12 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
Global Properties of Topological String Amplitudes and Orbifold Invariants
We derive topological string amplitudes on local Calabi-Yau manifolds in
terms of polynomials in finitely many generators of special functions. These
objects are defined globally in the moduli space and lead to a description of
mirror symmetry at any point in the moduli space. Holomorphic ambiguities of
the anomaly equations are fixed by global information obtained from boundary
conditions at few special divisors in the moduli space. As an illustration we
compute higher genus orbifold Gromov-Witten invariants for C^3/Z_3 and C^3/Z_4.Comment: 34 pages, 3 figure
The holomorphic anomaly for open string moduli
We complete the holomorphic anomaly equations for topological strings with
their dependence on open moduli. We obtain the complete system by standard path
integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165
(1994) 311) to strings with boundaries. We study both the anti-holomorphic
dependence on open moduli and on closed moduli in presence of Wilson lines. By
providing the compactification a' la Deligne-Mumford of the moduli space of
Riemann surfaces with boundaries, we show that the open holomorphic anomaly
equations are structured on the (real codimension one) boundary components of
this space.Comment: 1+14 pages, 6 figures! v2: ref. added v3: section 4 expanded, 1+17
pages, 11 figures!!, to be publ. in JHE
Counting BPS states on the Enriques Calabi-Yau
We study topological string amplitudes for the FHSV model using various
techniques. This model has a type II realization involving a Calabi-Yau
threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By
applying heterotic/type IIA duality, we compute the topological amplitudes in
the fibre to all genera. It turns out that there are two different ways to do
the computation that lead to topological couplings with different BPS content.
One of them leads to the standard D0-D2 counting amplitudes, and from the other
one we obtain information about bound states of D0-D4-D2 branes on the Enriques
fibre. We also study the model using mirror symmetry and the holomorphic
anomaly equations. We verify in this way the heterotic results for the D0-D2
generating functional for low genera and find closed expressions for the
topological amplitudes on the total space in terms of modular forms, and up to
genus four. This model turns out to be much simpler than the generic B-model
and might be exactly solvable.Comment: 62 pages, v3: some results at genus 3 corrected, more typos correcte
Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
We calculate the gravitational corrections to the effective action of N=2
SU(2) Seiberg-Witten theory with matter using modularity, the holomorphic
anomaly equation and expected behavior at the boundaries of the moduli space.
As in pure gauge theory we show that the gap condition at the dyon
singularities completely fixes the gravitational corrections. We discuss the
behavior of the gravitational corrections at the conformal points. We compare
our results with the recursive solution of the loop equation in the matrix
model approach, which provides in addition open amplitudes.Comment: 53 pages, no figure
A Matrix model for plane partitions
We construct a matrix model equivalent (exactly, not asymptotically), to the
random plane partition model, with almost arbitrary boundary conditions.
Equivalently, it is also a random matrix model for a TASEP-like process with
arbitrary boundary conditions. Using the known solution of matrix models, this
method allows to find the large size asymptotic expansion of plane partitions,
to ALL orders. It also allows to describe several universal regimes.Comment: Latex, 41 figures. Misprints and corrections. Changing the term TASEP
to self avoiding particle porces
3d-3d Correspondence Revisited
In fivebrane compactifications on 3-manifolds, we point out the importance of
all flat connections in the proper definition of the effective 3d N=2 theory.
The Lagrangians of some theories with the desired properties can be constructed
with the help of homological knot invariants that categorify colored Jones
polynomials. Higgsing the full 3d theories constructed this way recovers
theories found previously by Dimofte-Gaiotto-Gukov. We also consider the
cutting and gluing of 3-manifolds along smooth boundaries and the role played
by all flat connections in this operation.Comment: 43 pages + 1 appendix, 6 figures Version 2: new appendix on flat
connections in the 3d-3d correspondenc
M5-branes, toric diagrams and gauge theory duality
In this article we explore the duality between the low energy effective
theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge
theories compactified on S^1. The theories we study are the five-dimensional
uplifts of four-dimensional superconformal linear quivers. We study this
duality by comparing the Seiberg-Witten curves and the Nekrasov partition
functions of the two dual theories. The Seiberg-Witten curves are obtained by
minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov
partition functions are computed using topological string theory. The result of
our study is a map between the gauge theory parameters, i.e., Coulomb moduli,
masses and UV coupling constants, of the two dual theories. Apart from the
obvious physical interest, this duality also leads to compelling mathematical
identities. Through the AGTW conjecture these five-dimentional gauge theories
are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The
duality we study implies the relations between Liouville and Toda correlation
functions through the map we derive.Comment: 58 pages, 17 figures; v2: minor corrections, references adde