111 research outputs found
The hamiltonian reduction of the BRST complex and N=2 SUSY
We study the nonunitary representations of N=2 Super Virasoro algebra for the
rational central charges c<3. The resolutions for the irreducible
representations of N=2 SVir in terms of the "2-d gravity modules" are obtained
and their characters are computed. The correspondence between the N=2
nonunitary "minimal" models and the Virasoro minimal models coupled to 2-d
gravity is shown at the level of states. We also define the hamiltonian
reduction of the BRST complex of sl(N)/sl(N) coset to the BRST complex of the
W-gravity coupled to the W matter. The case of sl(2) is considered explicitly.
It leads to the presentation of N=2 Super Virasoro algebra by the Lie algebra
cohomology. Finally, we reveal the mechanism of the correspondence between
sl(2)/sl(2)$ coset and 2-d gravity.Comment: 28 pages, 6 pictures available on request; in the revised version
some misprints are correcte
On equivalence of Floer's and quantum cohomology
(In the revised version the relevant aspect of noncompactness of the moduli
of instantons is discussed. It is shown nonperturbatively that any BRST trivial
deformation of A-model which does not change the ranks of BRST cohomology does
not change the topological correlation functions either) We show that the Floer
cohomology and quantum cohomology rings of the almost Kahler manifold M, both
defined over the Novikov ring of the loop space LM of M, are isomorphic. We do
it using a BRST trivial deformation of the topological A-model. As an example
we compute the Floer = quantum cohomology of the 3-dimensional flag space Fl_3.Comment: 28 pages, HUTP-93/A02
Generalized Green-Schwarz mechanism in F theory
We derive the anomaly 8-form of 6-dimensional gauge theories arising in F
theory compactifications on elliptic Calabi-Yau threefolds. The result allows
to determine the matter content of certain such theories in terms of
intersection numbers on the base of elliptic fibration. We also discuss gauge
theories on 7-branes with double point singularities on the worldvolume.
Applications to Type II compactifications on Hirzebruch surfaces and are
outlined.Comment: 11 pages, harvmac. Normalization of (tr R^2)^2 term correcte
D-Branes and Topological Field Theories
In the presence of a D-brane a string theory develops a new subsector. We
show that for curved D-branes the corresponding sector is a (partially twisted)
topological field theory. We use this result to compute the degeneracy of
2-branes wrapped around cycles as well as 3-branes wrapped around CY
threefold vanishing 3-cycles. In both cases we find the degeneracy is in accord
with expectation. The counting of BPS states of a gas of 0-branes in the
presence of a 4-brane in is considered and it is noted that the effective
0-brane charge is shifted by 1, due to a quantum correction. This is in accord
with string duality and the fact that left-moving ground state energy of
heterotic string starts at . We also show that all the three different
topological twistings of four dimensional Yang-Mills theory do arise from
curved three-branes embedded in different spaces (Calabi-Yau manifolds and
manifolds with exceptional holonomy groups).Comment: 22 page
D-Strings on D-Manifolds
We study the mechanism for appearance of massless solitons in type II string
compactifications. We find that by combining -duality with strong/weak
duality of type IIB in 10 dimensions enhanced gauge symmetries and massless
solitonic hypermultiplets encountered in Calabi-Yau compactifications can be
studied perturbatively using D-strings (the strong/weak dual to type IIB
string) compactified on ``D-manifolds''. In particular the nearly massless
solitonic states of the type IIB compactifications correspond to elementary
states of D-strings. As examples we consider the D-string description of
enhanced gauge symmetries for type IIA string compactification on ALE spaces
with singularities and type IIB on a class of singular Calabi-Yau
threefolds. The class we study includes as a special case the conifold
singularity in which case the perturbative spectrum of the D-string includes
the expected massless hypermultiplet with degeneracy one.Comment: 23 pages, with 3 figures. A compact example is adde
Geometric Singularities and Enhanced Gauge Symmetries
Using ``Tate's algorithm,'' we identify loci in the moduli of F-theory
compactifications corresponding to enhanced gauge symmetry. We apply this to
test the proposed F-theory/heterotic dualities in six dimensions. We recover
the perturbative gauge symmetry enhancements of the heterotic side and the
physics of small instantons, and discover new mixed
perturbative/non-perturbative gauge symmetry enhancements. Upon further
toroidal compactification to 4 dimensions, we derive the chain of Calabi-Yau
threefolds dual to various Coulomb branches of heterotic strings.Comment: 49 pages harvmac big (must print in big mode for tables to appear
correctly); Typos and reference correcte
Quantum cohomology of partial flag manifolds
We compute the quantum cohomology rings of the partial flag manifolds
F_{n_1\cdots n_k}=U(n)/(U(n_1)\times \cdots \times U(n_k)). The inductive
computation uses the idea of Givental and Kim. Also we define a notion of the
vertical quantum cohomology ring of the algebraic bundle. For the flag bundle
F_{n_1\cdots n_k}(E) associated with the vector bundle E this ring is found.Comment: 33 page
Mapping 6D N = 1 supergravities to F-theory
We develop a systematic framework for realizing general anomaly-free chiral
6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one
tensor multiplet whose gauge group is a product of simple factors (modulo a
finite abelian group) with matter in arbitrary representations. Such theories
can be decomposed into blocks associated with the simple factors in the gauge
group; each block depends only on the group factor and the matter charged under
it. All 6D chiral supergravity models can be constructed by gluing such blocks
together in accordance with constraints from anomalies. Associating a geometric
structure to each block gives a dictionary for translating a supergravity model
into a set of topological data for an F-theory construction. We construct the
dictionary of F-theory divisors explicitly for some simple gauge group factors
and associated matter representations. Using these building blocks we analyze a
variety of models. We identify some 6D supergravity models which do not map to
integral F-theory divisors, possibly indicating quantum inconsistency of these
6D theories.Comment: 37 pages, no figures; v2: references added, minor typos corrected;
v3: minor corrections to DOF counting in section
- …