Related papers: Random Polynomials and the Friendly Landscape
Consistent coupling of effective field theories with a quantum theory of gravity appears to require bounds on the the rank of the gauge group and the amount of matter. We consider landscapes of field theories subject to such to boundedness…
We show that a certain class of nonlocal scalar models, with a kinetic operator inspired by string field theory, is equivalent to a system which is local in the coordinates but nonlocal in an auxiliary evolution variable. This system admits…
Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and non-supersymmetric string vacua fills out a ``landscape'' whose features are largely unknown. It is then hoped that progress in…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…
A natural extension of the Dijkgraaf-Vafa proposal is to include fields in the fundamental representation of the gauge group. In this paper we use field theory techniques to analyze gauge theories whose tree level superpotential is a…
Applied to field theory, the familiar symplectic technique leads to instantaneous Hamiltonian formalism on an infinite-dimensional phase space. A true Hamiltonian partner of first order Lagrangian theory on fibre bundles $Y\to X$ is…
The problem of obtaining a realistic, relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although non-local, is relativistic…
We utilize machine learning to study the string landscape. Deep data dives and conjecture generation are proposed as useful frameworks for utilizing machine learning in the landscape, and examples of each are presented. A decision tree…
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
We describe postulates for a novel realist version of relativistic quantum theory or quantum field theory in Minkowski space or other background spacetimes with suitable asymptotic properties. We illustrate their application in toy models.
I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the…
We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the…
The theory of freely-propagating massless higher spins is usually formulated via gauge fields and parameters subject to trace constraints. We summarize a proposal allowing to forego them by introducing only a pair of additional fields in…
Resonances are of particular importance to the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy $S$-wave resonance. Our starting point is the most…
String theory is canonically accompanied with a space-time interpretation which determines S-matrix-like observables, and connects to the standard physics at low energies in the guise of local effective field theory. Recently, we have…
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and…
We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed…
Effective Lagrangians were originally used only at the tree level as so-called phenomenological Lagrangians since they were in general non-renormalizable. Today they are treated as effective field theories valid below a characteristic…
The phenomenological aspects of string theory are briefly reviewed. Emphasis is given to the status of 4D string model building, effective Lagrangians, model independent results, supersymmetry breaking and duality symmetries.
We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring…