126 research outputs found
The geometric deformation of curved algebras and Lie algebroids
We investigate the deformation of an structure that encodes the
geometric information about a smooth vector bundle. We establish that this
specific type of deformation endows the bundle with a Lie algebroid structure.
Additionally, we compute the Atiyah class and Atiyah-Chern classes in the
geometrically deformed case. The precise relationship between the first
Atiyah-Chern class and the modular class is shown. In the case of action Lie
algebroids, the Atiyah-Chern classes at the leading order are given by the
equivariant Chern characters.Comment: Comments are welcome
N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heterotic
models were discovered previously on the world sheet of non-Abelian strings
supported by certain four-dimensional N=1 theories. We study geometric aspects
and holomorphic properties of these models, and derive a number of exact
expressions for the beta functions in terms of the anomalous dimensions
analogous to the NSVZ beta function in four-dimensional Yang-Mills. Instanton
calculus provides a straightforward method for the derivation. The anomalous
dimensions are calculated up to two loops implying that one of the beta
functions is explicitly known up to three loops. The fixed point in the ratio
of the couplings found previously at one loop is not shifted at two loops. We
also consider the N=(0,2) supercurrent supermultiplet (the so-called
hypercurrent) and its anomalies, as well as the "Konishi anomaly." This gives
us another method for finding exact functions. We prove that despite
the chiral nature of the models under consideration quantum loops preserve
isometries of the target space.Comment: 38 pages, 6 figures, minor changes in the text and references, the
journal versio
N=(0,2) Supersymmetry and a Nonrenormalization Theorem
In this paper we continue the study of perturbative renormalizations in an
supersymmetric model. Previously we analyzed one-loop
graphs in the heterotically deformed CP models. Now we extend the
analysis of the function and appropriate factors to two, and, in
some instances, all loops in the limiting case . The field contents
of the model, as well as the heterotic coupling, remain the same, but the
target space becomes flat. In this toy model we construct
supergraph formalism. We show, by explicit calculations up to two-loop order,
that the function is one-loop-exact. We derive a nonrenormalization
theorem valid to all orders. This nonrenormalization theorem is rather unusual
since it refers to (formally) terms. It is based on the fact that
supersymmetry combined with target space symmetries and "flavor"? symmetries is
sufficient to guarantee the absence of loop corrections. We analyze the
supercurrent supermultiplet (i.e., the hypercurrent) providing further evidence
in favor of the absence of higher loops in the function.Comment: 21 pages, 5 figures, a new section on supercurrent analysis added,
published versio
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