3,253 research outputs found
World-sheet Instantons via the Myers Effect and N=1^* Quiver Superpotentials
In this note we explore the stringy interpretation of non-perturbative
effects in N=1^* deformations of the A_{k-1} quiver models. For certain types
of deformations we argue that the massive vacua are described by Nk fractional
D3-branes at the orbifold polarizing into k concentric 5-brane spheres each
carrying fractional brane charge. The polarization of the D3-branes induces a
polarization of D-instantons into string world-sheets wrapped on the Myers
spheres. We show that the superpotentials in these models are indeed generated
by these world-sheet instantons. We point out that for certain parameter values
the condensates yield the exact superpotential for a relevant deformation of
the Klebanov-Witten conifold theory.Comment: 24 pages, JHEP, some small errors and typos correcte
A quantum McKay correspondence for fractional 2p-branes on LG orbifolds
We study fractional 2p-branes and their intersection numbers in non-compact
orbifolds as well the continuation of these objects in Kahler moduli space to
coherent sheaves in the corresponding smooth non-compact Calabi-Yau manifolds.
We show that the restriction of these objects to compact Calabi-Yau
hypersurfaces gives the new fractional branes in LG orbifolds constructed by
Ashok et. al. in hep-th/0401135. We thus demonstrate the equivalence of the
B-type branes corresponding to linear boundary conditions in LG orbifolds,
originally constructed in hep-th/9907131, to a subset of those constructed in
LG orbifolds using boundary fermions and matrix factorization of the
world-sheet superpotential. The relationship between the coherent sheaves
corresponding to the fractional two-branes leads to a generalization of the
McKay correspondence that we call the quantum McKay correspondence due to a
close parallel with the construction of branes on non-supersymmetric orbifolds.
We also provide evidence that the boundary states associated to these branes in
a conformal field theory description corresponds to a sub-class of the boundary
states associated to the permutation branes in the Gepner model associated with
the LG orbifold.Comment: LaTeX2e, 1+39 pages, 3 figures (v2) refs added, typos and report no.
correcte
Matrix Factorizations and Homological Mirror Symmetry on the Torus
We consider matrix factorizations and homological mirror symmetry on the
torus T^2 using a Landau-Ginzburg description. We identify the basic matrix
factorizations of the Landau-Ginzburg superpotential and compute the full
spectrum, taking into account the explicit dependence on bulk and boundary
moduli. We verify homological mirror symmetry by comparing three-point
functions in the A-model and the B-model.Comment: 41 pages, 9 figures, v2: reference added, minor corrections and
clarifications, version published in JHE
Central Limit Theorems for the Brownian motion on large unitary groups
In this paper, we are concerned with the large N limit of linear combinations
of the entries of a Brownian motion on the group of N by N unitary matrices. We
prove that the process of such a linear combination converges to a Gaussian
one. Various scales of time and various initial distribution are concerned,
giving rise to various limit processes, related to the geometric construction
of the unitary Brownian motion. As an application, we propose a quite short
proof of the asymptotic Gaussian feature of the linear combinations of the
entries of Haar distributed random unitary matrices, a result already proved by
Diaconis et al.Comment: 14 page
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