Related papers: ADHM and the 4d Quantum Hall Effect
States of strongly interacting particles are of fundamental interest in physics, and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the…
Yang--Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from the Laplacian and from a first-order differential operator. The…
We study an extension of the ADHM construction to give deformed anti-self-dual (ASD) instantons in N=1/2 super Yang-Mills theory with U(n) gauge group. First we extend the exterior algebra on superspace to non(anti)commutative superspace…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
We construct a 4-dimensional quantum field theory on a Hilbert space, dependent on a simple Lie Algebra of a compact Lie group, that satisfies Wightman's axioms. This Hilbert space can be written as a countable sum of non-separable Hilbert…
The low-lying excitations of a quantum Hall state on a disk geometry are edge excitations. Their dynamics is governed by a conformal field theory on the cylinder defined by the disk boundary and the time variable. We give a simple and…
It has been a long sought goal of Quantum Simulation to find answers to long standing questions in condensed matter physics. A famous example is the ground and the excitations of 2D Hubbard model with strong repulsion below half filling.…
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics…
The partition function of four dimensional SO(4) Yang-Mills theory is rewritten in terms of variables admitting straightforward relation to the partition function of pure 4D gravity. The gauge action turns into first-order Hilbert-Palatini…
We consider spaces of trial wavefunctions for ground states and edge excitations in the fractional quantum Hall effect that can be obtained in various ways. In one way, functions are obtained by analyzing the entanglement of the ground…
We provide details of a shorter letter and cond-mat/9702098 and some new results. We describe a Chern-Simons theory for the fractional quantum Hall states in which magnetoplasmon degrees of freedom enter. We derive correlated wavefunctions,…
ADHM Yang-Mills instantons are extended field theoretical objects. These are more general than the more familiar 't Hooft Yang-Mills instantons. Their counter parts exist in string theory in terms of sigma models. Nearly three decades ago…
We construct the n-instanton action for the above model with gauge group SU(2), as a function of the collective coordinates of the general self-dual configurations of Atiyah, Drinfeld, Hitchin and Manin (ADHM). We calculate the quantum…
The quantum of action $\hbar$, multiplying in certain powers perturbative vertices in 4D gauge theory, is related to the action of just-not-resolved selfdual and thermal gauge field configurations, calorons and anticalorons, of charge…
We interpret a class of 4k-dimensional instanton solutions found by Ward, Corrigan, Goddard and Kent as four-dimensional instantons at angles. The superposition of each pair of four-dimensional instantons is associated with four angles…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
In this work, we study the perturbative generation of the gauge invariant effective action for the non-Abelian gauge field in a $(2+1)$-dimensional spacetime. We present a detailed analysis of the two, three and four-point functions in…
The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are…
By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order $\exp(-|Q|/g_s)$ to certain protected couplings in the three-dimensional…