450 research outputs found
Liouville Theory and Elliptic Genera
The structure and modular properties of N = 4 superconformal characters are reviewed and exploited, in an attempt to construct elliptic genera-like functions by decompactifying K3. The construction is tested against expressions obtained in the context of strings propagating in background ALE spaces of type AN-1, using the underlying superconformal theory N = 2 minimal ⊗ N = 2 Liouville
Group theory of icosahedral virus capsid vibrations: a top-down approach
We explore the use of a top-down approach to analyse the dynamics of icosahedral virus capsids and complement the information obtained from bottom-up studies of viral vibrations available in the literature. A normal mode analysis based on protein association energies is used to study the frequency spectrum, in which we reveal a universal plateau of low-frequency modes shared by a large class of Caspar–Klug capsids. These modes break icosahedral symmetry and are potentially relevant to the genome release mechanism. We comment on the role of viral tiling theory in such dynamical considerations
Symmetry-surfing the moduli space of Kummer K3s.
A maximal subgroup of the Mathieu group M24 arises as the combined
holomorphic symplectic automorphism group of all Kummer surfaces whose Kaehler
class is induced from the underlying complex torus. As a subgroup of M24, this
group is the stabilizer group of an octad in the Golay code. To meaningfully
combine the symmetry groups of distinct Kummer surfaces, we introduce the
concepts of Niemeier markings and overarching maps between pairs of Kummer
surfaces. The latter induce a prescription for symmetry-surfing the moduli
space, while the former can be seen as a first step towards constructing a
vertex algebra that governs the elliptic genus of K3 in an M24-compatible
fashion. We thus argue that a geometric approach from K3 to Mathieu Moonshine
may bear fruit.Comment: 20 pages; minor changes; accepted for publication in the Proceedings
Volume of String-Math 201
Admissible sl(2/1) Characters and Parafermions
The branching functions of the affine superalgebra characters into
characters of the affine subalgebra are calculated for fractional
levels , u positive integer. They involve rational torus
and parafermion characters.Comment: 14 pages, Latex 2
Characters of admissible representations of the affine superalgebra sl(2|1)
We calculate characters and supercharacters for irreducible, admissible representations of the affine superalgebra sl(2|1) in both the Ramond and Neveu-Schwarz sectors and discuss their modular properties in the special case of level k=-1/2. We also show that the non-degenerate integrable characters coincide with some N=4 superconformal characters
DNA duplex cage structures with icosahedral symmetry
A construction method for duplex cage structures with icosahedral symmetry made out of single-stranded DNA molecules is presented and applied to an icosidodecahedral cage. It is shown via a mixture of analytic and computer techniques that there exist realisations of this graph in terms of two circular DNA molecules. These blueprints for the organisation of a cage structure with a noncrystallographic symmetry may assist in the design of containers made from DNA for applications in nanotechnology
Superconformal Algebras and Mock Theta Functions
It is known that characters of BPS representations of extended superconformal
algebras do not have good modular properties due to extra singular vectors
coming from the BPS condition. In order to improve their modular properties we
apply the method of Zwegers which has recently been developed to analyze
modular properties of mock theta functions. We consider the case of N=4
superconformal algebra at general levels and obtain the decomposition of
characters of BPS representations into a sum of simple Jacobi forms and an
infinite series of non-BPS representations.
We apply our method to study elliptic genera of hyper-Kahler manifolds in
higher dimensions. In particular we determine the elliptic genera in the case
of complex 4 dimensions of the Hilbert scheme of points on K3 surfaces K^{[2]}
and complex tori A^{[[3]]}.Comment: 28 page
Twenty-four near-instabilities of Caspar-Klug viruses
Group theoretical arguments combined with normal mode analysis techniques are applied to a coarse-grained approximation of icosahedral viral capsids which incorporates areas of variable flexibility. This highlights a remarkable structure of the low-frequency spectrum in this approximation, namely, the existence of a plateau of 24 near zero modes with universal group theory content
Parafermionic Representation of the Affine Algebra at Fractional Level
The four fermionic currents of the affine superalgebra at
fractional level , u positive integer, are shown to be realised in
terms of a free scalar field, an doublet field and a primary field of
the parafermionic algebra .Comment: 5 pages, Latex 2
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