11,950 research outputs found
The triangle-free graphs with rank 6
The rank of a graph G is defined to be the rank of its adjacency matrix A(G).
In this paper we characterize all connected triangle-free graphs with rank 6
Conical Defects, Black Holes and Higher Spin (Super-)Symmetry
We study the (super-)symmetries of classical solutions in the higher spin
(super-)gravity in AdS. We show that the symmetries of the solutions are
encoded in the holonomy around the spatial circle. When the spatial holonomies
of the solutions are trivial, they preserve maximal symmetries of the theory,
and are actually the smooth conical defects. We find all the smooth conical
defects in the , as well as in
and Chern-Simons gravity theories. In the bosonic higher spin
cases, there are one-to-one correspondences between the smooth conical defects
and the highest weight representations of Lie group. Furthermore we investigate
the higher spin black holes in and higher spin
(super-)gravity and find that they are only partially symmetric. In general,
the black holes break all the supersymmetries, but in some cases they preserve
part of the supersymmetries.Comment: 48 pages; more clarifications on conical defects in supersymmetric
cas
Black holes in Truncated Higher Spin AdS Gravity
We study the higher spin black holes in a truncated version of higher spin
gravity in . This theory contains only finite number of even spins
s=2,4,...,2N. We mainly focus on the simplest case, so-called (Type I and II)
spin gravity, which contains only spin 2 and spin 4 fields. This
spin gravity is as simple as spin 3 gravity, thus provides another
example to test various ideas on higher spin gravity. We find that the
asymptotical symmetry of this spin gravity is a classical
W(2,4)-symmetry. Moreover, we study the black hole solution with pure spin 4
hair and discuss its thermodynamics. One important feature of this black hole
is that its entropy could be written in compact forms. Furthermore, we
investigate a generated higher spin gravity. This higher spin gravity
only contains spin 2 and spin 6 fields which makes it different from other
kinds of higher spin gravity. We find the corresponding black hole with spin 6
hair, and discuss its thermodynamics analytically. It turns out that the black
holes with spin 4 or spin 6 hair constructed in this paper are the only black
holes with single higher spin hair, besides the spin 3 black hole found in
arXiv:1103.4304.Comment: 23 pages;minor revision, references added; published versio
Abelianization of BPS Quivers and the Refined Higgs Index
We count Higgs "phase" BPS states of general non-Abelian quiver, possibly
with loops, by mapping the problem to its Abelian, or toric, counterpart and
imposing Weyl invariance later. Precise Higgs index computation is particularly
important for quivers with superpotentials; the Coulomb "phase" index is
recently shown to miss important BPS states, dubbed intrinsic Higgs states or
quiver invariants. We demonstrate how the refined Higgs index is naturally
decomposed to a sum over partitions of the charge. We conjecture, and show in
simple cases, that this decomposition expresses the Higgs index as a sum over a
set of partition-induced Abelian quivers of the same total charge but
generically of smaller rank. Unlike the previous approach inspired by a similar
decomposition of the Coulomb index, our formulae compute the quiver invariants
directly, and thus offer a self-complete routine for counting BPS states.Comment: 38 pages, 13 figure
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