1,593 research outputs found
Exploring the Moduli Space of (0,2) Strings
We use an exactly solvable (0,2) supersymmetric conformal field theory with
gauge group SO(10) to investigate the superpotential of the corresponding
classical string vacuum. We provide evidence that the rational point lies in
the Landau-Ginzburg phase of the linear sigma-model and calculate exactly all
three- and four-point functions of the gauge singlets. These couplings already
put severe constraints on the possible flat directions of the superpotential.
Finally, we contemplate about the flat direction related to Kahler deformations
of the underlying linear sigma-model.Comment: 19 pages, plain TeX, 2 postscript figures, epsf include
D-Branes in Landau-Ginzburg Models and Algebraic Geometry
We study topological D-branes of type B in N=2 Landau-Ginzburg models,
focusing on the case where all vacua have a mass gap. In general, tree-level
topological string theory in the presence of topological D-branes is described
mathematically in terms of a triangulated category. For example, it has been
argued that B-branes for an N=2 sigma-model with a Calabi-Yau target space are
described by the derived category of coherent sheaves on this space. M.
Kontsevich previously proposed a candidate category for B-branes in N=2
Landau-Ginzburg models, and our computations confirm this proposal. We also
give a heuristic physical derivation of the proposal. Assuming its validity, we
can completely describe the category of B-branes in an arbitrary massive
Landau-Ginzburg model in terms of modules over a Clifford algebra. Assuming in
addition Homological Mirror Symmetry, our results enable one to compute the
Fukaya category for a large class of Fano varieties. We also provide a
(somewhat trivial) counter-example to the hypothesis that given a closed string
background there is a unique set of D-branes consistent with it.Comment: 51 pages, AMS latex; two eps figures. v2: a physical derivation of
Kontsevich's proposal is give
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
N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models
We study N=2 nonlinear two dimensional sigma models with boundaries and their
massive generalizations (the Landau-Ginzburg models). These models are defined
over either Kahler or bihermitian target space manifolds. We determine the most
general local N=2 superconformal boundary conditions (D-branes) for these sigma
models. In the Kahler case we reproduce the known results in a systematic
fashion including interesting results concerning the coisotropic A-type branes.
We further analyse the N=2 superconformal boundary conditions for sigma models
defined over a bihermitian manifold with torsion. We interpret the boundary
conditions in terms of different types of submanifolds of the target space. We
point out how the open sigma models correspond to new types of target space
geometry. For the massive Landau-Ginzburg models (both Kahler and bihermitian)
we discuss an important class of supersymmetric boundary conditions which
admits a nice geometrical interpretation.Comment: 48 pages, latex, references and minor comments added, the version to
appear in JHE
3D two-color QCD at finite temperature and baryon density
We study the phase diagram for two-color QCD in three-dimensional spacetime,
as a function of temperature and baryon chemical potential, using the
low-energy effective Lagrangian approach. We show one-loop renormalizability at
zero temperature, and then use the one-loop effective Lagrangian at finite
temperature and chemical potential to show that at low temperature there is a
critical line separating the normal and diquark phase, with this critical line
ending at a tricritical point. This phase structure is qualitatively similar to
that found recently by Splittorff et al for two-color QCD in four-dimensional
spacetime, although the details are quite different, due to the different
symmetries and the different loop and infrared properties of three-dimensional
spacetime.Comment: 14 pp, 1 fi
Matrix Factorizations and Kauffman Homology
The topological string interpretation of homological knot invariants has led
to several insights into the structure of the theory in the case of sl(N). We
study possible extensions of the matrix factorization approach to knot homology
for other Lie groups and representations. In particular, we introduce a new
triply graded theory categorifying the Kauffman polynomial, test it, and
predict the Kauffman homology for several simple knots.Comment: 45 pages, harvma
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