196,509 research outputs found
A Level-Depth Correspondence between Verlinde Rings and Subfactors
No full textWe establish a correspondence between the levels of Verlinde rings and the
depths of subfactors. Given the -level Verlinde ring of a simple
compact Lie group , the tensor products of fundamental representations give
us the inclusion of a pair of factors . For the depth
of , we first prove for type and . More
generally, the depth is shown to satisfy with
, where is uniquely determined by the simple type of
. We also show that the simple --bimodules contained in
generate the Verlinde ring as its fusion category
The Chern character of the Verlinde bundle over ℳ¯ g,n
No full textWe prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over M¯[subscript g,n] in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior M[subscript g,n] and the projective flatness of the Hitchin connection
The Chern character of the Verlinde bundle over ℳ¯ g,n
No full textWe prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over ℳ ¯ g , n \overline{\mathcal{M}}_{g,n} in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman's classification of semisimple CohFTs, there exists an element of Givental's group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior ℳ g , n {\mathcal{M}}_{g,n} and the projective flatness of the Hitchin connection
The Chern character of the Verlinde bundle over ℳ¯<sub> <i>g</i>,<i>n</i> </sub>
No full textAbstract
We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over
ℳ
¯
g
,
n
\overline{\mathcal{M}}_{g,n}
in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group
transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior
ℳ
g
,
n
{\mathcal{M}}_{g,n}
and the projective flatness of the Hitchin connection.</jats:p
The electrostatic view on M-theory LLM geometries
No full textWe describe the geometry of the R x SO(3) x SO(6) x U(1) invariant half-BPS M-theory configurations considered in LLM in terms of their electrostatic variables. We discuss both regular configurations, such as AdS_4 x S^7 and AdS_7 x S^4 vacua or simple excited solutions, and singular ones such as the superstar geometries. This allows us to identify the appropriate boundary conditions describing the most general smooth and superstar-like singular configurations. We also compute their masses, matching the expected result from their microscopic interpretation, but now at finite radius of curvature
Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
No full textIn this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the “Coulomb branch index” of the class SS theory T[Σ,G] on L(k,1)×S^1, the other is the LGLG “equivariant Verlinde formula”, or equivalently partition function of LGCLGC complex Chern–Simons theory on Σ×S^1. We first derive this equivalence using the M-theory geometry and show that the gauge groups appearing on the two sides are naturally G and its Langlands dual LGLG. When G is not simply-connected, we provide a recipe of computing the index of T[Σ,G] as summation over the indices of T[Σ,G] with non-trivial background ’t Hooft fluxes, where G is the universal cover of G. Then we check explicitly this relation between the Coulomb index and the equivariant Verlinde formula for G=SU(2) or SO(3). In the end, as an application of this newly found relation, we consider the more general case where G is SU(N) or PSU(N) and show that equivariant Verlinde algebra can be derived using field theory via (generalized) Argyres–Seiberg duality. We also attach a Mathematica notebook that can be used to compute the SU(3) equivariant Verlinde coefficients
Virtual Segre and Verlinde numbers of projective surfaces
No full textRecently, Marian-Oprea-Pandharipande established (a generalization of) Lehn's
conjecture for Segre numbers associated to Hilbert schemes of points on
surfaces. Extending work of Johnson, they provided a conjectural correspondence
between Segre and Verlinde numbers. For surfaces with holomorphic 2-form, we
propose conjectural generalizations of their results to moduli spaces of stable
sheaves of any rank.
Using Mochizuki's formula, we derive a universal function which expresses
virtual Segre and Verlinde numbers of surfaces with holomorphic 2-form in terms
of Seiberg-Witten invariants and intersection numbers on products of Hilbert
schemes of points. We prove that certain canonical virtual Segre and Verlinde
numbers of general type surfaces are topological invariants and we verify our
conjectures in examples.
The power series in our conjectures are algebraic functions, for which we
find expressions in several cases and which are permuted under certain Galois
actions. Our conjectures imply an algebraic analog of the Mari\~{n}o-Moore
conjecture for higher rank Donaldson invariants. For ranks and , we
obtain explicit expressions for Donaldson invariants in terms of Seiberg-Witten
invariants.Comment: Published version. 38 page
Gene Expression Microarray Public Dataset Reanalysis in Chronic Obstructive Pulmonary Disease
No full textData accompanying manuscript "Gene Expression Microarray Public Dataset Reanalysis in Chronic Obstructive Pulmonary Disease" by L.R.K. Rogers, M. Verlinde and G. Mia
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
Cardy-Verlinde Formula and Its Self-Gravitational Corrections for Regular Black Holes
No full textWe check the consistency of the entropy of Bardeen
and Ayón Beato-García-Bronnikov black holes with the entropy of
particular conformal field theory via Cardy-Verlinde formula. We also
compute the first-order semiclassical corrections of this formula due
to self-gravitational effects by modifying pure extensive and Casimir
energy in the context of Keski-Vakkuri, Kraus and Wilczek analysis.
It is concluded that the correction term remains positive for both black
holes, which leads to the violation of the holographic bound
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