
In this series of lectures (and seminar) I will cover the following:
- The basics of perturbation theory in AdS and how bootstrap ideas can be used to efficiently compute holographic correlators. The example of 4d N=4 SYM in the dual supergravity limit will be analyzed in detail.
- How the bootstrap approach can be extended to include holographic defects. In particular, I will present the...
I will discuss four dimensional non-abelian gauge theories in the background of Anti-de Sitter space. I will review how, imposing a Dirichlet boundary condition at small radius, there is a deconfinement/confinement transition as the radius is increased, while imposing a Neumann boundary condition a continuous extrapolation to the flat space limit is expected. I will then review recent...
I will introduce conformal field theories and the constraints imposed by conformal symmetry on correlation functions. After discussing primary operators, the operator product expansion, and conformal blocks, I will present the crossing equation for four-point functions. I will explain how unitarity - which guarantees positivity of OPE coefficients squared - enables the linear functional method...
I will explain the large N BPS phases of the ABJ vector Chern-Simons model dual to a higher spin gravity, from the saddle points of its index. Their physical aspects are discussed from the viewpoint of trace relations and fortuitous operators. I will compare them with the AdS string theory and its black holes.
Built from the gradient and Hessian of the Euclidean action, a new temperature estimator for lattice gauge theories is being introduced. Drawing from geometric statistical methods, the estimator offers a gauge-invariant and momentum-free tool for checking thermodynamic consistency in Monte Carlo simulations. Rather than adjusting temperature indirectly through lattice size or coupling, this...
In this lecture we will introduce basic facts about QFT in de Sitter, highlighting the main differences with its flat-space counterpart. We will start by discussing the geometry of dS, its isometries, and the admissible particle representations. We will also discuss the maximally analytic vacuum of any interacting QFT: the Bunch Davies state.
I will introduce CFTs at finite temperature, where the KMS condition replaces crossing symmetry as the central consistency constraint. Unlike at zero temperature, thermal OPE coefficients can have either sign, invalidating the linear functional approach. I will discuss neural networks as universal function approximators and explain how physics-informed neural networks (PINNs) can enforce the...
We introduce a novel method to bootstrap crossing equations in Conformal Field Theory and apply it to finite temperature theories on S1×Rd−1. Traditional bootstrap approaches relying on positivity constraints or truncation schemes are not applicable to this problem. Instead, we capture infinite towers of operators using suitable tail functions, which are bootstrapped numerically together with...
In this talk we describe the secondary invariants in bosonic vector models by employing a duality between bosonic and fermionic vector models. In this picture the set of bosonic secondary invariants are mapped, one-to-one, to the states of a fermionic bilinear color-singlet Hilbert space. We describe how the trace relations in the two descriptions are related.
In this talk, I will present a method to evaluate superconformal indices of four-dimensional N=1 superconformal field theories in closed form. For the (1/8 BPS) Macdonald index of the N=4 SU(2) super Yang-Mills theory, the resulting expression manifests features of the BPS spectrum at non-zero Yang-Mills coupling. I will argue that the expression suggests the absence of “fortuitous” or...
In this series of lectures (and seminar) I will cover the following:
- The basics of perturbation theory in AdS and how bootstrap ideas can be used to efficiently compute holographic correlators. The example of 4d N=4 SYM in the dual supergravity limit will be analyzed in detail.
- How the bootstrap approach can be extended to include holographic defects. In particular, I will present the...
The focus of this lecture will be on the various issues that arise when working with interacting QFTs on de Sitter using perturbation theory. Time permitting, we will also discuss the Euclidean approach to de Sitter QFT.
In this series of lectures (and seminar) I will cover the following:
- The basics of perturbation theory in AdS and how bootstrap ideas can be used to efficiently compute holographic correlators. The example of 4d N=4 SYM in the dual supergravity limit will be analyzed in detail.
- How the bootstrap approach can be extended to include holographic defects. In particular, I will present the...
QFT in dS: The Issues
In this lecture we will present what can be learned from exactly solvable models on de Sitter, working through examples.
Spread complexity can be solved for analytically in the case of simple Hamiltonians (i.e. Hamiltonians that are elements of some rank 1 algebra). For general Hamiltonians the Lanczos algorithm provides an algorithmic way to compute the Krylov basis and thus the spread complexity. A natural question to ask is what happens when one considers a Hamiltonian that is formed from a direct sum of...
