Center Symmetry Research Articles

Confinement and the quark Fermi surface inSU(2N)QCD-like theories

Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the centre symmetry is spontaneously broken and colour is liberated. Our findings are supported by lattice gauge simulations for N_c=2...5 and are illustrated by means of a simple quark model.

Polyakov–Nambu–Jona-Lasinio model for adjoint fermions with periodic boundary conditions

Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on ${R}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ can lead to a restoration of center symmetry and confinement for sufficiently small circumference $L$ of ${S}^{1}$. At small $L$, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop $P$ in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselves would lead to a deconfined phase at small $L$. In order for the fermionic effects to dominate gauge field effects in the effective potential, the fermion mass must be sufficiently small. This indicates that chiral symmetry breaking effects are potentially important. We develop a Polyakov--Nambu--Jona-Lasinio (PNJL) model which combines the known perturbative behavior of adjoint QCD models at small $L$ with chiral symmetry breaking effects to produce an effective potential for the Polyakov loop $P$ and the chiral order parameter $\overline{\ensuremath{\psi}}\ensuremath{\psi}$. A rich phase structure emerges from the effective potential. Our results are consistent with the recent lattice simulations of Cossu and D'Elia, which found no evidence for a direct connection between the small-$L$ and large-$L$ confining regions. Nevertheless, the two confined regions are connected indirectly if an extended field theory model with an irrelevant four-fermion interaction is considered. Thus the small-$L$ and large-$L$ regions are part of a single confined phase.

Enhancement of quark number susceptibility with an alternative pattern of chiral symmetry breaking in dense matter

We explore general features of thermodynamic quantities and hadron mass spectra in a possible phase where chiral $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ symmetry is spontaneously broken while its center ${Z}_{2}$ symmetry remains unbroken. In this phase, chiral symmetry breaking is driven by a quartic quark condensate although a bilinear quark condensate vanishes. A Ginzburg-Landau free energy leads to a new tricritical point between the ${Z}_{2}$ broken and unbroken phases. Furthermore, a critical point can appear even in the chiral limit where explicit breaking is turned off, instead of a tricritical point at which restoration of chiral and its center symmetries takes place simultaneously. The net quark number density exhibits an abrupt change near the restoration of the center symmetry rather than that of the chiral symmetry. Hadron masses in possible phases are also studied in a linear sigma model. We show that, in the ${Z}_{2}$ symmetric phase, the $\overline{q}q$-type scalar meson with zero isospin $I=0$ splits from the $\overline{q}q$-type pseudoscalar meson with $I=1$.

Finite volume phases of large-Ngauge theories with massive adjoint fermions

The phase structure of QCD-like gauge theories with fermions in various representations is an interesting but generally analytically intractable problem. One way to ensure weak coupling is to define the theory in a small finite volume, in this case S3 × S1. Genuine phase transitions can then occur in the large N theory. Here, we use this technique to investigate SU(N) gauge theory with a number Nf of massive adjoint-valued Majorana fermions having non-thermal boundary conditions around S1. For Nf = 1 we find a line of transitions that separate the weak-coupling analogues of the confined and de-confined phases for which the density of eigenvalues of the Wilson line transform from the uniform distribution to a gapped distribution. However, the situation for Nf > 1 is much richer and a series of weak-coupling analogues of partially-confined phases appear which leave unbroken a psubgroup of the centre symmetry. In these p phases the eigenvalue density has p gaps and they are separated from the confining phase and from one-another by first order phase transitions. We show that for small enough mR (the mass of the fermions times the radius of the S3) only the confined phase exists. The large N phase diagram is consistent with the finite N result and with other approaches based on 3 × S1 calculations and lattice simulations.

A Quenched Study for QCD Phase-Transition on Anisotropic Lattices

The QCD deconfinement phase transition in pure SU(3) gauge theory is studied on an anisotropic lattice. The critical temperature is determined to be Tc ≈ 285 MeV. The relation between the deconfinement phase transition and the breakdown of Z(3) center symmetry is also discussed.

Nonperturbative volume reduction of large-NQCD with adjoint fermions

We use nonperturbative lattice techniques to study the volume-reduced ``Eguchi-Kawai'' version of four-dimensional large-$N$ QCD with a single adjoint Dirac fermion. We explore the phase diagram of this single-site theory in the space of quark mass and gauge coupling using Wilson fermions for a number of colors in the range $8\ensuremath{\le}N\ensuremath{\le}15$. Our evidence suggests that these values of $N$ are large enough to determine the nature of the phase diagram for $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We identify the region in the parameter space where the $({Z}_{N}{)}^{4}$ center symmetry is intact. According to previous theoretical work using the orbifolding paradigm, and assuming that translation invariance is not spontaneously broken in the infinite-volume theory, in this region volume reduction holds: the single-site and infinite-volume theories become equivalent when $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We find strong evidence that this region includes both light and heavy quarks (with masses that are at the cutoff scale), and our results are consistent with this region extending toward the continuum limit. We also compare the action density and the eigenvalue density of the overlap Dirac operator in the fundamental representation with those obtained in large-$N$ pure-gauge theory.

Nonlinear plasmonics with gold nanoparticle antennas

We investigate the nonlinear optical properties of gold nanoparticle pairs. Two excitation beams of frequencies ω1 and ω2 are used to induce nonlinear polarizations at the junction of a particle dimer. Nonlinearities of the second and third order can be controllably induced as a function of the dimer geometry, leading predominantly to second-harmonic generation (SHG), sum frequency generation (SFG) and four-wave mixing (4WM). Due to their center symmetry, dimers with identical particle diameters give rise to a very weak second-order response, without affecting the third-order response. Therefore, a sharp probe functionalized with a symmetric metal dimer acts as a nanoscale photon source emitting narrow-band photons of frequency 2ω1 − ω2. We demonstrate that this source can be employed as a near-field optical probe for high-resolution fluorescence imaging.

Deconfinement Phase Transition and the Quark Condensate

We study the dual quark condensate as a signal for the confinement-deconfinement phase transition of QCD. This order parameter for center symmetry has been defined recently by Bilgici et al. within the framework of lattice QCD. In this work we determine the ordinary and the dual quark condensate with functional methods using a formulation of the Dyson-Schwinger equations for the quark propagator on a torus. The temperature dependence of these condensates serves to investigate the interplay between the chiral and deconfinement transitions of quenched QCD.

Finite size phase transitions in QCD with adjoint fermions

We perform a lattice investigation of QCD with three colors and 2 flavors of Dirac (staggered) fermions in the adjoint representation, defined on a 4d space with one spatial dimension compactified, and study the phase structure of the theory as a function of the size Lc of the compactified dimension. We show that four different phases take place, corresponding to different realizations of center symmetry: two center symmetric phases, for large or small values of Lc, separated by two phases in which center symmetry is broken in two different ways; the dependence of these results on the quark mass is discussed. We study also chiral properties and how they are affected by the different realizations of center symmetry; chiral symmetry, in particular, stays spontaneously broken at the phase transitions and may be restored at much lower values of the compactification radius. Our results could be relevant to a recently proposed conjecture [7] of volume indepedence of QCD with adjoint fermions in the large Nc limit.

Geometric unitaries in JB-algebras

In this note, we study geometric unitaries of JB -algebras (in particular, self-adjoint parts of C ∗ -algebras). By using order theoretical arguments, we show that the geometric unitaries of a JB -algebra are precisely the central algebraic unitaries (or central symmetries).

Quantum Phase Transitions and New Scales in QCD-like Theories

It is commonly believed that in confining vectorlike gauge theories the center and chiral symmetry transition scales are parametrically of the same order and take place around the strong scale Lambda -1. We demonstrate that (nonthermal) compactification of such theories on R 3 x S1 exhibit new phase transition scales and unexpected phenomena. There are cases with single chiral symmetry breaking at an exotic scale Lambda-1/Nc in the absence of any change in center symmetry. The scale Lambda -1/N c,invisible in perturbation theory, is also the scale where Abelian versus non-Abelian confinement regimes meet. Large N c volume independence provides new insights and independently confirms the existence of these scales. We also show that certain phases and scales are outside the reach of holographic (supergravity) modeling of QCD.

Laser consecutive pulse heating and phase change: Influence of spatial distribution of laser pulse intensity on melting

Laser consecutive pulse heating of solid surface and the influence of the laser pulse parameter on the melting and mushy zone formation in the irradiated region are investigated. The laser pulse parameter ( β) defines the spatial distribution of the laser pulse power at the irradiated surface; in which case, β = 0 represents the Gaussian profile while β = 1 corresponds to the ring type of laser power distribution with the peak intensity away from the center (symmetry axis). β is set in such a way that the energy content in each pulse with different β values becomes the same. The control volume approach is used when modeling the heating and phase change processes. The laser pulse parameter is selected to alter the laser power intensity distribution across the irradiated surface while modifying the location and magnitude of the laser peak power intensity at the irradiated surface. It is found that the laser pulse parameter alters the sizes of the melting and mushy zones in the surface region.

Center-symmetric dimensional reduction of hot Yang-Mills theory

It is expected that incorporating the center symmetry in the conventional dimensionally reduced effective theory for high-temperature SU ( N c ) Yang-Mills theory, EQCD, will considerably extend its applicability towards the deconfinement transition. The construction of such a center-symmetric effective theory for the case of two colors is reviewed and lattice simulation results are presented. The simulations demonstrate that unlike EQCD, the new center-symmetric theory undergoes a second order confining phase transition in complete analogy with the full theory.

Center symmetry and the orientifold planar equivalence

We study the center symmetry of SU(N) gauge theories with fermions in the two-index representations, by computing the effective potential of the Polyakov loop in the large-mass expansion on the lattice. In the large-N limit and at non-zero temperature, we find that the center symmetry is Z_N for fermions in the adjoint representation and just Z_2 for fermions in the (anti)symmetric representation. We discuss the fact that our results do not contradict the orientifold planar equivalence, which relates a common sector defined by the bosonic gauge-invariant C-even states of theories with fermions in different two-index representations. Our results complement the work of Armoni et al. (2007), who showed how at zero temperature a Z_N center symmetry is dynamically recovered also for fermions in the (anti)symmetric representation, by considering the theories at finite temperature.

QCD Phase Transitions : Chiral and Center Symmetries(Current Topics)

QCD Phase Transitions : Chiral and Center Symmetries(Current Topics)

Electroweak phase transition in nearly conformal technicolor

We examine the temperature-dependent electroweak phase transition in extensions of the standard model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly conformal dynamics. In particular, we focus on the low energy effective theory used to describe minimal walking technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify significant regions of parameter space which yield a sufficiently strong first-order transition for electroweak baryogenesis. The composite particle spectrum corresponding to these regions can be produced and studied at the Large Hadron Collider experiment. We note the possible emergence of a second phase transition at lower temperatures. This occurs when the underlying technicolor theory possesses a nontrivial center symmetry.

Center-stabilized Yang-Mills theory: Confinement and largeNvolume independence

We examine a double trace deformation of $SU(N)$ Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/{N}^{2})$ corrections. In contrast to the unmodified theory, large $N$ volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large $N$ volume independence in small volumes. For small values of $N$, if the theory is formulated on ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ with a sufficiently small compactification size $L$, then an analytic treatment of the nonperturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference $L$ or number of colors $N$ decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small $N$ the deformed theory provides a novel example of a locally four-dimensional pure-gauge theory in which one has analytic control over confinement, while for large $N$ it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.

Theoretical Developments in SUSY

In this talk I review three topics: (i) Heterotic strings from N=1 gauge theories; (ii) Planar equivalence and emergent center symmetry in QCD-like theories; (iii) Exact result for gluon scattering amplitudes in N=4 (dual conformality).

Center-symmetric effective theory for high-temperature SU(2) Yang-Mills theory

We construct and study a dimensionally reduced effective theory for high-temperature SU(2) Yang-Mills theory that respects all the symmetries of the underlying theory. Our main motivation is to study whether the correct treatment of the center symmetry can help extend the applicability of the dimensional reduction procedure towards the confinement transition. After performing perturbative matching to the full theory at asymptotically high temperatures, we map the phase diagram of the effective theory using nonperturbative lattice simulations. We find that at lower temperature the theory undergoes a second-order confining phase transition, in complete analogy with the full theory, which is a direct consequence of having incorporated the center symmetry.

Dual quark condensate and dressed Polyakov loops

We construct a new order parameter for finite temperature QCD by considering the quark condensate for U(1)-valued temporal boundary conditions for the fermions. Fourier transformation with respect to the boundary condition defines the dual condensate. This quantity corresponds to an equivalence class of Polyakov loops, thereby being an order parameter for the center symmetry. We explore the duality relation between the quark condensate and these dressed Polyakov loops numerically, using quenched lattice QCD configurations below and above the QCD phase transition. It is demonstrated that the Dirac spectrum responds differently to changing the boundary condition, in a manner that reproduces the expected Polyakov loop pattern. We find the dressed Polyakov loops to be dominated by the lowest Dirac modes, in contrast to thin Polyakov loops investigated earlier.