You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
the o(3 ) sigma model in ( 2 + 1 ) dimensions is a popular model in theoretical physics and has been studied extensively @xcite@xcite . as far as static solutions are concerened
, the model is integrable and of bogomolnyi type @xcite .
the exact solutions are therefore available via simple analytical expressions . in contrast ,
similar models in ( 3 + 1 ) dimensions ( @xcite,@xcite,@xcite,@xcite ) , are neither integrable nor of bogomolnyi type . nevertheless , the soliton solutions of models in 3 + 1 dimensions are extensively studied numerically and have found application in particle and nuclear physics @xcite .
soliton solutions in ( 2 + 1 ) dimensions , modified by the addition of the hopf term are topologically stable and are classified according to the homotopy @xmath0 .
these solutions are scale - invariant .
this property leads to some difficulties upon quantization .
moreover , upon interacting with each other , solitons undergo change of size and tend to become singular @xcite .
the soliton solutions of the o(3 ) sigma model with a suitable choice of potential are presented explicitly in @xcite together with their interaction behavior .
these solitons are also called q - lumps .
there are two natural ways for breaking the scale - invariance : gauging the symmetry , and including a potential term @xcite .
it has been shown that gauging the u(1 ) subgroup by a chern - simons term and including a suitable potential leads to both topological and nontopological solitons which are not scale - invariant @xcite .
the potential discussed in @xcite has two discrete minima @xmath1 for which the u(1 ) symmetry is not spontaneously broken in ( 2 + 1 ) dimensions .
this model was further studied by mukherjee @xcite , where it was shown that the degeneracy of topological solitons is removed by including a potential with symmetry - breaking minima .
solutions with azimuthal vector potentials ( @xmath2 ) , have quantized magnetic flux ( @xmath3 ) , spin ( @xmath4 ) , and charge ( @xmath5 ) .    in the present paper
, we will show that within the framework of the model presented in @xcite , exact soliton solutions exist which depend on one spatial dimension , resembling domain - wall solutions of the @xmath6 theory . because of the non - trivial mapping between the boundaries and the discrete vacua , the solutions are topologically stable .
the stability and lack of the scale invariance are also verified using the energy functional of the system .
the lagrangian of the model considered here , is the one partially studied in @xcite , in ( 2 + 1 ) dimensions : @xmath7 here @xmath8 is a triplet of scalar fields , constrained to a @xmath9 : @xmath10 where @xmath11 and @xmath12 ( a=1,2,3 ) are unit orthogonal vectors in the internal space .
we work in the minkowski spacetime with the metric tensor @xmath13 .
@xmath14 is the covariant derivative given by @xcite : @xmath15 where @xmath16 is the ( constant ) unit vector defined by @xmath17    the u(1 ) subgroup is gauged by the vector potential @xmath18 whose dynamics is dictated by the chern - simons term .
the potential @xmath19 gives a self interaction of the field @xmath20 .
note that the minima of the potential reside either on , @xmath21 or @xmath22 in 2 + 1 dimensions , soliton solutions of this system has been studied @xcite . in such a case , the u(1 )
symmetry is unbroken in ( [ vac1 ] ) , whereas ( [ vac2 ] ) corresponds to the spontaneous breaking of this symmetry .    in 1 + 1 dimensions
, we expect that the disconnected vacua facilitate the existence of solitons . because of the existence of disconnected vacua
, we can have non - trivial mappings between the boundaries of the 1-dimensional space and these disconnected vacua and thus topological stability ( figure [ vacua ] ) . in order to obtain these soliton solutions ,
we start with schwinger s energy - momentum tensor @xcite , which in the static limit becomes : @xmath23 where @xmath24 is the magnetic field .
a conserved current can also be constructed : @xmath25.\ ] ] for static solutions which depend on one space coordinate ( say @xmath26 ) , @xmath27 becomes : @xmath28 + \frac{1}{4}\phi_3\frac{\partial a_2}{\partial x},\ ] ] and the corresponding conserved total charge is : @xmath29 we also have @xmath30 with @xmath31 which leads to @xmath32    rearranging ( [ energeq ] ) , we can write @xcite@xcite : @xmath33 \pm 4\pi t.\ ] ] this leads to the bogomolnyi conditions : @xmath34 and @xmath35 which minimize the energy functional in a particular topological sector .
in this section , we obtain analytical domain - wall - like solutions in the case where the fields depend on only one of the space coordinates ( say @xmath26 ) .
the @xmath36-fields , which are constrained on a @xmath9 , are assumed to vary on a longitude .
because of the u(1 ) subgroup , this longitude is arbitrarily rotated to @xmath37 , in order to simplify the solutions .
let us expand the bogomolnyi equations ( [ bog1 ] ) and ( [ bog2 ] ) as : @xmath38 @xmath39 @xmath40 @xmath41 and @xmath42 it can be easily shown that the above equations , together with appropriate boundary conditions , lead to : @xmath43 and @xmath44 which implies @xmath45 note that @xmath46 for the desired solutions .
we also have @xmath47 equations ( [ dphi3 ] ) and ( [ da2 ] ) are readily solved to obtain @xmath48 @xmath45and@xmath31 from these , the @xmath49 field is also calculated : @xmath30 or @xmath50 @xmath51 is plotted in figure [ fig1 ] , and @xmath52 is shown in figure [ fig2 ] .
using ( [ energeq ] ) , the energy density can be easily calculated @xmath53 which is plotted in figure ( [ fig3 ] ) .
it is seen that the magnetic field and energy are concentrated in a thin region around @xmath54 , quite similar to the domain wall solutions of the @xmath6 theory in ( 3 + 1 ) dimensions . here
, the solution corresponds to a string on the @xmath55-plane which extends along the @xmath56-axis . integrating the energy density over @xmath26 ,
the total energy per unit length of the string is obtained : @xmath57 in order to check for the stability of the solution , we apply the scale transformation @xmath58 which leads to @xmath59 where @xmath60 and @xmath61 are positive quantities independent of @xmath62 .
the energy is found to be a minimum at @xmath63 , signalling the stability .
let us calculate the topological charge density ( the zero component of topological current ) . from ( [ topcharge ] ) , we obtain @xmath64,\ ] ] which is shown in figure ( [ fig4 ] ) .
the total topological charge is subsequently obtained : @xmath65 the values of @xmath66 and @xmath67 are seen to satisfy the well known inequality @xmath68 .
the spin of the solution @xcite@xcite is easily shown to vanish : @xmath69
in a field theory possessing the vacuum manifold @xmath70 , formulated in a d - dimensional space plus 1 time dimension , the localized static solutions constitute a mapping @xmath71 , where @xmath72 is the boundary of the d - dimensional space .
if the homotopy group of this mapping is nontrivial , then topological , soliton - like solutions are expected @xcite .
we showed that the nonlinear o(3 ) sigma model with a chern - simons term and a suitable potential is such a model .
we obtained examples of these solutions which satisfy the bogomolnyi s conditions . on the @xmath55-plane
, solutions correspond to a string along the @xmath56-axis , with energy density , charge density , and magnetic field confined to a thin band near to @xmath54 .
the width of this band ( string ) depends on the value of the parameter @xmath73 .
we also showed that the solutions are not scale invariant under @xmath74 .
rather , the energy is minimum for @xmath75 , indicating the stability of the solutions .
schroers , _ phys
b _ , * 356 * ( 1995 ) 291 . a.a . belavin and a.m.
polyakov , _ jetp lett . _
* 22 * ( 1975 ) 245 .
bogomolnyi , _ sov .
_ , * 24 * ( 1976 ) 449 . m. barriola and a. vilenkin , _ phys
_ , * 63 * ( 1989 ) 341 .
m. peyrard , b. m. a. g. piette and w.j .
zakrzewski , _ nonlinearity _ * 5 * ( 1992 ) 563 , 585 .
b.m.a.g piette , b.j .
schroers and w.j .
zakrzewski , _ nucl .
b _ * 439 * ( 1995 ) 205 . t.h.r .
skyrme , _ proc .
_ , * a260 * ( 1960 ) 127 .
e. witten , _ nucl .
_ , * b223 * ( 1983 ) 433 . r.a .
leese , m. peyrard and w.j .
zakrzewski , _ nonlinearity _ * 3 * ( 1990 ) 387 .
leese , _ nucl .
* b366 * ( 1991 ) 283 .
ghosh and s.k .
ghosh , _ phys .
b _ * 366 * ( 1996 ) 199 .
p. mukherjee , arxiv : hep - th/9905203 , 27 may 1999 , _ phys
. lett . _ ,
* b403 * ( 1997 ) 70 .
j. schwinger , _ phys .
* 127 * ( 1962 ) 324 .
r. rajaraman , _ solitons and instantons _ ,
elsevier , the netherlands , 1987 .
r. banerjee , _ phys .
_ , * 69 * ( 1992 ) 17 .
r. banerjee and p. mukherjee , _ nucl .
b _ * 478 * ( 1996 ) 235 .
n. riazi , _ int .
* 8 * no . 2 ( 2002 ) 115 .
we show that the least energy conditions in the gauged nonlinear sigma model with chern - simons term lead to exact soliton - like solutions which have the same features as domain walls . we will derive and discuss the corresponding solutions , and compute the total energy , charge , and spin of the resulting system .