360 research outputs found
N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons
We consider supersymmetric sigma models on the Kahler target spaces, with
twisted mass. The Kahler spaces are assumed to have holomorphic Killing
vectors. Introduction of a superpotential of a special type is known to be
consistent with N=2 superalgebra (Alvarez-Gaume and Freedman). We show that the
algebra acquires central charges in the anticommutators {Q_L, Q_L} and {Q_R,
Q_R}. These central charges have no parallels, and they can exist only in two
dimensions. The central extension of the N=2 superalgebra we found paves the
way to a novel phenomenon -- spontaneous breaking of a part of supersymmetry.
In the general case 1/2 of supersymmetry is spontaneously broken (the vacuum
energy density is positive), while the remaining 1/2 is realized linearly. In
the model at hand the standard fermion number is not defined, so that the
Witten index as well as the Cecotti-Fendley-Intriligator-Vafa index are
useless. We show how to construct an index for counting short multiplets in
internal algebraic terms which is well-defined in spite of the absence of the
standard fermion number. Finally, we outline derivation of the quantum anomaly
in {\bar Q_L, Q_R}.Comment: 21 pages, Latex, 1 eps figure. Two important references adde
Ultrabroad-bandwidth multifrequency Raman generation
We report on the modeling of transient stimulated rotational Raman scattering in H2 gas. We predict a multifrequency output, spanning a bandwidth greater than the pump frequency, that may be generated without any significant delay with respect to the pump pulses. The roles of dispersion and transiency are quantified
Calculations of the Local Density of States for some Simple Systems
A recently proposed convolution technique for the calculation of local
density of states is described more thouroughly and new results of its
application are presented. For separable systems the exposed method allows to
construct the ldos for a higher dimensionality out of lower dimensional parts.
Some practical and theoretical aspects of this approach are also discussed.Comment: 5 pages, 3 figure
Topological-charge anomalies in supersymmetric theories with domain walls
Domain walls in 1+2 dimensions are studied to clarify some general features
of topological-charge anomalies in supersymmetric theories, by extensive use of
a superfield supercurrent. For domain walls quantum modifications of the
supercharge algebra arise not only from the short-distance anomaly but also
from another source of long-distance origin, induced spin in the domain-wall
background, and the latter dominates in the sum. A close look into the
supersymmetric trace identity, which naturally accommodates the central-charge
anomaly and its superpartners, shows an interesting consequence of the
improvement of the supercurrent: Via an improvement the anomaly in the central
charge can be transferred from induced spin in the fermion sector to an induced
potential in the boson sector. This fact reveals a dual character, both
fermionic and bosonic, of the central-charge anomaly, which reflects the
underlying supersymmetry. The one-loop superfield effective action is also
constructed to verify the anomaly and BPS saturation of the domain-wall
spectrum.Comment: 8 pages, Revte
ON SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS FOR HARMONIC FUNCTION ON NONCOMPACT RIEMANNIAN MANIFOLDS
We study questions of existence and belonging to the
given functional class of solutions of the Laplace-Beltrami equations on a noncompact Riemannian manifold M with no boundary.
In the present work we suggest the concept of φ-equivalency in the
class of continuous functions and establish some interrelation between problems of existence of solutions of the Laplace-Beltrami
equations on M and off some compact B ⊂ M with the same
growth "at infinity". A new conception of φ-equivalence classes of
functions on M develops and generalizes the concept of equivalence
of function on M and allows us to more accurately estimate the rate
of convergence of the solution to boundary conditions
ON SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS FOR THE INHOMOGENEOUS ELLIPTIC EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS
We study questions of existence and belonging to a given functional class of solutions of the inhomogeneous elliptic equations ∆u - c(x)u = g(x), where c(x) >(=)0, g(x) are H¨older fuctions on a noncompact Riemannian manifold M without boundary. In this work we develop an approach to evaluation of solutions to boundary-value problems for linear and quasilinear equations of the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique is essentially based on an approach from the papers by E. A. Mazepa and S. A. Korol’kov connected with an introduction of equivalency classes of functions and representations. We investigate the relationship between the existence of solutions of this equation on M and outside some compact set B ⊂ M with the same growth "at infinity"
From Zwiebach invariants to Getzler relation
We introduce the notion of Zwiebach invariants that generalize Gromov-Witten
invariants and homotopical algebra structures. We outline the induction
procedure that induces the structure of Zwiebach on the subbicomplex, that
gives the structure of Gromov-Witten invariants on subbicomplex with zero
diffferentials. We propose to treat Hodge dGBV with 1/12 axiom as the simplest
set of Zwiebach invariants, and explicitely prove that it induces WDVV and
Getzler equations in genera 0 and 1 respectively.Comment: 35 page
On Combinatorial Expansions of Conformal Blocks
In a recent paper (arXiv:0906.3219) the representation of Nekrasov partition
function in terms of nontrivial two-dimensional conformal field theory has been
suggested. For non-vanishing value of the deformation parameter
\epsilon=\epsilon_1+\epsilon_2 the instanton partition function is identified
with a conformal block of Liouville theory with the central charge c = 1+
6\epsilon^2/\epsilon_1\epsilon_2. If reversed, this observation means that the
universal part of conformal blocks, which is the same for all two-dimensional
conformal theories with non-degenerate Virasoro representations, possesses a
non-trivial decomposition into sum over sets of the Young diagrams, different
from the natural decomposition studied in conformal field theory. We provide
some details about this intriguing new development in the simplest case of the
four-point correlation functions.Comment: 22 page
Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
In N=2 super Yang-Mills theory, the Matone's relation relates instanton
corrections of the prepotential to instanton corrections of scalar field
condensation . This relation has been proved to hold for Omega
deformed theories too, using localization method. In this paper, we first give
a case study supporting the relation, which does not rely on the localization
technique. Especially, we show that the magnetic expansion also satisfies a
relation of Matone's type. Then we discuss implication of the relation for the
spectrum of periodic Toda chain, in the context of recently proposed
Nekrasov-Shatashvili scheme.Comment: 17 pages; v2 minor changes, references added; v3 more material added
in 2nd section, clarification in 4th sectio
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