1,756 research outputs found
The Even and the Odd Spectral Flows on the N=2 Superconformal Algebras
There are two different spectral flows on the N=2 superconformal algebras
(four in the case of the Topological algebra). The usual spectral flow, first
considered by Schwimmer and Seiberg, is an even transformation, whereas the
spectral flow previously considered by the author and Rosado is an odd
transformation. We show that the even spectral flow is generated by the odd
spectral flow, and therefore only the latter is fundamental. We also analyze
thoroughly the four ``topological'' spectral flows, writing two of them here
for the first time. Whereas the even and the odd spectral flows have
quasi-mirrored properties acting on the Antiperiodic or the Periodic algebras,
the topological even and odd spectral flows have drastically different
properties acting on the Topological algebra. The other two topological
spectral flows have mixed even and odd properties. We show that the even and
the even-odd topological spectral flows are generated by the odd and the
odd-even topological spectral flows, and therefore only the latter are
fundamental.Comment: 15 pages, Latex. Minor improvements in the last paragraph of the
conclusions. Numbering of references has change
Transmutations between Singular and Subsingular Vectors of the N=2 Superconformal Algebras
We present subsingular vectors of the N=2 superconformal algebras other than
the ones which become singular in chiral Verma modules, reported recently by
Gato-Rivera and Rosado. We show that two large classes of singular vectors of
the Topological algebra become subsingular vectors of the Antiperiodic NS
algebra under the topological untwistings. These classes consist of BRST-
invariant singular vectors with relative charges and zero conformal
weight, and no-label singular vectors with . In turn the resulting NS
subsingular vectors are transformed by the spectral flows into subsingular and
singular vectors of the Periodic R algebra. We write down these singular and
subsingular vectors starting from the topological singular vectors at levels 1
and 2.Comment: 21 pages, Latex. Minor improvements. Very similar to the version
published in Nucl. Phys.
Topological Descendants: DDK and KM Realizations
The "minimal matter + scalar" system can be embedded into the twisted N=2
topological algebra in two ways: a la DDK or a la KM. Here we present some
results concerning the topological descendants and their DDK and KM
realizations. In particular, we prove four "no-ghost" theorems (two for null
states) regarding the reduction of the topological descendants into secon-
daries of the "minimal matter + scalar" conformal field theory. We write down
the relevant expressions for the case of level 2 descendants.Comment: 10 pgs, Late
Spectral Flows and Twisted Topological Theories
We analyze the action of the spectral flows on N=2 twisted topological
theories. We show that they provide a useful mapping between the two twisted
topological theories associated to a given N=2 superconformal theory. This
mapping can also be viewed as a topological algebra automorphism. In particular
null vectors are mapped into null vectors, considerably simplifying their
computation. We give the level 2 results. Finally we discuss the spectral flow
mapping in the case of the DDK and KM realizations of the topological algebra.Comment: The presentation of the results has been very much improved. Some
references have been adde
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