327 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
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
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
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
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
The Virasoro vertex algebra and factorization algebras on Riemann surfaces
This paper focuses on the connection of holomorphic two-dimensional
factorization algebras and vertex algebras which has been made precise in the
forthcoming book of Costello-Gwilliam. We provide a construction of the
Virasoro vertex algebra starting from a local Lie algebra on the complex plane.
Moreover, we discuss an extension of this factorization algebra to a
factorization algebra on the category of Riemann surfaces. The factorization
homology of this factorization algebra is computed as are the correlation
functions. We provide an example of how the Virasoro factorization algebra
implements conformal symmetry of the beta-gamma system using the method of
effective BV quantization
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 the Chiral Ring of N=1 Supersymmetric Gauge Theories
We consider the chiral ring of the pure N=1 supersymmetric gauge theory with
SU(N) gauge group and show that the classical relation S^{N^2}=0 is modified to
the exact quantum relation (S^N-\Lambda^{3N})^N=0.Comment: 5 pages. Comments and references adde
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
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