271 research outputs found
Extended modular operad
This paper is a sequel to [LoMa] where moduli spaces of painted stable curves
were introduced and studied. We define the extended modular operad of genus
zero, algebras over this operad, and study the formal differential geometric
structures related to these algebras: pencils of flat connections and Frobenius
manifolds without metric. We focus here on the combinatorial aspects of the
picture. Algebraic geometric aspects are treated in [Ma2].Comment: 38 pp., amstex file, no figures. This version contains additional
references and minor change
Single State Supermultiplet in 1+1 Dimensions
We consider multiplet shortening for BPS solitons in N=1 two-dimensional
models. Examples of the single-state multiplets were established previously in
N=1 Landau-Ginzburg models. The shortening comes at a price of loosing the
fermion parity due to boundary effects. This implies the disappearance
of the boson-fermion classification resulting in abnormal statistics. We
discuss an appropriate index that counts such short multiplets.
A broad class of hybrid models which extend the Landau-Ginzburg models to
include a nonflat metric on the target space is considered. Our index turns out
to be related to the index of the Dirac operator on the soliton reduced moduli
space (the moduli space is reduced by factoring out the translational modulus).
The index vanishes in most cases implying the absence of shortening. In
particular, it vanishes when there are only two critical points on the compact
target space and the reduced moduli space has nonvanishing dimension.
We also generalize the anomaly in the central charge to take into account the
target space metric.Comment: LaTex, 42 pages, no figures. Contribution to the Michael Marinov
Memorial Volume, ``Multiple facets of quantization and supersymmetry'' (eds.
M.Olshanetsky and A. Vainshtein, to be publish by World Scientific). The
paper is drastically revised compared to the first version. We add sections
treating the following issues: (i) a new index counting one-state
supermultiplets; (ii) analysis of hybrid models of general type; (iii)
generalization of the anomaly in the central charge accounting for the target
space metri
Transverse effects in multifrequency Raman generation
The theory of ultrabroadband multifrequency Raman generation is extended, for the first time, to allow for beam-propagation effects in one and two transverse dimensions. We show that a complex transverse structure develops even when diffraction is neglected. In the general case, we examine how the ultrabroadband multifrequency Raman generation process is affected by the intensity, phase quality, and width of the input beams, and by the length of the Raman medium. The evolution of power spectra, intensity profiles, and global characteristics of the multifrequency beams are investigated and explained. In the two-dimensional transverse case, bandwidths comparable to the optical carrier frequency, spanning the whole visible spectrum and beyond, are still achievable
On Microscopic Origin of Integrability in Seiberg-Witten Theory
We discuss microscopic origin of integrability in Seiberg-Witten theory,
following mostly the results of hep-th/0612019, as well as present their
certain extension and consider several explicit examples. In particular, we
discuss in more detail the theory with the only switched on higher perturbation
in the ultraviolet, where extra explicit formulas are obtained using
bosonization and elliptic uniformization of the spectral curve.Comment: 24 pages, 1 figure, LaTeX, based on the talks at 'Geometry and
Integrability in Mathematical Physics', Moscow, May 2006; 'Quarks-2006',
Repino, May 2006; Twente conference on Lie groups, December 2006 and
'Classical and Quantum Integrable Models', Dubna, January 200
Instanton Calculus in R-R 3-form Background and Deformed N=2 Super Yang-Mills Theory
We study the ADHM construction of instantons in N=2 supersymmetric Yang-Mills
theory deformed in constant Ramond-Ramond (R-R) 3-form field strength
background in type IIB superstrings. We compare the deformed instanton
effective action with the effective action of fractional D3/D(-1) branes at the
orbifold singularity of C^2/Z_2 in the same R-R background. We find discrepancy
between them at the second order in deformation parameters, which comes from
the coupling of the translational zero modes of the D(-1)-branes to the R-R
background. We improve the deformed action by adding a term with space-time
dependent gauge coupling. Although the space-time action differs from the
action in the omega-background, both actions lead to the same instanton
equations of motion at the lowest order in gauge coupling.Comment: 27 pages, version to appear in JHE
The influence of traveling magnetic field inductor asymmetric power supply on the liquid metal flow
In modern times, exposure to a liquid metal by a travelling magnetic field is widely applied. There are laboratory studies on the processes of stirring and crystallization under the action of a traveling magnetic field. However, in the majority of studies it is assumed that the inductor power supply of the linear induction machine is carried out by a symmetrical three-phase system of currents with an equal phase shift, which, in some cases, is not quite correct. To approximate the model to real operating conditions, a numerical simulation of the magnetic field and the flow of liquid metal was carried out when supplied from a power source of symmetric three-phase voltage. The distortion of magnetic field, which, in turn, causes an nonuniform distribution of forces and the flow of a liquid metal, is shown. Evaluation of asymmetrical effect on the liquid metal flow was carried out by means of finite element method. That effect is caused by different coefficients of mutual coils induction of the linear induction machine, which is confirmed by experimental data. © Published under licence by IOP Publishing Ltd.Russian Foundation for Basic Research, RFBR: 17-48-590539 r aUral Federal University, UrFUThe work of Institute of Continuous Media Mechanics team is supporting by the RFBR grant 17-48-590539 r a and the work of Ural Federal University team is supporting by Act 211 Government of the Russian Federation, contract 02.A03.21.0006
Holomorphic Currents and Duality in N=1 Supersymmetric Theories
Twisted supersymmetric theories on a product of two Riemann surfaces possess
non-local holomorphic currents in a BRST cohomology. The holomorphic currents
act as vector fields on the chiral ring. The OPE's of these currents are
invariant under the renormalization group flow up to BRST-exact terms. In the
context of electric-magnetic duality, the algebra generated by the holomorphic
currents in the electric theory is isomorphic to the one on the magnetic side.
For the currents corresponding to global symmetries this isomorphism follows
from 't Hooft anomaly matching conditions. The isomorphism between OPE's of the
currents corresponding to non-linear transformations of fields of matter
imposes non-trivial conditions on the duality map of chiral ring. We consider
in detail the SQCD with matter in fundamental and adjoint
representations, and find agreement with the duality map proposed by Kutasov,
Schwimmer and Seiberg.Comment: 19 pages, JHEP3 LaTex, typos correcte
On two-dimensional quantum gravity and quasiclassical integrable hierarchies
The main results for the two-dimensional quantum gravity, conjectured from
the matrix model or integrable approach, are presented in the form to be
compared with the world-sheet or Liouville approach. In spherical limit the
integrable side for minimal string theories is completely formulated using
simple manipulations with two polynomials, based on residue formulas from
quasiclassical hierarchies. Explicit computations for particular models are
performed and certain delicate issues of nontrivial relations among them are
discussed. They concern the connections between different theories, obtained as
expansions of basically the same stringy solution to dispersionless KP
hierarchy in different backgrounds, characterized by nonvanishing background
values of different times, being the simplest known example of change of the
quantum numbers of physical observables, when moving to a different point in
the moduli space of the theory.Comment: 20 pages, based on talk presented at the conference "Liouville field
theory and statistical models", dedicated to the memory of Alexei
Zamolodchikov, Moscow, June 200
Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two K\"ahler Forms
In this paper, we extend our geometrical derivation of expansion coefficients
of mirror maps by localization computation to the case of toric manifolds with
two K\"ahler forms. Especially, we take Hirzebruch surfaces F_{0}, F_{3} and
Calabi-Yau hypersurface in weighted projective space P(1,1,2,2,2) as examples.
We expect that our results can be easily generalized to arbitrary toric
manifold.Comment: 45 pages, 2 figures, minor errors are corrected, English is refined.
Section 1 and Section 2 are enlarged. Especially in Section 2, confusion
between the notion of resolution and the notion of compactification is
resolved. Computation under non-zero equivariant parameters are added in
Section
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