33 research outputs found
Isotropic A-branes and the stability condition
The existence of a new kind of branes for the open topological A-model is
argued by using the generalized complex geometry of Hitchin and the SYZ picture
of mirror symmetry. Mirror symmetry suggests to consider a bi-vector in the
normal direction of the brane and a new definition of generalized complex
submanifold. Using this definition, it is shown that there exists generalized
complex submanifolds which are isotropic in a symplectic manifold. For certain
target space manifolds this leads to isotropic A-branes, which should be
considered in addition to Lagrangian and coisotropic A-branes. The Fukaya
category should be enlarged with such branes, which might have interesting
consequences for the homological mirror symmetry of Kontsevich. The stability
condition for isotropic A-branes is studied using the worldsheet approach.Comment: 19 page
Applications of Exact Renormalization Group techniques to the non-perturbative study of supersymmetric gauge field theory
Exact Renormalization Group techniques are applied to supersymmetric models
in order to get some insights into the low energy effective actions of such
theories. Starting from the ultra-violet finite mass deformed N=4
supersymmetric Yang-Mills theory, one varies the regularising mass and
compensates for it by introducing an effective Wilsonian action. (Polchinski's)
Renormalization Group equation is modified in an essential way by the presence
of rescaling (a.k.a. Konishi) anomaly, which is responsible for the
beta-function. When supersymmetry is broken up to N=1 the form of effective
actions in terms of massless fields is quite reasonable, while in the case of
the N=2 model we appear to have problems related to instantons.Comment: 14 pages, uses ws-p9-75x6-50.cls, presented at the 2nd Conference on
the Exact RG, Rome 200
A sigma model field theoretic realization of Hitchin's generalized complex geometry
We present a sigma model field theoretic realization of Hitchin's generalized
complex geometry, which recently has been shown to be relevant in
compactifications of superstring theory with fluxes. Hitchin sigma model is
closely related to the well known Poisson sigma model, of which it has the same
field content. The construction shows a remarkable correspondence between the
(twisted) integrability conditions of generalized almost complex structures and
the restrictions on target space geometry implied by the Batalin--Vilkovisky
classical master equation. Further, the (twisted) classical Batalin--Vilkovisky
cohomology is related non trivially to a generalized Dolbeault cohomology.Comment: 28 pages, Plain TeX, no figures, requires AMS font files AMSSYM.DEF
and amssym.tex. Typos in eq. 6.19 and some spelling correcte
Topological Strings and Integrable Hierarchies
We consider the topological B-model on local Calabi-Yau geometries. We show
how one can solve for the amplitudes by using W-algebra symmetries which
encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the
highly effective fermionic/brane formulation this leads to a free fermion
description of the amplitudes. Furthermore we argue that topological strings on
Calabi-Yau geometries provide a unifying picture connecting non-critical
(super)strings, integrable hierarchies, and various matrix models. In
particular we show how the ordinary matrix model, the double scaling limit of
matrix models, and Kontsevich-like matrix model are all related and arise from
studying branes in specific local Calabi-Yau three-folds. We also show how
A-model topological string on P^1 and local toric threefolds (and in particular
the topological vertex) can be realized and solved as B-model topological
string amplitudes on a Calabi-Yau manifold.Comment: 82 pages, harvmac, 1 figur
Supersymmetric D-branes and calibrations on general N=1 backgrounds
We study the conditions to have supersymmetric D-branes on general {\cal N}=1
backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms
of the two pure spinors associated to the SU(3)\times SU(3) structure on
T_M\oplus T^\star_M, and can be split into two parts each involving a different
pure spinor. The first involves the integrable pure spinor and requires the
D-brane to wrap a generalised complex submanifold with respect to the
generalised complex structure associated to it. The second contains the
non-integrable pure spinor and is related to the stability of the brane. The
two conditions can be rephrased as a generalised calibration condition for the
brane. The results preserve the generalised mirror symmetry relating the type
IIA and IIB backgrounds considered, giving further evidence for this duality.Comment: 23 pages. Some improvements and clarifications, typos corrected and
references added. v3: Version published in JHE
An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills
We study relevant deformations of an N=1 superconformal theory which is an
exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory
has a classical Higgs branch that is a complex deformation of the orbifold
C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold
singularities. At these singular points in moduli space the theory exhibits a
duality cascade and flows to a confining theory with a mass gap. By exactly
solving the corresponding holomorphic matrix model we compute the exact quantum
superpotential generated at the end of the duality cascade and calculate
precisely how quantum effects deform the classical moduli space by replacing
the conifold singularities with three-cycles of finite size. Locally the
structure is that of the deformed conifold, but the global geometry is
different. This desingularized quantum deformed geometry is the moduli space of
probe D3-branes at the end of a duality cascade realized on the worldvolume of
(fractional) D3-branes placed at the isolated conifold singularities in the
deformation of the orbifold C^3/Z_n x Z_n with discrete torsion.Comment: Uses Latex, JHEP.cls, 43 pages, 3 figure
Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model
We propose a formula for the eigenvalue integral of the hermitian one matrix
model with infinite well potential in terms of dressed twist fields of the
su(2) level one WZW model. The expression holds for arbitrary matrix size n,
and provides a suggestive interpretation for the monodromy properties of the
matrix model correlators at finite n, as well as in the 1/n-expansion.Comment: 27 pages, 4 figures; v2: typos corrected, reference added, version to
be published in JHE
Geometric Metastability, Quivers and Holography
We use large N duality to study brane/anti-brane configurations on a class of
Calabi-Yau manifolds. With only branes present, the Calabi-Yau manifolds in
question give rise to N=2 ADE quiver theories deformed by superpotential terms.
We show that the large N duality conjecture of hep-th/0610249 reproduces
correctly the known qualitative features of the brane/anti-brane physics. In
the supersymmetric case, the gauge theories have Seiberg dualities which are
represented as flops in the geometry. Moreover, the holographic dual geometry
encodes the whole RG flow of the gauge theory. In the non-supersymmetric case,
the large N duality predicts that the brane/anti-brane theories also enjoy such
dualities, and allows one to pick out the good description at a given energy
scale.Comment: v2: 56 pages, 4 figures, harvmac, abstract correcte