A construction of N=2 and centerless N=4 superconformal fields via affine superalgebras

In this note we give a new construction of the N=2 superconformal algebra using currents of the affine superalgebra $\hat{sl}(2 | 1)$ and free bosonic fields, and also the N=4 superconformal algebra without central charge in terms of currents of $\hat{sl}(2 | 2)$ and free bosonic fields. Arguments on commutants and invariant subspaces are added.Comment: 20 pages, amslate

Finite growth representations of infinite Lie conformal algebras

We classify all finite growth representations of all infinite rank subalgebras of the Lie conformal algebra gc_1 that contain a Virasoro subalgebra.Comment: 22 page

KdV type hierarchies, the string equation and W1+∞W_{1+\infty} constraints

To every partition $n=n_1+n_2+\cdots+n_s$ one can associate a vertex operator realization of the Lie algebras $a_{\infty}$ and $\hat{gl}_n$. Using this construction we make reductions of the $s$--component KP hierarchy, reductions which are related to these partitions. In this way we obtain matrix KdV type equations. Now assuming that (1) $\tau$ is a $\tau$--function of the $[n_1,n_2,\ldots,n_s]$--th reduced KP hierarchy and (2) $\tau$ satisfies a `natural' string equation, we prove that $\tau$ also satisfies the vacuum constraints of the $W_{1+\infty}$ algebra.Comment: 29 pages of amstex, Correction of some errors and 1 reference adde

Finite conformal modules over the N=2,3,4 superconformal algebras

In this paper we continue the study of representation theory of formal distribution Lie superalgebras initiated in q-alg/9706030. We study finite Verma-type conformal modules over the N=2, N=3 and the two N=4 superconformal algebras and also find explicitly all singular vectors in these modules. From our analysis of these modules we obtain a complete list of finite irreducible conformal modules over the N=2, N=3 and the two N=4 superconformal algebras.Comment: 36 pages, no figures, LaTeX forma

Dirac operators and the Very Strange Formula for Lie superalgebras

Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.Comment: Latex file, 25 pages. A few misprints corrected. To appear in the forthcoming volume "Advances in Lie Superalgebras", Springer INdAM Serie

The return of the bursts: Thermonuclear flashes from Circinus X-1

We report the detection of 15 X-ray bursts with RXTE and Swift observations of the peculiar X-ray binary Circinus X-1 during its May 2010 X-ray re-brightening. These are the first X-ray bursts observed from the source after the initial discovery by Tennant and collaborators, twenty-five years ago. By studying their spectral evolution, we firmly identify nine of the bursts as type I (thermonuclear) X-ray bursts. We obtain an arcsecond location of the bursts that confirms once and for all the identification of Cir X-1 as a type I X-ray burst source, and therefore as a low magnetic field accreting neutron star. The first five bursts observed by RXTE are weak and show approximately symmetric light curves, without detectable signs of cooling along the burst decay. We discuss their possible nature. Finally, we explore a scenario to explain why Cir X-1 shows thermonuclear bursts now but not in the past, when it was extensively observed and accreting at a similar rate.Comment: Accepted for publication in The Astrophysical Journal Letters. Tables 1 & 2 merged. Minor changes after referee's comments. 5 pages, 4 Figure

Ramond sector of superconformal algebras via quantum reduction

Quantum hamiltonian reduction of affine superalgebras is studied in the twisted case. The Ramond sector of "minimal" superconformal W-algebras is described in detail, the determinant formula is obtained. Extensive list of examples includes all the simple Lie superalgebras of rank up to 2. The paper generalizes the results of Kac and Wakimoto (math-ph/0304011) to the twisted case.Comment: 50 pages, 8 figures; v2: examples added, determinant formula derivation modified, section order change

Associated varieties of modules over Kac-Moody algebras and C2C_2-cofiniteness of W-algebras

First, we establish the relation between the associated varieties of modules over Kac-Moody algebras \hat{g} and those over affine W-algebras. Second, we prove the Feigin-Frenkel conjecture on the singular supports of G-integrable admissible representations. In fact we show that the associated variates of G-integrable admissible representations are irreducible G-invariant subvarieties of the nullcone of g, by determining them explicitly. Third, we prove the C_2-cofiniteness of a large number of simple W-algebras, including all minimal series principal W-algebras and the exceptional W-algebras recently discovered by Kac-Wakimoto.Comment: revised, to appear in IMR