6,260 research outputs found
Supermembrane limit of Yang-Mills theory
We consider Yang-Mills theory with super translation group in eleven
auxiliary dimensions as the structure group. The gauge theory is defined on a
direct product manifold , where is a
three-dimensional Lorentzian manifold and is a circle. We show that in
the infrared limit, when the metric on is scaled down, the Yang-Mills
action supplemented by a Wess-Zumino-type term reduces to the action of an
M2-brane.Comment: 1+6 page
Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
It is well known that there are no static non-Abelian monopole solutions in
pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions
exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times
S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions
of pure Yang-Mills theory on T^1\times S^2, where T^1 is R^1 or S^1. Namely,
imposing SO(3)-invariance and some reality conditions, we consistently reduce
the Yang-Mills model on the above spaces to a non-Abelian analog of the \phi^4
kink model whose static solutions give SU(N) monopole (-antimonopole)
configurations on the space R^{1,1}\times S^2 via the above-mentioned
correspondence. These solutions can also be considered as instanton
configurations of Yang-Mills theory in 2+1 dimensions. The kink model on
R^1\times S^1 admits also periodic sphaleron-type solutions describing chains
of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They
correspond to chains of n static monopole-antimonopole pairs on the space
R^1\times S^1\times S^2 which can also be interpreted as instanton
configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature
(thermal time circle). We also describe similar solutions in Euclidean SU(N)
gauge theory on S^1\times S^3 interpreted as chains of n
instanton-antiinstanton pairs.Comment: 16 pages; v2: subsection on topological charges added, title
expanded, some coefficients corrected, version to appear in PR
Integrable vortex-type equations on the two-sphere
We consider the Yang-Mills instanton equations on the four-dimensional
manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or
its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge
potential, we reduce the instanton equations on S^2xSigma to vortex-type
equations on the sphere S^2. It is shown that when the scalar curvature of the
manifold S^2xSigma vanishes, the vortex-type equations are integrable, i.e. can
be obtained as compatibility conditions of two linear equations (Lax pair)
which are written down explicitly. Thus, the standard methods of integrable
systems can be applied for constructing their solutions. However, even if the
scalar curvature of S^2xSigma does not vanish, the vortex equations are well
defined and have solutions for any values of the topological charge N. We show
that any solution to the vortex equations on S^2 with a fixed topological
charge N corresponds to a Yang-Mills instanton on S^2xSigma of charge (g-1)N.Comment: 14 pages; v2: clarifying comments added, published versio
String theories as the adiabatic limit of Yang-Mills theory
We consider Yang-Mills theory with a matrix gauge group on a direct
product manifold , where is a two-dimensional
Lorentzian manifold and is a two-dimensional open disc with the boundary
. The Euler-Lagrange equations for the metric on
yield constraint equations for the Yang-Mills energy-momentum tensor. We show
that in the adiabatic limit, when the metric on is scaled down, the
Yang-Mills equations plus constraints on the energy-momentum tensor become the
equations describing strings with a worldsheet moving in the based
loop group , where is the boundary of
. By choosing and putting to zero all parameters in besides , we get a string moving in . In
arXiv:1506.02175 it was described how one can obtain the Green-Schwarz
superstring action from Yang-Mills theory on while
shrinks to a point. Here we also consider Yang-Mills theory on a
three-dimensional manifold and show that in the limit when
the radius of tends to zero, the Yang-Mills action functional
supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring
action.Comment: 11 pages, v3: clarifying remarks added, new section on embedding of
the Green-Schwarz superstring into d=3 Yang-Mills theory include
Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
Correlation functions related to the dynamic density response of the
one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An
exact Bose-Fermi mapping is used to work in a fermionic representation with a
pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase
approximations are derived and the dynamic polarizability is calculated. The
results are valid to first order in 1/\gamma where \gamma is Lieb-Liniger
coupling parameter. Approximations for the dynamic and static structure factor
at finite temperature are presented. The results preclude superfluidity at any
finite temperature in the large-\gamma regime due to the Landau criterion. Due
to the exact Bose-Fermi duality, the results apply for spinless fermions with
weak p-wave interactions as well as for strongly interacting bosons.Comment: 13 pages, 5 figures, the journal versio
Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter
The subject of the study is the contact interaction of deformable elements of linear complementarity problem (LCP). To solve the linear complementarity problem, the Lemke method with the introduction of an increasing parameter of external loading is used. The proposed approach solves the degenerated matrix in a finite number of steps, while the dimensionality of the problem is limited to the area of contact. To solve the problem, the initial table of the Lemke method is generated using the contact matrix of stiffness and the contact load vector. The unknowns in the problem are mutual displacements and interaction forces of contacting pairs of points of deformable solids. The proposed approach makes it possible to evaluate the change in working schemes as the parameter of external load increases. The features of the proposed formulation of the problem are shown, the criteria for stopping the stepwise process of solving such problems are considered. Model examples for the proposed algorithm are given. The algorithm has shown its efficiency in application, including for complex model problems. Recommendations on the use of the proposed approach are given
On Explicit Point Multi-Monopoles in SU(2) Gauge Theory
It is well known that the Dirac monopole solution with the U(1) gauge group
embedded into the group SU(2) is equivalent to the SU(2) Wu-Yang point monopole
solution having no Dirac string singularity. We consider a multi-center
configuration of m Dirac monopoles and n anti-monopoles and its embedding into
SU(2) gauge theory. Using geometric methods, we construct an explicit solution
of the SU(2) Yang-Mills equations which generalizes the Wu-Yang solution to the
case of m monopoles and n anti-monopoles located at arbitrary points in R^3.Comment: 1+7 pages, LaTe
Palladium (II) Oxide Nanostructures as Promising Materials for Gas Sensors
One of the most important environment monitoring problems is the detection of oxidizing gases in the ambient air. Negative impact of noxious oxidizing gases (ozone and nitrogen oxides) on human health, sensitive vegetation, and ecosystems is very serious. For this reason, palladium (II) oxide nanostructures have been employed for oxidizing gas detection. Thin and ultrathin films of palladium (II) oxide were prepared by thermal oxidation at dry oxygen of previously formed pure palladium layers on polished poly-Al2O3, SiO2/Si (100), optical quality quartz, and amorphous carbon/KCl substrates. At ozone and nitrogen dioxide detection, PdO films prepared by oxidation at T = 870 K have demonstrated good values of sensitivity, signal stability, operation speed, and reproducibility of sensor response. In comparison with other materials, palladium (II) oxide thin and ultrathin films have some advantages at gas sensor fabrication. Firstly, for oxidizing gas detection, PdO films with p-type conductivity are more perspective than the material with n-type conductivity. Secondly, at ambient conditions, palladium (II) oxide is insoluble in water and does not react with it. These facts are favorable for the fabrication of gas detectors because they make possible to minimize the air humidity influence on PdO sensor response values. Thirdly, the synthesis procedure of PdO films is rather simple and is compatible with planar processes of microelectronic industry
Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory
We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski
signature (-+++). The condition of SO(4)-invariance imposed on gauge fields
yields a bosonic matrix model which is a consistent truncation of the plane
wave matrix model. For matrices parametrized by a scalar \phi, the Yang-Mills
equations are reduced to the equation of a particle moving in the double-well
potential. The classical solution is a bounce, i.e. a particle which begins at
the saddle point \phi=0 of the potential, bounces off the potential wall and
returns to \phi=0. The gauge field tensor components parametrized by \phi are
smooth and for finite time both electric and magnetic fields are nonvanishing.
The energy density of this non-Abelian dyon configuration does not depend on
coordinates of R^1\times S^3 and the total energy is proportional to the
inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N)
Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy
is proportional to the square of the inverse radius of S^2. From the viewpoint
of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian
(dyonic) flux tubes extended along the x^3-axis.Comment: 11 pages; v2: one formula added, some coefficients correcte
Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions
It was recently shown by Witten on the basis of several examples that the
topological B-model whose target space is a Calabi-Yau (CY) supermanifold is
equivalent to holomorphic Chern-Simons (hCS) theory on the same supermanifold.
Moreover, for the supertwistor space CP^{3|4} as target space, it has been
demonstrated that hCS theory on CP^{3|4} is equivalent to self-dual N=4 super
Yang-Mills (SYM) theory in four dimensions. We consider as target spaces for
the B-model the weighted projective spaces WCP^{3|2}(1,1,1,1|p,q) with two
fermionic coordinates of weight p and q, respectively - which are CY
supermanifolds for p+q=4 - and discuss hCS theory on them. By using twistor
techniques, we obtain certain field theories in four dimensions which are
equivalent to hCS theory. These theories turn out to be self-dual truncations
of N=4 SYM theory or of its twisted (topological) version.Comment: 12 pages; v2: minor clarification, 3 references added, published
versio
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