89 research outputs found

### Current Algebra of Classical Non-Linear Sigma Models

The current algebra of classical non-linear sigma models on arbitrary
Riemannian manifolds is analyzed. It is found that introducing, in addition to
the Noether current $j_\mu$ associated with the global symmetry of the theory,
a composite scalar field $j$, the algebra closes under Poisson brackets.Comment: 6 page

### Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD

In this paper we investigate the nature of the transition from Abelian to
non-Abelian confinement (i.e. crossover vs. phase transition). To this end we
consider the basic N=2 model where non-Abelian flux tubes (strings) were first
found: supersymmetric QCD with the U(N) gauge group and N_f=N flavors of
fundamental matter (quarks). The Fayet-Iliopoulos term \xi triggers the squark
condensation and leads to the formation of non-Abelian strings. There are two
adjustable parameters in this model: \xi and the quark mass difference \Delta
m. We obtain the phase diagram on the (\xi, \Delta m) plane. At large \xi and
small \Delta m the world-sheet dynamics of the string orientational moduli is
described by N=2 two-dimensional CP(N-1) model. We show that as we reduce \xi
the theory exhibits a crossover to the Abelian (Seiberg-Witten) regime. Instead
of N^2 degrees of freedom of non-Abelian theory now only N degrees of freedom
survive in the low-energy spectrum. Dyons with certain quantum numbers condense
leading to the formation of the Abelian Z_N strings whose fluxes are fixed
inside the Cartan subalgebra of the gauge group. As we increase N this
crossover becomes exceedingly sharper becoming a genuine phase transition at N
=\infty.Comment: 40 pages, 4 figure

### Integrated Lax Formalism for PCM

By solving the first-order algebraic field equations which arise in the dual
formulation of the D=2 principal chiral model (PCM) we construct an integrated
Lax formalism built explicitly on the dual fields of the model rather than the
currents. The Lagrangian of the dual scalar field theory is also constructed.
Furthermore we present the first-order PDE system for an exponential
parametrization of the solutions and discuss the Frobenious integrability of
this system.Comment: 24 page

### The Hyperbolic Heisenberg and Sigma Models in (1+1)-dimensions

Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg
Ferromagnet and sigma models are discussed in the context of topological
solutions classifiable by an integer `winding number'. Some explicit solutions
are presented and the existence of certain classes of such winding solutions
examined.Comment: 13 pages, 1 figure, Latex, personal style file included tensind.sty,
Proof in section 3 altered, no changes to conclusion

### Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure

The Faddeev-Reshetikhin procedure corresponds to a removal of the
non-ultralocality of the classical SU(2) principal chiral model. It is realized
by defining another field theory, which has the same Lax pair and equations of
motion but a different Poisson structure and Hamiltonian. Following earlier
work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible
to alleviate in a similar way the non-ultralocality of symmetric space sigma
models. The equivalence of the equations of motion holds only at the level of
the Pohlmeyer reduction of these models, which corresponds to symmetric space
sine-Gordon models. This work therefore shows indirectly that symmetric space
sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an
integrable potential, have a mild non-ultralocality. The first step needed to
construct an integrable discretization of these models is performed by
determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change

### Integrable models: from dynamical solutions to string theory

We review the status of integrable models from the point of view of their
dynamics and integrability conditions. Some integrable models are discussed in
detail. We comment on the use it is made of them in string theory. We also
discuss the Bethe Ansatz solution of the SO(6) symmetric Hamiltonian with SO(6)
boundary.
This work is especially prepared for the seventieth anniversaries of
Andr\'{e} Swieca (in memoriam) and Roland K\"{o}berle.Comment: 24 pages, to appear in Brazilian Journal of Physic

### Gauge symmetry enhancement in Hamiltonian formalism

We study the Hamiltonian structure of the gauge symmetry enhancement in the
enlarged CP(N) model coupled with U(2) Chern-Simons term, which contains a free
parameter governing explicit symmetry breaking and symmetry enhancement. After
giving a general discussion of the geometry of constrained phase space suitable
for the symmetry enhancement, we explicitly perform the Dirac analysis of our
model and compute the Dirac brackets for the symmetry enhanced and broken
cases. We also discuss some related issues.Comment: 8 pages, typos correcte

### Quantum String Dynamics in the conformal invariant SL(2,R) WZWN Background: Anti-de Sitter Space with Torsion

We consider classical and quantum strings in the conformally invariant
background corresponding to the SL(2,R) WZWN model. This background is locally
anti-de Sitter spacetime with non-vanishing torsion. Conformal invariance is
expressed as the torsion being parallelized. The precise effect of the
conformal invariance on the dynamics of both circular and generic classical
strings is extracted. In particular, the conformal invariance gives rise to a
repulsive interaction of the string with the background which precisely cancels
the dominant attractive term arising from gravity. We perform both
semi-classical and canonical string-quantization, in order to see the effect of
the conformal invariance of the background on the string mass spectrum. Both
approaches yield that the high-mass states are governed by m sim HN (N,`large
integer'), where m is the string mass and H is the Hubble constant. It follows
that the level spacing grows proportionally to N: d(m^2 alpha')/dN sim N, while
the entropy goes like: S sim sqrt{m}. Moreover, it follows that there is no
Hagedorn temperature,so that the partition function is well defined at any
positive temperature. All results are compared with the analogue results in
Anti- de Sitter spacetime, which is a non conformal invariant background.
Conformal invariance simplifies the mathematics of the problem but the physics
remains mainly unchanged. Differences between conformal and non-conformal
backgrounds only appear in the intermediate region of the string spectrum, but
these differences are minor. For low and high masses, the string mass spectra
in conformal and non-conformal backgrounds are identical. Interestingly enough,
conformal invariance fixes the value of the spacetime curvature to be -69/(26
alpha').Comment: Latex file, 23 pages, no figure

### New Linear Systems for 2D Poincare Supergravities

A new linear system is constructed for Poincar\'e supergravities in two
dimensions. In contrast to previous results, which were based on the conformal
gauge, this linear system involves the topological world sheet degrees of
freedom (the Beltrami and super-Beltrami differentials). The associated
spectral parameter likewise depends on these and is itself subject to a pair of
differential equations, whose integrability condition yields one of the
equations of motion. These results suggest the existence of an extension of the
Geroch group mixing propagating and topological degrees of freedom on the world
sheet. We also develop a chiral tensor formalism for arbitrary Beltrami
differentials, in which the factorization of $2d$ diffeomorphisms is always
manifest.Comment: 26 pages, report DESY93-12

### The Coupled Modified Korteweg-de Vries Equations

Generalization of the modified KdV equation to a multi-component system, that
is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j
u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 0, i=0,
1, ..., M-1$, is studied. We apply a new extended version of the inverse
scattering method to this system. It is shown that this system has an infinite
number of conservation laws and multi-soliton solutions. Further, the initial
value problem of the model is solved.Comment: 26 pages, LaTex209 file, uses jpsj.st

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