Color Degrees Of Freedom Research Articles

Quantum lozenge tiling and entanglement phase transition

While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system L as Llog⁡L. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.

Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models

We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions by building quantum six- and nineteen-vertex models with correlated interactions. The Hamiltonian is frustration free, and its projectors generate ergodic dynamics within the subspace of height configuration that are non negative. The ground state is a volume- and color-weighted superposition of classical bi-color vertex configurations with non-negative heights in the bulk and zero height on the boundary. The entanglement entropy between subsystems has a phase transition as the qq-deformation parameter is tuned, which is shown to be robust in the presence of an external field acting on the color degree of freedom. The ground state undergoes a quantum phase transition between area- and volume-law entanglement phases with a critical point where entanglement entropy scales as a function L\log LLlogL of the linear system size LL. Intermediate power law scalings between L\log LLlogL and L^2L2 can be achieved with an inhomogeneous deformation parameter that approaches 1 at different rates in the thermodynamic limit. For the q>1q>1 phase, we construct a variational wave function that establishes an upper bound on the spectral gap that scales as q^{-L^3/8}q−L3/8.

Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation

It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The <I>D</I>-theory then helps us to associate the continuum limit of the <i>(4+1)D </i>aniferromagnet to <i>4D </i>principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the<i> D</i>-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.

Transverse-momentum-dependent parton distribution functions for spin-1 hadrons

We show transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions by taking the decomposition of a quark correlation function in the Lorentz-invariant way with the conditions of Hermiticity and parity invariance. We found 30 new TMDs in the tensor-polarized spin-1 hadron at twists 3 and 4 in addition to 10 TMDs at twist 2. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtained new sum rules for the time-reversal-odd structure functions, {\int d^2 k_T g_{LT} = \int d^2 k_T h_{LL} = \int d^2 k_T h_{3LL} =0}∫d2kTgLT=∫d2kThLL=∫d2kTh3LL=0, at twists 3 and 4. We also indicated that transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs can probe color degrees of freedom, so that they are valuable in providing unique opportunities for creating interdisciplinary physics fields such as gluon condensate, color Aharonov-Bohm effect, and color entanglement. We also found three new collinear PDFs at twists 3 and 4, and a twist-2 relation and a sum rule were derived in analogy to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule on the structure function {g_2}g2.

Color confinement, dark matter and the missing anti-matter

Quantum chromodynamics is the fundamental theory to describe strong interaction, where quarks and gluons have the color degrees of freedom. However, a single quark or gluon cannot be separated out and all observable particles are color singlet states. Color confinement or quark confinement conjecture can be proved by considering not only the strong interaction but also the electroweak interaction, which is the SU(3) c invariant. Any measurable state that has to be a color singlet is the direct consequence of the common symmetry of the standard model. Color non-singlet objects are created from the big bang when the interaction breaks SU(3) c symmetry based on the non-local Lagrangian. There is nearly no interaction between colored objects and the color singlet Universe when the momentum transfer is not large enough. Colored objects are reasonable candidates of dark matter and the missing anti-matter in the Universe can also be easily explained. Dark matter can be produced in a laboratory, which can be tested by measuring the energy loss and baryon number change in the extremely high energy collisions of particles and anti-particles.

Color confinement at the boundary of the conformally compactified AdS5

The topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal boundary of AdS5 spacetime, topologically equivalent to the closed manifold S1× S3, by considering the coupling of two massless opposite charges on it. Taking the interaction potential as the analog of Coulomb interaction (derived from a fundamental solution of the S3 Laplace-Beltrami operator), a conformal S1× S3 metric deformation is proposed, such that free motion on the deformed metric is equivalent to motion on the round metric in the presence of the interaction potential. We give explicit expressions for the generators of the conformal algebra in the representation induced by the metric deformation.By identifying the charge as the color degree of freedom in QCD, and the two charges system as a quark-anti-quark system, we argue that the associated conformal wave operator equation could provide a realistic quantum mechanical description of the simplest QCD system, the mesons.Finally, we discuss the possibility of employing the compactification radius, R, as an- other scale along ΛQCD, by means of which, upon reparametrizing Q2c2 as (Q2c2+ħ2c2/R2), a perturbative treatment of processes in the infrared could be approached.

Bulk geometry in gauge/gravity duality and color degrees of freedom

$\mathrm{U}(N)$ supersymmetric Yang-Mills theory naturally appears as the low-energy effective theory of a system of $N$ D-branes and open strings between them. Transverse spatial directions emerge from scalar fields, which are $N\ifmmode\times\else\texttimes\fi{}N$ matrices with color indices; roughly speaking, the eigenvalues are the locations of D-branes. In the past, it was argued that this simple ``emergent space'' picture cannot be used in the context of gauge/gravity duality, because the ground-state wave function delocalizes at large $N$, leading to a conflict with the locality in the bulk geometry. In this paper, we show that this conventional wisdom is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. This conclusion is obtained by clarifying the meaning of the ``diagonalization of a matrix'' in Yang-Mills theory, which is not as obvious as one might think. This observation opens up the prospect of characterizing the bulk geometry via the color degrees of freedom in Yang-Mills theory, all the way down to the center of the bulk.

Entanglement and confinement in coupled quantum systems

We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings make the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-q limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.

Lightest flavor-singlet qqq baryons as witnesses to color

We present a new computation in a field-theoretical model of Coulomb gauge QCD of the first radial and angular excitations of a qqq system in a SU(3) flavor singlet state, Lambda_S. The traditional motivation for the study is that the absence of flavor singlets in the lowest-lying spectrum is a direct consequence of the color degree of freedom. (The calculation is tested with decuplet baryons Delta(1232) and Omega(1672).) We also analyze decay branching fractions of the flavor singlet baryon for various masses with the simplest effective Lagrangians.

High-Energy Standard Model from the Gauge Group Contraction

The evolution of properties and interactions of elementary particles is described, beginning with the Planck scale of $10^{19}$ GeV. The description is based on the hypothesis that high-temperature (high-energy) limit of the Standard Model is generated by the gauge group contraction. In the infinite-temperature limit, properties of particles fundamentally change: all particles lose their masses, only massless neutral $Z$ bosons and $u$ quarks together with neutrinos and photons survive. Weak interactions become long-range ones and are generated by neutral currents. Quarks have only one color degree of freedom.

Thermodynamics of hot strong-interaction matter from ultrarelativistic nuclear collisions

Collisions between heavy atomic nuclei at ultra-relativistic energies are carried out at particle colliders to produce the quark-gluon plasma, a state of matter where quarks and gluons are not confined into hadrons, and colour degrees of freedom are liberated. This state is thought to be produced as a transient phenomenon before it fragments into thousands of particles that reach the particle detectors. Despite two decades of investigations, one of the big open questions is to obtain an experimental determination of the temperature reached in a heavy-ion collision, and a simultaneous determination of another thermodynamic quantity, such as the entropy density, that would give access to the number of degrees of freedom. Here we obtain the first such determination, utilizing state-of-the-art hydrodynamic simulations. We define an effective temperature, averaged over the space-time evolution of the medium. Then, using experimental data, we determine this temperature, the corresponding entropy density and speed of sound in the matter created in lead-lead collisions at the Large Hadron Collider. Our results agree with first-principles calculations from lattice quantum chromodynamics and confirm that a deconfined phase of matter is indeed produced.

Anatomy of deconfinement

In the weak coupling limit of SUN Yang-Mills theory and the O(N) vector model, explicit state counting allows us to demonstrate the existence of a partially deconfined phase: M of N colors deconfine, and frac{M}{N} gradually grows from zero (confinement) to one (complete deconfinement). We point out that the mechanism admits a simple interpretation in the form of spontaneous breaking of gauge symmetry. In terms of the dual gravity theory, such breaking occurs during the formation of a black hole. We speculate whether the breaking and restoration of gauge symmetry can serve as an alternative definition of the deconfinement transition in theories without center symmetry, such as QCD. We also discuss the role of the color degrees of freedom in the emergence of the bulk geometry in holographic duality.

On Standard Model, Topological Skyrme Model and Revival of the Sakaton

We study the basic conflict between the standard model of particle physics and an another similarly structured but quite different model having the electric charge with color degrees of freedom, and how they connect to a consistent study of QCD for arbitrary number of colors. Further, with the imposition of the consistency with electric charges (i.e. with QED), the topological Skyrme model is shown to lead to a clear revival of the concept of the Sakaton as a physical reality which provides a new perspective to the hypernuclei.

On Standard Model, Topological Skyrme Model and Revival of the Sakaton

We study the basic conflict between the standard model of particle physics and an another similarly structured but quite different model having the electric charge with color degrees of freedom, and how they connect to a consistent study of QCD for arbitrary number of colors. Further, with the imposition of the consistency with electric charges (i.e. with QED), the topological Skyrme model is shown to lead to a clear revival of the concept of the Sakaton as a physical reality which provides a new perspective to the hypernuclei.

U(N) Yang-Mills in non-commutative space time

We present an approach to U⋆(N) Yang-Mills theory in non-commutative space based upon a novel phase-space analysis of the dynamical fields with additional auxiliary variables that generate Lorentz structure and colour degrees of freedom. To illustrate this formalism we compute the quadratic terms in the effective action focusing on the planar divergences so as to extract the β-function for the Yang-Mills coupling constant. Nonetheless the method presented is general and can be applied to calculate the effective action at arbitrary order of expansion in the coupling constant and is well suited to the computation of low energy one-loop scattering amplitudes.

Excess Higgs to gauge boson couplings

We predict slightly enhanced signal strengths in the Higgs coupling to the intermediate W and Z gauge bosons with a three percent excess relative to those of the Standard Model. The base of the prediction is a slightly different electroweak energy scale. The modified electroweak energy scale follows from an intrinsic conception of baryon dynamics that links to electroweak decays. Here electroweak interactions are fostered by a spontaneous symmetry break in baryonic configurations described on an intrinsic U(3) configuration space. The electroweak flavour degrees of freedom become intermingled with the colour degrees of freedom via a spontaneous U(2) pairing of two toroidal degrees of freedom in the intrinsic dynamics. The intrinsic potential thereby shapes the Higgs potential. This leads to the up-down quark mixing matrix element modifying the gauge boson couplings relative to the Standard Model expectations.

Perturbiner methods for effective field theories and the double copy

Perturbiner expansion provides a generating function for all Berends-Giele currents in a given quantum field theory. We apply this method to various effective field theories with and without color degrees of freedom. In the colored case, we study the U(N) non-linear sigma model of Goldstone bosons (NLSM) in a recent parametrization due to Cheung and Shen, as well as its extension involving a coupling to the bi-adjoint scalar. We propose a Lagrangian and a Cachazo-He-Yuan formula for the latter valid in multi-trace sectors and systematically calculate its amplitudes. Furthermore, we make a similar proposal for a higher-derivative correction to NLSM that agrees with the subleading order of the abelian Z-theory. In the colorless cases, we formulate perturbiner expansions for the special Galileon and Born-Infeld theories. Finally, we study Kawai-Lewellen-Tye-like double-copy relations for Berends-Giele currents between the above colored and colorless theories. We find that they hold up to pure gauge terms, but without the need for further field redefinitions.

Relativistic Studies of Few-Body Systems Using the Bethe–Salpeter Approach

The Bethe–Salpeter equation is one of the most appropriate tools in quantum field theory for the treatment of bound state systems. We review two problems in this approach: (i) the influence of the cross-ladder (non-planar) interaction kernel with color degrees of freedom in two-boson systems; and (ii) the higher Fock-state contributions to the three-boson bound state. Some new calculations have been performed to illustrate the previous topics.

Worldline colour fields and non-Abelian quantum field theory

In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline “colour” fields. The colour fields generate Wilson loop interactions whilst Chern-Simons terms project onto an irreducible representation of the gauge group. We analyse this augmented worldline theory in phase space focusing on its supersymmetry and constraint algebra, arriving at a locally supersymmetric theory in superspace. We demonstrate canonical quantisation and the path integral on S1for simple representations of SU(N).

High temperature limit of the Standard Model due to gauge groups contraction

The high temperature (high energy) limit of the Standard Model is developed with the help of contractions its gauge groups. The elementary particles evolution in the early Universe from Plank time up to several milliseconds is deduced from this limit theory. Particle properties at the infinite temperature look very unusual: all particles are massless, only neutral Z-bosons, u-quarks, neutrinos and photons are survived in this limit. The weak interactions become long-range and are mediated by neutral currents, quarks have only one color degree of freedom.