Related papers: Real-Time Dynamics at Large $N$
A spin system on a lattice can usually be modelled at large scales by an effective quantum field theory. A key mathematical result relating the two descriptions is the quantum central limit theorem, which shows that certain spin observables…
L\"uscher's local bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions is applied to the simulation of a possibly supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint representation.…
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle…
Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number $N$ of fields of some type becomes large. These include extended versions of the U(N) Gross-Neveu model, the…
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…
A procedure of bosonization of Fermions in an arbitrary dimension is suggested. It is shown that a quadratic expression in the fermionic fields after rescaling time $t\to t/\lambda^2$ and performing the limit $\lambda\to0$ (stochastic…
The different large $N$ limits of supersymmetric quantum field theories in three, four, and five dimensions are reviewed. We distinguish between the planar limit of SQCD theories, the M-theory limit suited in three and five dimensions, and…
The excitations referred to as oscillons are long-lived time-dependent field configurations which emerge dynamically from non-linear field theories. Such long-lived solutions are of interest in applications that include systems of Condensed…
Large N gauge theories with adjoint matter can be numerically studied using lattice techniques. Eguchi-Kawai reductions holds for this theory and one can reduce the lattice model to a single site. Hybrid Monte Carlo algorithm can be used to…
In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may…
Lattice QCD with an even number of degenerate quark flavours is shown to be a limit of a local bosonic field theory. The action of the bosonic theory is real and bounded from below so that standard simulation algorithms can be expected to…
In this paper, we extend the recent analysis of the new large $D$ limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases…
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in…
Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model. Lattice field theory provides a non-perturbative regularization suitable for strongly…
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same…
We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and {\it twisted} versions of conventional supersymmetric sigma models with N=2…
Various nonsupersymmetric theories at large but finite $N$ are argued to permit light scalars and large hierarchies without fine-tuning. In a dual string description, the hierarchy results from competition between classical and quantum…
We show how to use quantum mechanics on the group manifold U(N) as a tool for problems in U(N) representation theory. The quantum mechanics reduces to free fermions on the circle, which in the large N limit become relativistic. The theory…
Bosonic mean-field theories can approximate the dynamics of systems of $n$ bosons provided that $n \gg 1$. We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions…
We investigate the real-time dynamics of U(1) and SU(N) gauge theories coupled to fermions on a lattice. While real-time lattice gauge theory is not amenable to standard importance sampling techniques, for a large class of time-dependent…