Hooft Instanton Research Articles

On rank 3 instanton bundles on P3$\mathbb {P}^3$

AbstractWe investigate rank 3 instanton vector bundles on of charge and its correspondence with rational curves of degree . For , we present a correspondence between stable rank 3 instanton bundles and stable rank 2 reflexive linear sheaves of Chern classes and we use this correspondence to compute the dimension of the family of stable rank 3 instanton bundles of charge 2. Finally, we use the results above to prove that the moduli space of rank 3 instanton bundles on of charge 2 coincides with the moduli space of rank 3 stable locally free sheaves on of Chern classes . This moduli space is irreducible, has dimension 16 and its generic point corresponds to a generalized't Hooft instanton bundle.

The inhomogeneous phase of dense skyrmion matter

It was predicted qualitatively in ref. [1] that skyrmion matter at low density is stable in an inhomogeneous phase where skyrmions condensate into lumps while the remaining space is mostly empty. The aim of this paper is to proof quantitatively this prediction. In order to construct an inhomogeneous medium we distort the original FCC crystal to produce a phase of planar structures made of skyrmions. We implement mathematically these planar structures by means of the 't Hooft instanton solution using the Atiyah-Manton ansatz. The results of our calculation of the average density and energy confirm the prediction suggesting that the phase diagram of the dense skyrmion matter is a lot more complex than a simple phase transition from the skyrmion FCC crystal lattice to the half-skyrmion CC one. Our results show that skyrmion matter shares common properties with standard nuclear matter developing a skin and leading to a binding energy equation which resembles the Weiszäcker mass formula.

Three-body force for baryons from the D0-D4/D8 brane matrix model

This is an extensive work to our previous paper [S. Li and T. Jia, Matrix model and holographic baryons in the D0-D4 background, Phys. Rev. D 92, 046007 (2015)] that studied the D0-D4/D8 holographic system. We compute the three-body force for baryons with the D0-D4/D8 matrix model derived in [S. Li and T. Jia, Matrix model and holographic baryons in the D0-D4 background, Phys. Rev. D 92, 046007 (2015)] with considering the nonzero QCD vacuum. We obtain the three-body force at short distances but modified by the appearance of the smeared D0-branes, i.e., considering the effects from the nontrivial QCD vacuum. We first test our matrix model in the case of 't Hooft instanton and then in two more realistic cases: (1) three-neutrons with averaged spins and (2) proton-proton-neutron (or proton-neutron-proton). The three-body potential vanishes in the former case while in the two latter cases it is positive, i.e., repulsive and makes sense only if the constraint for stable baryonic state is satisfied. We require all the baryons in our computation aligned on a line. These may indicate that the cases in dense states of neutrons such as in neutron stars, Helium-3 or Tritium nucleus all with the nontrivial QCD vacuum.

Symplectic instanton bundles on $${\mathbb {P}}^3$$ P 3 and ’t Hooft instantons

We study the moduli space $$I_{n,r}$$ of rank-2r symplectic instanton vector bundles on $${\mathbb {P}}^3$$ with $$r\geqslant 2$$ and second Chern class $$n\geqslant r+1,\,n-r\equiv 1\,(\mathrm {mod}\,2)$$ . We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $$I^*_{n,r}$$ of tame symplectic instantons is irreducible and has the expected dimension equal to $$4n(r+1)-r(2r+1)$$ . The proof is inherently based on a relation between the spaces $$I^*_{n,r}$$ and the moduli spaces of ’t Hooft instantons.

Rational families of instanton bundles on ${\mathbb{P}}^{2n+1}$

This paper is devoted to the theory of symplectic instanton bundles on an odd dimensional projective space P 2n+1 with n > 2. We study the ’t Hooft instanton bundles introduced by Ottaviani and a new family of instanton bundles which generalizes one introduced on P 3 independently by Rao and Skiti. The main result is the determination of the birational types of the moduli spaces of ’t Hooft and of Rao{Skiti instanton bundles, respectively. Assuming a conjecture of Ottaviani, we show that the moduli space of all symplectic instanton bundles on P 2n+1 with n > 2 is reducible.

Some properties of two Nambu-Jona-Lasinio -type models with inputs from lattice QCD

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero chemical potential. The calculations are performed in the light and strange quark sectors ($u$, $d$, $s$), which includes the 't Hooft instanton induced interaction term that breaks the axial symmetry, and the quarks are coupled to the (spatially constant) temporal background gauge field. On one hand, a special attention is payed to the critical end point (CEP). The strength of the flavor-mixing interaction alters the CEP location, since when it becomes weaker the CEP moves to low temperatures and can even disappear. On the other hand, we also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type model and the Landau gauge gluon propagator. Possible links between the quenched gluon propagator and low energy hadronic phenomenology are investigated.

Classification of 't Hooft instantons over multi-centered gravitational instantons

This work presents a classification of all smooth 't Hooft–Jackiw–Nohl–Rebbi instantons over Gibbons–Hawking spaces. That is, we find all smooth SU(2) Yang–Mills instantons over these spaces which arise by conformal rescalings of the metric with suitable functions. Since the Gibbons–Hawking spaces are hyper-Kähler gravitational instantons, the rescaling functions must be positive harmonic. By using twistor methods we present integral formulae for the kernel of the Laplacian associated to these spaces. These integrals are generalizations of the classical Whittaker–Watson formula. By the aid of these we prove that all 't Hooft instantons have already been found in a recent paper [Commun. Math. Phys. 235 (2003) 275]. This result also shows that actually all such smooth 't Hooft–Jackiw–Nohl–Rebbi instantons describe singular magnetic monopoles on the flat three-space with zero magnetic charge moreover the reducible ones generate the full L 2 cohomolgy of the Gibbons–Hawking spaces.

Remarks on the noncommutative Atiyah-Drinfeld-Hitchin-Manin construction

We extend the method of matrix partition to obtain explicitly the gauge field for noncommutative ADHM construction in some general cases. As an application of this method we apply it to the U(2) 2-instanton and get explicit result for the gauge fields in the coincident instanton limit. We also easily apply it to the noncommutative 't Hooft instantons in the appendix.

Strong two-body decays of light mesons

In this paper, we present results on strong two-body decay widths of light $q\bar q$ mesons calculated in a covariant quark model. The model is based on the Bethe-Salpeter equation in its instantaneous approximation and has already been used for computing the complete meson mass spectrum and many electroweak decay observables. Our approach relies on the use of a phenomenological confinement potential with an appropriate spinorial Dirac structure and 't Hooft's instanton--induced interaction as a residual force for pseudoscalar and scalar mesons. The transition matrix element for the decay of one initial meson into two final mesons is evaluated in lowest order by considering conventional decays via quark loops as well as Zweig rule violating instanton--induced decays generated by the six--quark vertex of 't Hooft's interaction; the latter mechanism only contributes if all mesons in the decay have zero total angular momentum. We show that the interference of both decay mechanisms plays an important role in the description of the partial widths of scalar and pseudoscalar mesons.

Hopf defects as seeds for monopole loops

We investigate the relation between instantons and monopoles in the Laplacian Abelian Gauge using analytical methods in the continuum. Our starting point is the fact that the 't Hooft instanton with its high symmetry leads to a pointlike defect with Hopf invariant one. In order to generalise this result we partly break the symmetry by a local perturbation. We find that for generic configurations near the 't Hooft instanton the defects become loops. The analytical results show explicitly that these defects are magnetic monopoles with unit charge. In addition, the monopoles are twisted to account for the instanton number of the background.

Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge

We investigate the Laplacian Abelian gauge on the sphere S^4 in the background of a single `t Hooft instanton. To this end we solve the eigenvalue problem of the covariant Laplace operator in the adjoint representation. The ground state wave function serves as an auxiliary Higgs field. We find that the ground state is always degenerate and has nodes. Upon diagonalisation, these zeros induce toplogical defects in the gauge potentials. The nature of the defects crucially depends on the order of the zeros. For first-order zeros one obtains magnetic monopoles. The generic defects, however, arise from zeros of second order and are pointlike. Their topological invariant is the Hopf index S^3 -> S^2. These findings are corroborated by an analysis of the Laplacian gauge in the fundamental representation where similar defects occur. Possible implications for the confinement scenario are discussed.

Instantons and Gribov copies in the maximally Abelian gauge

We calculate the Faddeev-Popov operator corresponding to the maximally Abelian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the field theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single `t Hooft instanton. Accordingly, such an instanton corresponds to a horizon configuration in the maximally Abelian gauge. Possible physical implications are discussed.

Strong U A(1) breaking in radiative η decays

We study the η → γγ, η → γμ − μ + and η → π 0 γγ decays using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't Hooft instanton induced U A (1) breaking interaction. We find that the η-meson mass, the η → γγ, η → γμ − μ + and η → π 0 γγ decay widths are in good agreement with the experimental values when the U A (1) breaking is strong and the flavor SU(3) singlet-octet mixing angle θ is about zero.

Strong UA(1)breaking in radiative η decays and baryon systems

We study the \egg, \egm and \epg decays using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't~Hooft instanton induced interaction. We find that the $\eta$-meson mass, the \egg, \egm and \epg decay widths are in good agreement with the experimental values when the $U_{A}(1)$ breaking is strong and the flavor $SU(3)$ singlet-octet mixing angle $\theta$ is about zero. The calculated $\eta \gamma \gamma^\ast$ transition form factor has somewhat weaker dependence on the squared four-momentum of the virtual photon. The effects of the $U_A(1)$ anomaly on the scalar quark contents in the nucleon, the $\Sigma_{\pi N}$ and $\Sigma_{KN}$ terms and the baryon number one and two systems are also studied.

Supersymmetric sigma models and 't Hooft instantons

Witten's linear sigma model for ADHM instantons possesses a natural (0, 4) supersymmetry. We study generalizations of the infrared limit of the model that are invariant under (4, 4) supersymmetry. In the case of four spacetime dimensions a background with a conformally flat metric and torsion is required. The geometry is specified by a single real scalar function satisfying Laplace's equation. It gives rise to 't Hooft instantons for the gauge group SU(2), instead of the general ADHM instantons for an SO(n) gauge group in the case (0, 4).

Effects of the UA(1) anomaly on η → 2γ decay

We study the η → 2γ decay using an extended three-flavor Nambu-Jona-Lasinio model that includes the 't Hooft instanton induced interaction. The η meson mass and the η → 2γ decay width are reproduced simultaneously with a rather strong instanton induced interaction. The calculated η decay constant is f η = 2.23 f π and it suggests that the η meson is no longer a Goldstone boson.

N-soliton-type solutions of SU(2) self-duality Yang-Mills equations in various spaces and their Backlund transformations

We show that Getmov's N-soliton-type solutions in the selfduality Yang-Mills (SDYM) equations in lhe (+ - - -)-signatured M4-space can be derived in a unified way similar to that of deriving '1 Hooft's instanton solutions in the (+ t t t)-signaNred E4-space, Further. we show that such N-soliton-type solutions can also be constructed for the SDYM equations in

How many gravitational't Hooft instantons are there past the first one?

Using the necessary and sufficient condition of Capovilla, Jacobson and Dell, it is shown that a result of Samuel for gravitational instantons does not extend to 't Hooft's instantons of winding numbers larger than one. A formula for the next instanton satisfying this condition is given.

Numerical study of the electroweak total cross section in semiclassical approximation

We discuss constraint instanton contributions to the total electroweak cross section given as a double path integral with “R- term” . Starting from an O(4) symmetric ansatz interpolating between the original instanton of size ϱ and large- x exponential falloff, we use numerical methods to find a constraint instanton. The final action agrees well with that from the 't Hooft instanton but there are deviations for the ϱ-dependence of the pole residues, leading to a decrease in the cross section.