6 research outputs found
Gravitational corrections in supersymmetric gauge theory and matrix models
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are
obtained from topological string amplitudes. We show how they are recovered in
matrix model computations. This provides a test of the proposal by Dijkgraaf
and Vafa beyond the planar limit. Both, matrix model and topological string
theory, are used to check a conjecture of Nekrasov concerning these
gravitational couplings in Seiberg-Witten theory. Our analysis is performed for
those gauge theories which are related to the cubic matrix model, i.e. pure
SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic
superpotential. We outline the computation of the topological amplitudes for
the local Calabi-Yau manifolds which are relevant for these two cases.Comment: 27 pages, one eps figur
Matrix Model as a Mirror of Chern-Simons Theory
Using mirror symmetry, we show that Chern-Simons theory on certain manifolds
such as lens spaces reduces to a novel class of Hermitian matrix models, where
the measure is that of unitary matrix models. We show that this agrees with the
more conventional canonical quantization of Chern-Simons theory. Moreover,
large N dualities in this context lead to computation of all genus A-model
topological amplitudes on toric Calabi-Yau manifolds in terms of matrix
integrals. In the context of type IIA superstring compactifications on these
Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2
manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric
gauge theories with superpotentials involving certain multi-trace operators.Comment: harvmac, 54 pages, 13 figure
Superpotentials from flux compactifications of M-theory
In flux compactifications of M-theory a superpotential is generated whose
explicit form depends on the structure group of the 7-dimensional internal
manifold. In this note, we discuss superpotentials for the structure groups:
G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For
SU(3) structures, the non-zero flux components entering the superpotential
describe an effective 1-dimensional model and a Chern-Simons model if there are
SU(2) structures.Comment: 10 page
Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
We present the most complete list of mirror pairs of Calabi-Yau complete
intersections in toric ambient varieties and develop the methods to solve the
topological string and to calculate higher genus amplitudes on these compact
Calabi-Yau spaces. These symplectic invariants are used to remove redundancies
in examples. The construction of the B-model propagators leads to compatibility
conditions, which constrain multi-parameter mirror maps. For K3 fibered
Calabi-Yau spaces without reducible fibers we find closed formulas for all
genus contributions in the fiber direction from the geometry of the fibration.
If the heterotic dual to this geometry is known, the higher genus invariants
can be identified with the degeneracies of BPS states contributing to
gravitational threshold corrections and all genus checks on string duality in
the perturbative regime are accomplished. We find, however, that the BPS
degeneracies do not uniquely fix the non-perturbative completion of the
heterotic string. For these geometries we can write the topological partition
function in terms of the Donaldson-Thomas invariants and we perform a
non-trivial check of S-duality in topological strings. We further investigate
transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2
quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur