Vortices, tunneling, and deconfinement in bilayer quantum Hall excitonic superfluid

The physics of vortices, instantons, and deconfinement is studied for layered superfluids in connection to bilayer quantum Hall systems at filling fraction nu = 1. We develop an effective gauge theory taking into account both vortices and instantons induced by interlayer tunneling. The renormalization group flow of the gauge charge and the instanton fugacity shows that the coupling of the gauge field to vortex matter produces a continuous transition between the confining phase of free instantons and condensed vortices and a deconfined gapless superfluid where magnetic charges are bound into dipoles. The interlayer tunneling conductance and the layer-imbalance induced inhomogeneous exciton condensate are discussed in connection to experiments.     

Noncommutative Instantons: A New Approach

We discuss instantons on noncommutative four-dimensional Euclidean space. In the commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field at infinity. However, technically it is more convenient to work on the four-dimensional sphere. We will show that the situation in the noncommutative case is quite similar. One can analyze instantons taking as a starting point the algebra of smooth functions vanishing at infinity, but it is convenient to add a unit element to this algebra (this corresponds to a transition to a sphere at the level of topology). Our approach is more rigorous than previous considerations; it seems that it is also simpler and more transparent. In particular, we obtain the ADHM equations in a very simple way. Received: 30 March 2001 / Accepted: 3 April 2001     

LETTER: Gauge Field Corrections to Domain Walls

Gauge field corrections to domain walls are obtained by making use of perturbation method on the usual flat domain wall. The gauge vector field introduces a damping term and an external force on the motion equation for the perturbed domain wall. A thin domain wall approximation solution is found. The vector gauge field also introduces a gauge mass term correction into the perturbed Lagrangean.     

Monopoles, instantons and chiral condensate in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD at finite temperature on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons. Studies are performed in both pure and full QCD and in both the confinement and deconfinement phase. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover the correlation of monopole loops and instantons with the chiral condensate is investigated. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.     

Domain wall solutions with Abelian gauge fields

We study kink (domain wall) solutions in a model consisting of two complex scalar fields coupled to two independent Abelian gauge fields in a Lagrangian that has U(1)×U(1) gauge plus discrete symmetry. We find consistent solutions such that while the U(1) symmetries of the fields are preserved while in their respective vacua, they are broken on the domain wall. The gauge field solutions show that the domain wall is sandwiched between domains with constant magnetic fields.     

Noncommutative Instantons Revisited

We find a new gauge in which U(1) noncommutative instantons are explicitly non-singular on noncommutative R ⁴. We also present a pedagogical introduction into noncommutative gauge theories.     

The “instanton liquid”

We review the theory of interacting topological fluctuations in the ground state of quantum gauge theories, the so called “instanton liquid”. First we outline some known phenomenological facts, both coming from “real” experiments (for QCD) and from the lattice data. Then we describe interaction of instantons and the statistical mechanics of their ensemble for theSU(2) gauge theory. The very essential role of the light quarks is considered using numerical experiments. One of the main conclusions is that instantons induce chiral symmetry breaking in vacuum, but as they are suppressed (e.g. by the nonzero temperature) this symmetry is restored. Phase transition is found to be very strong and of the first order.     

Supersymmetric Yang-Mills,octonionic instantons and triholomorphic curves

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of ten-dimensional supersymmetric Yang-Mills theory. More precisely we show that the dimensional reduction of the (5+1)-dimensional supersymmetric sigma model with hyper-Kähler (but otherwise arbitrary) target X to a four-dimensional hyper-Kähler manifold M is a topological sigma model localising on the space of triholomorphic maps M -+ X (or hyperinstantons). When X is the moduli space M_k of instantons on a four-dimensional hyper-Kdhler manifold K, this theory has an interpretation in terms of supersymmetric gauge theory. In this case, the topological sigma model can be understood as an adiabatic limit of the dimensional reduction of ten-dimensional supersymmetric Yang-Mills on the eight-dimensional manifold M × K of holonomy Sp(1) × Sp(1) ⊂ Spin(7), which is a cohomological theory localising on the moduli space of octonionic instantons.     

How instantons solve the U(1) problem

The gauge theory for strong interactions, QCD, has an apparent U(1) symmetry that is not realized in the real world. The violation of the U(1) symmetry can be attributed to a well-known anomaly in the regularization of the theory, which in field configurations called “instantons” can be seen to give rise to interactions that explicitly break the symmetry. A simple polynomial effective Lagrangian describes these effects qualitatively very well. In particular it is seen that no unwanted Goldstone bosons appear and the eta particle owes a large fraction of its mass to instantons. There is no need for field configurations with fractional winding numbers and it is explained how a spurious U(1) symmetry that remains in QCD even after introducing instantons, does not affect these results.     

Small instantons in string theory

A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra SU(2) gauge symmetry appears that is supported in the core of the instanton. Thus in particular the quantum heterotic string has vacua with higher rank than is possible in conformal field theory. When k instantons collapse at the same point, the enhanced gauge symmetry is Sp(k). These results, which can be tested by comparison to Dirichlet five-branes of Type I superstrings and to the ADHM construction of instantons, give the first example for the heterotic string of a non-perturbative phenomenon that cannot be turned off by making the coupling smaller. They have applications to several interesting puzzles about string duality.     

Instanton Effects on Gluon Propagator

Gluon propagator is investigated for pure Yang-Mills SU(3) gauge theory in field-strength approach. It is found that instantons provide a homogeneous solid-like medium background which generates finite nonzero momentum gluon propagator and gluon receives effective mass.     

Periodic instantons and domain structure in a ferromagnetic film

We in this paper study periodic instantons and domain structures in a theoretical film consisting of biaxial-anisotropic ferromagnets. In a proper approximation the equation of motion of the magnetization vector as a space-time function in the film is reduced to the 1 + 2-dimensional sine-Gordon field equation in strong anisotropy limit. Static periodic instantons, which are solutions of Euclidean field equantion, and various new domain structures are obtained analytically. We also investigate the energy density and stability of the periodic instantons.Received: 6 August 2003, Published online: 8 December 2003PACS: 05.45.Yv Solitons - 75.70.Kw Domain structure (including magnetic bubbles)     

Fermion Flavors in Quaternion Basis and Infrared QCD

I analyze the lattice simulation data of the Domain Wall Fermion in quaternion basis. As pointed out by Atiyah and Ward, the minimum action solution for SU(2) Yang–Mills fields in Euclidean 4-space correspond, via Penrose twistor transform, to algebraic bundles on the complex projective 3-space. Assuming dominance of correlation between the fermions on the domain walls via exchange of instantons, I extract parameters necessary for defining gauge fields of Atiyah–Ward ansatz. The QCD effective coupling in the infrared and the relation between the number of flavors and the infrared fixed point is investigated. Consequence of this lepton flavor assignment to phenomenology of baryons is also discussed.     

Self-dual fields harbored by a Kerr–Taub-bolt instanton

We present a new exact solution for self-dual Abelian gauge fields living on the space of the Kerr–Taub-bolt instanton, which is a generalized example of asymptotically flat instantons with non-self-dual curvature, by constructing the corresponding square integrable harmonic form on this space.     

Moduli Spaces of Instantons on the Taub-NUT Space

We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkähler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton.We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.     

Supersymmetric instantons and topological quantum field theory

We present an action which generates the supersymmetric self-dual equations corresponding to euclidean super Yang-Mills theory in four dimensions. By adding additional constraint fields with new local symmetries, the classical equations of this system are the usual super self-dual equations when a gauge is chosen for the constraint fields. This construction is a supersymmetric generalization of the Labastida-Pernici action which corresponds to a gauge unfixed version of Witten's topological quantum field theory. We discuss some topological prospects for this model, and the role of supersymmetric instantons in Donaldson theory.     

Event-Symmetry for Superstrings

I apply the principle of event-symmetry tosimple string models and discuss how these lead to theconviction that multiple quantization is linked todimension. It may be that string theory has to beformulated in the absence of space-time, which will thenemerge as a derived property of the dynamics. Anotherinterpretation of the event-symmetric approach whichembodies this is that instantons are fundamental. Just as solitons may be dual to fundamentalparticles, instantons may be dual to space-time events.Event-symmetry is then dual to instanton statistics. Inthat case a unification between particle statistics and gauge symmetry follows on naturally fromthe principle of event-symmetry. I build algebras whichrepresent symmetries of superstring theories extendingevent-symmetry, but which are also isomorphic to an algebra of creation and annihilationoperators for strings of fermionic partons.     

Gauge Theory on Infinite Connected Sum and Mean Dimension

We study the geometry of infinite dimensional moduli spaces in the Yang-Mills gauge theory over infinite connected sum spaces. We develop the technique of gluing infinitely many instantons, and apply it to the evaluation of the mean dimension of the moduli spaces.