Collective Coordinate Quantization Research Articles

Skyrme Crystals, Nuclear Matter and Compact Stars

A general review of the crystalline solutions of the generalized Skyrmemodel and their application to the study of cold nuclear matter at finite density and the Equation of State (EOS) of neutron stars is presented. For the relevant range of densities, the ground state of the Skyrmemodel on the three torus is shown to correspond to configurations with different symmetries, with a sequence of phase transitions between such configurations. The effects of nonzero finite isospin asymmetry are taken into account by the canonical quantization of isospin collective coordinates, and some thermodynamical and nuclear observables (such as the symmetry energy) are computed as a function of the density. We also explore the extension of the model to accommodate strange degrees of freedom, and find a first-order transition for the condensation of kaons in the Skyrme crystal background in a thermodynamically consistent, non-perturbative way. Finally, an approximate EOS of dense matter is constructed by fitting the free parameters of the model to some nuclear observables close to saturation density, which are particularly relevant for the description of nuclear matter. The resulting neutron star mass–radius curves already reasonably satisfy current astrophysical constraints.

Heavy baryons in holographic QCD with higher dimensional degrees of freedom

We try to introduce heavy flavors to Sakai-Sugimoto model by regarding higher dimensional components of gauge fields as heavy mesons. Using the Forg\'acs and Manton approach, we obtain a theory composed of heavy mesons and the instanton of light flavors. Applying the collective coordinate quantization method, we derived a mass formula of heavy baryons. In the leading order of $1/m_{H}$ expansion ($m_{H}$ the mass of a heavy quark), we find singlet and doublet states in the heavy quark symmetry (HQS). Also, we obtain the degenerate Roper like and odd parity excitations. By virtue of heavy meson degrees of freedom, our mass formula reproduces the mass ordering of $\Sigma^*_c$ and $\Lambda_c^*$ correctly.

Collective coordinate quantization and spin statistics of the solitons in theCPNSkyrme-Faddeev model

The $\mathbb{C}P^N$ extended Skyrme-Faddeev model possesses planar soliton solutions. We consider quantum aspects of the solutions applying collective coordinate quantization in regime of rigid body approximation. In order to discuss statistical properties of the solutions we include an Abelian Chern-Simons term (the Hopf term) in the Lagrangian. Since $\Pi_3(\mathbb{C}P^1)=\mathbb{Z}$ then for $N=1$ the term becomes an integer. On the other hand for $N>1$ it became perturbative because $\Pi_3(\mathbb{C}P^N)$ is trivial. The prefactor of the Hopf term (anyon angle) $\Theta$ is not quantized and its value depends on the physical system. The corresponding fermionic models can fix value of the angle $\Theta$ for all $N$ in a way that the soliton with $N=1$ is not an anyon type whereas for $N>1$ it is always an anyon even for $\Theta=n\pi, n\in \mathbb{Z}$. We quantize the solutions and calculate several mass spectra for $N=2$. Finally we discuss generalization for $N\geqq 3$.

Heavy baryons with strangeness in a soliton model

We present results from a chiral soliton model calculation for the spectrum of baryons with a single heavy quark (charm or bottom) and non-zero strangeness. We treat the strange components within a three flavor collective coordinate quantization of the soliton that fully accounts for light flavor symmetry breaking. Heavy baryons emerge by binding a heavy meson to the soliton. The dynamics of this heavy meson is described by the heavy quark effective theory with finite mass effects included.

Bogomol’nyi-Prasad-Sommerfield Skyrme Model and Nuclear Binding Energies

We use the classical Bogomol'nyi-Prasad-Sommerfield (BPS) soliton solutions of the BPS Skyrme model together with corrections from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit breaking of the isospin symmetry-accounting for the proton-neutron mass difference-to calculate nuclear binding energies. We find that the resulting binding energies are already in excellent agreement with their physical values for heavier nuclei, demonstrating thereby that the BPS Skyrme model is a distinguished starting point for a detailed quantitative investigation of nuclear and low-energy strong interaction physics.

Nuclear binding energies from a Bogomol'nyi-Prasad-Sommerfield Skyrme model

Recently, within the space of generalized Skyrme models, a submodel with a Bogomol'nyi-Prasad-Sommerfield (BPS) bound was identified that reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is expected to be more accurate on theoretical grounds, the resulting binding energies are already in excellent agreement with their physical values. This result provides further strong evidence for the viability of the BPS Skyrme model as a distinguished starting point and lowest-order approximation for the detailed quantitative investigation of nuclear and hadron physics.

Aspects of 3d $ \mathcal{N}=2 $ Chern-Simons-Matter theories

We comment on various aspects of the the dynamics of 3d N=2 Chern-Simons gauge theories and their possible phases. Depending on the matter content, real masses and FI parameters, there can be non-compact Higgs or Coulomb branches, compact Higgs or Coulomb branches, and isolated vacua. We compute the Witten index of the theories, and show that it does not change when the system undergoes a phase transition. We study aspects of monopole operators and solitons in these theories, and clarify subtleties in the soliton collective coordinate quantization. We show that solitons are compatible with a mirror symmetry exchange of Higgs and Coulomb branches, with BPS solitons on one branch related to the modulus of the other. Among other results, we show how to derive Aharony duality from Giveon-Kutasov duality.

Relativistic collective coordinate quantization of solitons: Spinning Skyrmion

We develop a consistent relativistic generalization of collective coordinate quantization of field theory solitons. Our principle of introducing collective coordinates is that the equations of motion of the collective coordinates ensure those of the original field theory. We illustrate this principle with the quantization of spinning degrees of freedom of Skyrmion representing baryons. We calculate the leading relativistic corrections to the static properties of nucleons, and find that the corrections are non-negligible ones of 10% to 20%.

Bound kaon approach for the ppK − system in the Skyrme model

The lightest nuclear $\overline K$ bound state, ppK −, is investigated in the Skyrme model. We describe the ppK − as two-Skyrmion around which a kaon field fluctuates. The two-Skyrmion is projected onto the (pp) S=0 state using the collective coordinate quantization method. We find that the energy of K − can be considerably small, and that ppK − is a molecular state. The binding energy of the ppK − and the mean pp distance are estimated to be B.E. = 104–126 MeV and $\sqrt{\langle r_{pp}^{2}\rangle}$ = 1.6–1.8 fm, respectively.

Formula omitted] dibaryons in the Einstein–Skyrme model

SU(3) collective coordinate quantization to the regular solution of the B=2 axially symmetric Einstein–Skyrme system is performed. For the symmetry breaking term, exact diagonalization method called Yabu–Ando approach are used. The effect of the gravity on the mass spectra of the SU(3) dibaryons and the symmetry breaking term is studied in detail. In the strong gravity limit, the symmetry breaking term significantly reduces and exact SU(3) flavor symmetry is recovered.

Baryons and the Chern-Simons Term in Holographic QCD with Three Flavors

We study dynamical baryons in the holographic QCD model of Sakai and Sugimoto in the case of three flavors, with special interest in the construction of the Chern-Simons (CS) term. The baryon classical solution in this model is given by the BPST instanton, and we carry out the collective coordinate quantization of this solution. The CS term should give rise to a first-class constraint which selects baryon states with the correct spins. However, the original CS term written in terms of the CS 5-form does not do so. Considering this fact, we propose a new CS term that is gauge invariant and takes the form of an integral over a six-dimensional space whose boundary is the original five-dimensional spacetime of the holographic model. Collective coordinate quantization using our new CS term leads to the correct baryon states and their mass formula.

On the spin of the B = 7 skyrmion

We investigate the collective coordinate quantization of the icosahedrally symmetric B = 7 skyrmion, which is known to have a ground state with spin and isospin . We find a particular quantum state maximally preserving the symmetries of the classical solution, and also present a novel relationship between the quantum state and the rational map approximation to the classical solution. We also investigate the allowed spin states if the icosahedral symmetry is partially broken. Skyrme field configurations with D5 residual symmetry can be quantized with spin , giving a realistic model for the ground states of the 7Li/7Be isospin doublet.

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.

BPSR-balls in Script N = 4 SYM onR×S3, quantum Hall analogy and AdS/CFT holography

In this paper, we propose a new approach to study the BPS dynamics in N=4 supersymmetric U(N) Yang-Mills theory on R X S^3, in order to better understand the emergence of gravity in the gauge theory. Our approach is based on supersymmetric, space-filling Q-balls with R-charge, which we call R-balls. The usual collective coordinate method for non-topological scalar solitons is applied to quantize the half and quarter BPS R-balls. In each case, a different quantization method is also applied to confirm the results from the collective coordinate quantization. For finite N, the half BPS R-balls with a U(1) R-charge have a moduli space which, upon quantization, results in the states of a quantum Hall droplet with filling factor one. These states are known to correspond to the ``sources'' in the Lin-Lunin-Maldacena geometries in IIB supergravity. For large N, we find a new class of quarter BPS R-balls with a non-commutativity parameter. Quantization on the moduli space of such R-balls gives rise to a non-commutative Chern-Simons matrix mechanics, which is known to describe a fractional quantum Hall system. In view of AdS/CFT holography, this demonstrates a profound connection of emergent quantum gravity with non-commutative geometry, of which the quantum Hall effect is a special case.

Fermions from half-BPS supergravity

We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena (hep-th/0409174). The LLM geometries are parameterized by a single function $u$ on a plane. We treat this function as a collective coordinate. We arrive at the collective coordinate action as well as path integral measure by considering D3 branes in an arbitrary LLM geometry. The resulting functional integral is shown, using known methods (hep-th/9309028), to be the classical limit of a functional integral for free fermions in a harmonic oscillator. The function $u$ gets identified with the classical limit of the Wigner phase space distribution of the fermion theory which satisfies u * u = u. The calculation shows how configuration space of supergravity becomes a phase space (hence noncommutative) in the half-BPS sector. Our method sheds new light on counting supersymmetric configurations in supergravity.

Effective Theory Approach to the Skyrme Model and Application to Pentaquarks

The Skyrme model is reconsidered from an effective theory point of view. From the most general chiral Lagrangian up to including terms of order $p^4$, $N_c$ and $\delta m^2$ ($\delta m\equiv m_s-m$), new interactions, which have never been considered before, appear upon collective coordinate quantization. We obtain the parameter set best fitted to the observed low-lying baryon masses, by performing the second order perturbative calculations with respect to $\delta m$. We calculate the masses and the decay widths of the other members of (mainly) anti-decuplet pentaquark states. The formula for the decay widths is reconsidered and its baryon mass dependence is clarified.

Exotic baryons with charm number±1from the Skyrme model

We illustrate the exotic SU(3) baryon sub-multiplets in the SU(4) baryon multiplets predicted from the flavor SU(4) collective-coordinate quantization, and investigate the exotic states with charm number $C=\pm1$ up to leading order of $1/N_c$ under chiral $SU(3)_L\times SU(3)_R$ symmetry and the heavy quark limit from bound state approach. We find that there exist the $\bar{15}$-plets and 24-plets with C=1 and the $\bar{6}$-plets, 15-plets and $15^{\prime}$-plets with $C=-1$ bounded in this approach, qualitatively consistent with predictions from the flavor SU(4) collective-coordinate quantization. By fitting one unique parameter of leading SU(3) flavor symmetry breaking term with the mass difference between $\Xi_c$ and $\Sigma_c$ and up to $O(m_Q^0N_c^{-1})$, we give all the average masses of baryons in $\bar{6}$-plet and 15-plet. Several general relations of these masses without any parameter are also introduced.

Is Θ+(1540) a kaon–skyrmion resonance?

We reconsider the relationship between the bound state and the SU(3) rigid rotator approaches to strangeness in the Skyrme model. For non-exotic S=−1 baryons the bound state approach matches for small m K onto the rigid rotator approach, and the bound state mode turns into the rotator zero-mode. However, for small m K , we find no S=+1 kaon bound states or resonances in the spectrum, confirming previous work. This suggests that, at least for large N and small m K , the exotic state may be an artifact of the rigid rotator approach to the Skyrme model. An S=+1 near-threshold state comes into existence only for sufficiently large SU(3) breaking. If such a state exists, then it has the expected quantum numbers of Θ +: I=0, J= 1 2 and positive parity. Other exotic states with (I=1,J P= 3 2 +) , (I=1,J P= 1 2 +) , (I=2,J P= 5 2 +) and (I=2,J P= 3 2 +) appear as its SU(2) rotator excitations. As a test of our methods, we also identify a D-wave S=−1 near-threshold resonance that, upon SU(2) collective coordinate quantization, reproduces the mass splittings of the observed states Λ(1520), Σ(1670) and Σ(1775) with good accuracy.

COLLECTIVE COORDINATE QUANTIZATION OF CP1 MODEL COUPLED TO HOPF TERM REVISITED

We show that the system where CP1 model coupled to Hopf term can reveal fractional spin in a collective coordinate quantization scheme, provided that one makes a transition to physically inequivalent sector within the same solitonic sector characterized by a nonvanishing topological number.

BRST INVARIANT CP1 MODEL THROUGH IMPROVED DIRAC QUANTIZATION

The Batalin–Fradkin–Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the CP1 model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through the standard path-integral procedure. Furthermore, performing collective coordinate quantization we obtain energy spectrum of rigid rotator in the CP1 model. Exploiting the Hopf bundle, we also show that the CP1 model is exactly equivalent to the O(3) nonlinear sigma model at the canonical level.