13,411 research outputs found
The Effective Lagrangian of Three Dimensional Quantum Chromodynamics
We consider the low energy limit of three dimensional Quantum Chromodynamics
with an even number of flavors. We show that Parity is not spontaneously
broken, but the global (flavor) symmetry is spontaneously broken. The low
energy effective lagrangian is a nonlinear sigma model on the Grassmannian.
Some Chern--Simons terms are necessary in the lagrangian to realize the
discrete symmetries correctly. We consider also another parametrization of the
low energy sector which leads to a three dimensional analogue of the
Wess--Zumino--Witten--Novikov model. Since three dimensional QCD is believed to
be a model for quantum anti--ferromagnetism, our effective lagrangian can
describe their long wavelength excitations (spin waves).Comment: 18 page
Three Dimensional Quantum Chromodynamics
The subject of this talk was the review of our study of three ()
dimensional Quantum Chromodynamics. In our previous works, we showed the
existence of a phase where parity is unbroken and the flavor group is
broken to a subgroup . We derived the low energy effective
action for the theory and showed that it has solitonic excitations with Fermi
statistic, to be identified with the three dimensional ``baryon''. Finally, we
studied the current algebra for this effective action and we found a
co-homologically non trivial generalization of Kac-Moody algebras to three
dimensions.Comment: 7 pages, Plain TEX, talk presented by S.G. Rajeev at the XXVI
INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS, DALLAS TX AUG. 199
Baryons as Solitons in Three Dimensional Quantum Chromodynamics
We show that baryons of three dimensional Quantum Chromodynamics can be
understood as solitons of its effective lagrangian. In the parity preserving
phase we study, these baryons are fermions for odd and bosons for even
, never anyons. We quantize the collective variables of the solitons and
there by calculate the flavor quantum numbers, magnetic moments and mass
splittings of the baryon. The flavor quantum numbers are in agreement with
naive quark model for the low lying states. The magnetic moments and mass
splittings are smaller in the soliton model by a factor of . We also show that there is a dibaryon solution that is an analogue
of the deuteron. These solitons can describe defects in a quantum
anti--ferromagnet.Comment: 22 pages + 4 figures (figures not included, postscript files
available upon request
A generalization of the Subspace Theorem with polynomials of higher degree
Recently, Corvaja and Zannier obtained an extension of the Subspace Theorem
with arbitrary homogeneous polynomials of arbitrary degreee instead of linear
forms. Their result states that the set of solutions in P^n(K) (K number field)
of the inequality being considered is not Zariski dense. In our paper we prove
by a different method a generalization of their result, in which the solutions
are taken from an arbitrary projective variety X instead of P^n. Further, we
give a quantitative version which states in a precise form that the solutions
with large height lie ina finite number of proper subvarieties of X, with
explicit upper bounds for the number and for the degrees of these subvarieties.Comment: 31 page
A further improvement of the quantitative Subspace Theorem
In 2002, Evertse and Schlickewei obtained a quantitative version of the
so-called Absolute Parametric Subspace Theorem. This result deals with a
parametrized class of twisted heights. One of the consequences of this result
is a quantitative version of the Absolute Subspace Theorem, giving an explicit
upper bound for the number of subspaces containing the solutions of the
Diophantine inequality under consideration.
In the present paper, we further improve Evertse's and Schlickewei's
quantitative version of the Absolute Parametric Subspace Theorem, and deduce an
improved quantitative version of the Absolute Subspace Theorem. We combine
ideas from the proof of Evertse and Schlickewei (which is basically a
substantial refinement of Schmidt's proof of his Subspace Theorem from 1972,
with ideas from Faltings' and Wuestholz' proof of the Subspace Theorem.Comment: 93 page
Relative Prym varieties associated to the double cover of an Enriques surface
Given an Enriques surface T , its universal K3 cover f : S → T , and a genus g linear system |C| on T, we construct the relative Prym variety PH = Prymv,H(D/C), where C → |C| and D → |f∗C| are the universal families, v is the Mukai vector (0, [D], 2−2g) and H is a polarization on S. The relative Prym variety is a (2g−2)-dimensional possibly singular variety, whose smooth locus is endowed with a hyperk ̈ahler structure. This variety is constructed as the closure of the fixed locus of a symplectic birational involution defined on the moduli space Mv,H (S). There is a natural Lagrangian fibration η : PH → |C|, that makes the regular locus of PH into an integrable system whose general fiber is a (g − 1)-dimensional (principally polarized) Prym variety, which in most cases is not the Jacobian of a curve. We prove that if |C| is a hyperelliptic linear system, then PH admits a symplectic resolution which is birational to a hyperk ̈ahler manifold of K3[g−1]-type, while if |C| is not hyperelliptic, then PH admits no symplectic resolution. We also prove that any resolution of PH is simply connected and, when g is odd, any resolution of PH has h2,0-Hodge number equal to one
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