17,461 research outputs found
On the Casimir operator dependences of QCD amplitudes
In eikonal and quenched approximations at least, it is argued that the strong
coupling fermionic QCD amplitudes obtained with the help of the newly
discovered effective locality property, depart from a dependence on the sole
quadratic Casimir operator, evaluated over the fundamental gauge
group representation. This result, in contradistinction with Perturbation
Theory, but also with a number of non-perturbative approaches such as the MIT
Bag, the Stochastic Vacuum Models, and Lattice simulations, accounts, instead,
for the full algebraic content of the rank-2 -Lie algebraComment: New Eq.(6) is more general than the previous one, and is further
detailed by Eqs.(7) and (8). Conclusion is a bit more detailed, and the
References completed with the titles of article
Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
We propose a new lattice superfield formalism in momentum representation
which accommodates species doublers of the lattice fermions and their bosonic
counterparts as super multiplets. We explicitly show that one dimensional N=2
model with interactions has exact Lie algebraic supersymmetry on the lattice
for all super charges. In coordinate representation the finite difference
operator is made to satisfy Leibnitz rule by introducing a non local product,
the ``star'' product, and the exact lattice supersymmetry is realized. The
standard momentum conservation is replaced on the lattice by the conservation
of the sine of the momentum, which plays a crucial role in the formulation.
Half lattice spacing structure is essential for the one dimensional model and
the lattice supersymmetry transformation can be identified as a half lattice
spacing translation combined with alternating sign structure. Invariance under
finite translations and locality in the continuum limit are explicitly
investigated and shown to be recovered. Supersymmetric Ward identities are
shown to be satisfied at one loop level. Lie algebraic lattice supersymmetry
algebra of this model suggests a close connection with Hopf algebraic exactness
of the link approach formulation of lattice supersymmetry.Comment: 34 pages, 2 figure
Zero-temperature Monte Carlo study of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice
We investigate the ground-state properties of the highly degenerate
non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on
the triangular lattice with Monte Carlo simulations. For that purpose, we
introduce an Ising pseudospin representation of the ground states, and we use a
simple Metropolis algorithm with local updates, as well as a powerful cluster
algorithm. At sizes that can be sampled with local updates, the presence of
long-range order is surprisingly combined with an algebraic decay of
correlations and the complete disordering of the chirality. It is only thanks
to the investigation of unusually large systems (containing spins)
with cluster updates that the true asymptotic regime can be reached and that
the system can be proven to consist of equivalent (i.e., equally ordered)
sublattices. These large-scale simulations also demonstrate that the scalar
chirality exhibits long-range order at zero temperature, implying that the
system has to undergo a finite-temperature phase transition. Finally, we show
that the average distance in the order parameter space, which has the structure
of an infinite Cayley tree, remains remarkably small between any pair of
points, even in the limit when the real space distance between them tends to
infinity.Comment: 15 pages, 10 figure
High energy QCD as a completely integrable model
We show that the one-dimensional lattice model proposed by Lipatov to
describe the high energy scattering of hadrons in multicolor QCD is completely
integrable. We identify this model as the XXX Heisenberg chain of noncompact
spin and find the conservation laws of the model. A generalized Bethe
ansatz is developed for the diagonalization of the hamiltonian and for the
calculation of hadron-hadron scattering amplitude.Comment: Latex style, 16 pages, ITP-SB-94-1
Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
The lattice superalgebra of the link approach is shown to satisfy a Hopf
algebraic supersymmetry where the difference operator is introduced as a
momentum operator. The breakdown of the Leibniz rule for the lattice difference
operator is accommodated as a coproduct operation of (quasi)triangular Hopf
algebra and the associated field theory is consistently defined as a braided
quantum field theory. Algebraic formulation of path integral is perturbatively
defined and Ward-Takahashi identity can be derived on the lattice. The claimed
inconsistency of the link approach leading to the ordering ambiguity for a
product of fields is solved by introducing an almost trivial braiding structure
corresponding to the triangular structure of the Hopf algebraic superalgebra.
This could be seen as a generalization of spin and statistics relation on the
lattice. From the consistency of this braiding structure of fields a grading
nature for the momentum operator is required.Comment: 45 page
Algebras, BPS States, and Strings
We clarify the role played by BPS states in the calculation of threshold
corrections of D=4, N=2 heterotic string compactifications. We evaluate these
corrections for some classes of compactifications and show that they are sums
of logarithmic functions over the positive roots of generalized Kac-Moody
algebras. Moreover, a certain limit of the formulae suggests a reformulation of
heterotic string in terms of a gauge theory based on hyperbolic algebras such
as . We define a generalized Kac-Moody Lie superalgebra associated to
the BPS states. Finally we discuss the relation of our results with string
duality.Comment: 64 pages, harvmac (b), Discussion of BRST improved, typos fixed, two
references adde
Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension
Nonperturbative exact solutions are allowed for quantum integrable models in
one space-dimension. Going beyond this class we propose an alternative Lax
matrix approach, exploiting the hidden multi-time concept in integrable systems
and construct a novel quantum nonlinear Schroedinger model in quasi-two
dimensions. An intriguing field commutator is discovered, confirming the
integrability of the model and yielding its exact Bethe ansatz solution with
rich scattering and bound-state properties. The universality of the scheme is
expected to cover diverse models, opening up a new direction in the field.Comment: 12 pages, 1 figure, Latex (This version to be published in Nucl Phys
B as Frontiers Article
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