3,199 research outputs found
New Phases of SU(3) and SU(4) at Finite Temperature
The addition of an adjoint Polyakov loop term to the action of a pure gauge
theory at finite temperature leads to new phases of SU(N) gauge theories. For
SU(3), a new phase is found which breaks Z(3) symmetry in a novel way; for
SU(4), the new phase exhibits spontaneous symmetry breaking of Z(4) to Z(2),
representing a partially confined phase in which quarks are confined, but
diquarks are not. The overall phase structure and thermodynamics is consistent
with a theoretical model of the effective potential for the Polyakov loop based
on perturbation theory.Comment: 18 pages, 17 figures, RevTeX
PT symmetry and large-N models
Recently developed methods for PT-symmetric models can be applied to
quantum-mechanical matrix and vector models. In matrix models, the calculation
of all singlet wave functions can be reduced to the solution a one-dimensional
PT-symmetric model. The large-N limit of a wide class of matrix models exists,
and properties of the lowest-lying singlet state can be computed using WKB. For
models with cubic and quartic interactions, the ground state energy appears to
show rapid convergence to the large-N limit. For the special case of a quartic
model, we find explicitly an isospectral Hermitian matrix model. The Hermitian
form for a vector model with O(N) symmetry can also be found, and shows many
unusual features. The effective potential obtained in the large-N limit of the
Hermitian form is shown to be identical to the form obtained from the original
PT-symmetric model using familiar constraint field methods. The analogous
constraint field prescription in four dimensions suggests that PT-symmetric
scalar field theories are asymptotically free.Comment: 15 pages, to be published in J. Phys. A special issue on Pseudo
Hermitian Hamiltonians in Quantum Physic
The Large-N Limit of PT-Symmetric O(N) Models
We study a -symmetric quantum mechanical model with an O(N)-symmetric
potential of the form using its
equivalent Hermitian form. Although the corresponding classical model has
finite-energy trajectories that escape to infinity, the spectrum of the quantum
theory is proven to consist only of bound states for all . We show that the
model has two distinct phases in the large- limit, with different scaling
behaviors as goes to infinity. The two phases are separated by a
first-order phase transition at a critical value of the dimensionless parameter
, given by .Comment: 7 pages, 2 figure
Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows
The nature of dynamo action in shear flows prone to magnetohydrodynamic
instabilities is investigated using the magnetorotational dynamo in Keplerian
shear flow as a prototype problem. Using direct numerical simulations and
Newton's method, we compute an exact time-periodic magnetorotational dynamo
solution to the three-dimensional dissipative incompressible
magnetohydrodynamic equations with rotation and shear. We discuss the physical
mechanism behind the cycle and show that it results from a combination of
linear and nonlinear interactions between a large-scale axisymmetric toroidal
magnetic field and non-axisymmetric perturbations amplified by the
magnetorotational instability. We demonstrate that this large scale dynamo
mechanism is overall intrinsically nonlinear and not reducible to the standard
mean-field dynamo formalism. Our results therefore provide clear evidence for a
generic nonlinear generation mechanism of time-dependent coherent large-scale
magnetic fields in shear flows and call for new theoretical dynamo models.
These findings may offer important clues to understand the transitional and
statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review
PT-symmetric interpretation of double-scaling
The conventional double-scaling limit of an O(N)-symmetric quartic quantum
field theory is inconsistent because the critical coupling constant is
negative. Thus, at the critical coupling the Lagrangian defines a quantum
theory with an upside-down potential whose energy appears to be unbounded
below. Worse yet, the integral representation of the partition function of the
theory does not exist. It is shown that one can avoid these difficulties if one
replaces the original theory by its PT-symmetric analog. For a zero-dimensional
O(N)-symmetric quartic vector model the partition function of the PT-symmetric
analog is calculated explicitly in the double-scaling limit.Comment: 11 pages, 2 figure
Center-stabilized Yang-Mills theory: confinement and large volume independence
We examine a double trace deformation of SU(N) Yang-Mills theory which, for
large and large volume, is equivalent to unmodified Yang-Mills theory up to
corrections. In contrast to the unmodified theory, large 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 volume independence in small
volumes. For small values of , if the theory is formulated on with a sufficiently small compactification size , then an analytic
treatment of the non-perturbative 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 or number of
colors 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 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 it provides a simple
fully reduced model for Yang-Mills theory. The construction is easily
generalized to QCD and other QCD-like theories.Comment: 29 pages, expanded discussion of multiple compactified dimension
Experimental demonstration of ray-rotation sheets
We have built microstructured sheets that rotate, on transmission, the direction of light rays by an arbitrary, but fixed, angle around the sheet normal. These ray-rotation sheets comprise two pairs of confocal lenticular arrays. In addition to rotating the direction of transmitted light rays, our sheets also offset ray position sideways on the scale of the diameter of the lenticules. If this ray offset is sufficiently small so that it cannot be resolved, our ray-rotation sheets appear to perform generalized refraction
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