1,110 research outputs found

### 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

### q,k-generalized gamma and beta functions

We introduce the q,k-generalized Pochhammer symbol. We construct
$\Gamma_{q,k}$ and $B_{q,k}$, the q,k-generalized gamma and beta fuctions, and
show that they satisfy properties that generalize those satisfied by the
classical gamma and beta functions. Moreover, we provide integral
representations for $\Gamma_{q,k}$ and $B_{q,k}.$Comment: 17 page

### Vacuum structure in supersymmetric Yang-Mills theories with any gauge group

We consider the pure supersymmetric Yang--Mills theories placed on a small
3-dimensional spatial torus with higher orthogonal and exceptional gauge
groups. The problem of constructing the quantum vacuum states is reduced to a
pure mathematical problem of classifying the flat connections on 3-torus. The
latter problem is equivalent to the problem of classification of commuting
triples of elements in a connected simply connected compact Lie group which is
solved in this paper. In particular, we show that for higher orthogonal SO(N),
N > 6, and for all exceptional groups the moduli space of flat connections
involves several distinct connected components. The total number of
vacuumstates is given in all cases by the dual Coxeter number of the group
which agrees with the result obtained earlier with the instanton technique.Comment: 41 pages, 9 figures, 9 tables. Final version to be published in the
Yuri Golfand memorial volume. We added the Appendix D with classification of
all non-trivial commuting n-tuples for arbitrary

### News from the Virasoro algebra

It is shown that the local quantum field theory of the chiral energy-
momentum tensor with central charge $c=1$ coincides with the gauge invariant
subtheory of the chiral $SU(2)$ current algebra at level 1, where the gauge
group is the global $SU(2)$ symmetry. At higher level, the same scheme gives
rise to $W$-algebra extensions of the Virasoro algebra.Comment: 4 pages, Latex, DESY 93-11

### Highest weight irreducible representations of the Lie superalgebra $gl(1/\infty)$

Two classes of irreducible highest weight modules of the general linear Lie
superalgebra $gl(1/\infty)$ are constructed. Within each module a basis is
introduced and the transformation relations of the basis under the action of
the algebra generators are written down.Comment: 24 pages, TeX; Journ. Math. Phys. (to be published

### Higher level twisted Zhu algebras

The study of twisted representations of graded vertex algebras is important
for understanding orbifold models in conformal field theory. In this paper we
consider the general set-up of a vertex algebra $V$, graded by \G/\Z for some
subgroup \G of $\R$ containing $\Z$, and with a Hamiltonian operator $H$
having real (but not necessarily integer) eigenvalues. We construct the
directed system of twisted level $p$ Zhu algebras \zhu_{p, \G}(V), and we
prove the following theorems: For each $p$ there is a bijection between the
irreducible \zhu_{p, \G}(V)-modules and the irreducible \G-twisted positive
energy $V$-modules, and $V$ is (\G, H)-rational if and only if all its Zhu
algebras \zhu_{p, \G}(V) are finite dimensional and semisimple. The main
novelty is the removal of the assumption of integer eigenvalues for $H$. We
provide an explicit description of the level $p$ Zhu algebras of a universal
enveloping vertex algebra, in particular of the Virasoro vertex algebra
\vir^c and the universal affine Kac-Moody vertex algebra V^k(\g) at
non-critical level. We also compute the inverse limits of these directed
systems of algebras.Comment: 47 pages, no figure

### Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras

We describe the group of continuous automorphisms of all simple
infinite-dimensional linearly compact Lie superalgebras and use it in order to
classify F-forms of these superalgebras over any field F of characteristic
zero.Comment: 24 page

### Irreducible modules over finite simple Lie conformal superalgebras of type K

We construct all finite irreducible modules over Lie conformal superalgebras
of type KComment: Accepted for publication in J. Math. Phys

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