2,456 research outputs found
Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings
We study cohomological gauge theories on total spaces of holomorphic line
bundles over complex manifolds and obtain their reduction to the base manifold
by U(1) equivariant localization of the path integral. We exemplify this
general mechanism by proving via exact path integral localization a reduction
for local curves conjectured in hep-th/0411280, relevant to the calculation of
black hole entropy/Gromov-Witten invariants. Agreement with the
four-dimensional gauge theory is recovered by taking into account in the latter
non-trivial contributions coming from one-loop fluctuations determinants at the
boundary of the total space. We also study a class of abelian gauge theories on
Calabi-Yau local surfaces, describing the quantum foam for the A-model,
relevant to the calculation of Donaldson-Thomas invariants.Comment: 17 page
Conifold geometries, matrix models and quantum solutions
This paper is a continuation of hepth/0507224 where open topological B-models
describing D-branes on 2-cycles of local Calabi--Yau geometries with conical
singularities were studied. After a short review, the paper expands in
particular on two aspects: the gauge fixing problem in the reduction to two
dimensions and the quantum matrix model solutions.Comment: 17 p. To appear in proc. Symposium QTS-4, Varna (Bulgaria), August
200
Heterotic Matrix String Theory and Riemann Surfaces
We extend the results found for Matrix String Theory to Heterotic Matrix
String Theory, i.e. to a 2d O(N) SYM theory with chiral (anomaly free) matter
and N=(8,0) supersymmetry. We write down the instanton equations for this
theory and solve them explicitly. The solutions are characterized by branched
coverings of the basis cylinder, i.e. by compact Riemann surfaces with
punctures. We show that in the strong coupling limit the action becomes the
heterotic string action plus a free Maxwell action. Moreover the amplitude
based on a Riemann surface with p punctures and h handles is proportional to
g^{2-2h-p}, as expected for the heterotic string interaction theory with string
coupling g_s=1/g.Comment: 17 pages, JHEP LaTeX style, sentence delete
Branched Coverings and Interacting Matrix Strings in Two Dimensions
We construct the lattice gauge theory of the group G_N, the semidirect
product of the permutation group S_N with U(1)^N, on an arbitrary Riemann
surface. This theory describes the branched coverings of a two-dimensional
target surface by strings carrying a U(1) gauge field on the world sheet. These
are the non-supersymmetric Matrix Strings that arise in the unitary gauge
quantization of a generalized two-dimensional Yang-Mills theory. By classifying
the irreducible representations of G_N, we give the most general formulation of
the lattice gauge theory of G_N, which includes arbitrary branching points on
the world sheet and describes the splitting and joining of strings.Comment: LaTeX2e, 25 pages, 4 figure
Flavour from partially resolved singularities
In this letter we study topological open string field theory on D--branes in
a IIB background given by non compact CY geometries on with a singular point at which an extra fiber sits. We wrap
D5-branes on and effective D3-branes at singular points, which
are actually D5--branes wrapped on a shrinking cycle. We calculate the
holomorphic Chern-Simons partition function for the above models in a deformed
complex structure and find that it reduces to multi--matrix models with
flavour. These are the matrix models whose resolvents have been shown to
satisfy the generalized Konishi anomaly equations with flavour. In the
case, corresponding to a partial resolution of the singularity, the
quantum superpotential in the unitary SYM with one adjoint and
fundamentals is obtained. The case is also studied and shown to give rise
to two--matrix models which for a particular set of couplings can be exactly
solved. We explicitly show how to solve such a class of models by a quantum
equation of motion technique
N=2 SYM RG Scale as Modulus for WDVV Equations
We derive a new set of WDVV equations for N=2 SYM in which the
renormalization scale is identified with the distinguished modulus
which naturally arises in topological field theories.Comment: 6 pages, LaTe
Algebraic-geometrical formulation of two-dimensional quantum gravity
We find a volume form on moduli space of double punctured Riemann surfaces
whose integral satisfies the Painlev\'e I recursion relations of the genus
expansion of the specific heat of 2D gravity. This allows us to express the
asymptotic expansion of the specific heat as an integral on an infinite
dimensional moduli space in the spirit of Friedan-Shenker approach. We outline
a conjectural derivation of such recursion relations using the
Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil
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