2,400 research outputs found
The hamiltonian reduction of the BRST complex and N=2 SUSY
We study the nonunitary representations of N=2 Super Virasoro algebra for the
rational central charges c<3. The resolutions for the irreducible
representations of N=2 SVir in terms of the "2-d gravity modules" are obtained
and their characters are computed. The correspondence between the N=2
nonunitary "minimal" models and the Virasoro minimal models coupled to 2-d
gravity is shown at the level of states. We also define the hamiltonian
reduction of the BRST complex of sl(N)/sl(N) coset to the BRST complex of the
W-gravity coupled to the W matter. The case of sl(2) is considered explicitly.
It leads to the presentation of N=2 Super Virasoro algebra by the Lie algebra
cohomology. Finally, we reveal the mechanism of the correspondence between
sl(2)/sl(2)$ coset and 2-d gravity.Comment: 28 pages, 6 pictures available on request; in the revised version
some misprints are correcte
On Root Multiplicities of Some Hyperbolic Kac-Moody Algebras
Using the coset construction, we compute the root multiplicities at level
three for some hyperbolic Kac-Moody algebras including the basic hyperbolic
extension of and .Comment: 10 pages, LaTe
A note on the algebraic engineering of 4D super Yang-Mills theories
Some BPS quantities of 5D quiver gauge theories, like
instanton partition functions or qq-characters, can be constructed as algebraic
objects of the Ding-Iohara-Miki (DIM) algebra. This construction is applied
here to super Yang-Mills theories in four dimensions using a
degenerate version of the DIM algebra. We build up the equivalent of horizontal
and vertical representations, the first one being defined using vertex
operators acting on a free boson's Fock space, while the second one is
essentially equivalent to the action of Vasserot-Shiffmann's Spherical Hecke
central algebra. Using intertwiners, the algebraic equivalent of the
topological vertex, we construct a set of -operators acting on the
tensor product of horizontal modules, and the vacuum expectation values of
which reproduce the instanton partition functions of linear quivers. Analysing
the action of the degenerate DIM algebra on the -operator in the
case of a pure gauge theory, we further identify the degenerate version
of Kimura-Pestun's quiver W-algebra as a certain limit of q-Virasoro algebra.
Remarkably, as previously noticed by Lukyanov, this particular limit reproduces
the Zamolodchikov-Faddeev algebra of the sine-Gordon model.Comment: 13 pages (v3: references added
Ternary Virasoro - Witt Algebra
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the
use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets
acting on other 3-brackets in the algebra are discussed and verified in various
situations.Comment: 6 pages, Late
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