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

Matrix String Theory, 2D SYM Instantons and affine Toda systems

Extending a recent result of S.B. Giddings, F. Hacquebord and H. Verlinde, we show that in the U(N) SYM Matrix theory there exist classical BPS instantons which interpolate between different closed string configurations via joining/splitting interactions similar to those of string field theory. We construct them starting from branched coverings of Riemann surfaces. For the class of them which we analyze in detail the construction can be made explicit in terms U(N) affine Toda field theories.Comment: 12 pages, 1 eps figure, JHEP.cls LaTeX2e class file; sign corrected, ref. and acknowledgements update

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

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 ${\cal O}(n)\oplus{\cal O}(-2-n)$ on $\P1$ with a singular point at which an extra fiber sits. We wrap $N$ D5-branes on $\P1$ and $M$ 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 $n=0$ case, corresponding to a partial resolution of the $A_2$ singularity, the quantum superpotential in the ${\cal N}=1$ unitary SYM with one adjoint and $M$ fundamentals is obtained. The $n=1$ 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

Matrix String Theory and its Moduli Space

The correspondence between Matrix String Theory in the strong coupling limit and IIA superstring theory can be shown by means of the instanton solutions of the former. We construct the general instanton solutions of Matrix String Theory which interpolate between given initial and final string configurations. Each instanton is characterized by a Riemann surface of genus h with n punctures, which is realized as a plane curve. We study the moduli space of such plane curves and find out that, at finite N, it is a discretized version of the moduli space of Riemann surfaces: instead of 3h-3+n its complex dimensions are 2h-3+n, the remaining h dimensions being discrete. It turns out that as $N$ tends to infinity, these discrete dimensions become continuous, and one recovers the full moduli space of string interaction theory.Comment: 30 pages, LaTeX, JHEP.cls class file, minor correction

Magnetic Resonance Imaging of Optic Nerve Traction During Adduction in Primary Open-Angle Glaucoma With Normal Intraocular Pressure.

PurposeWe used magnetic resonance imaging (MRI) to ascertain effects of optic nerve (ON) traction in adduction, a phenomenon proposed as neuropathic in primary open-angle glaucoma (POAG).MethodsSeventeen patients with POAG and maximal IOP ≤ 20 mm Hg, and 31 controls underwent MRI in central gaze and 20° to 30° abduction and adduction. Optic nerve and sheath area centroids permitted computation of midorbital lengths versus minimum paths.ResultsAverage mean deviation (±SEM) was -8.2 ± 1.2 dB in the 15 patients with POAG having interpretable perimetry. In central gaze, ON path length in POAG was significantly more redundant (104.5 ± 0.4% of geometric minimum) than in controls (102.9 ± 0.4%, P = 2.96 × 10-4). In both groups the ON became significantly straighter in adduction (28.6 ± 0.8° in POAG, 26.8 ± 1.1° in controls) than central gaze and abduction. In adduction, the ON in POAG straightened to 102.0% ± 0.2% of minimum path length versus 104.5% ± 0.4% in central gaze (P = 5.7 × 10-7), compared with controls who straightened to 101.6% ± 0.1% from 102.9% ± 0.3% in central gaze (P = 8.7 × 10-6); and globes retracted 0.73 ± 0.09 mm in POAG, but only 0.07 ± 0.08 mm in controls (P = 8.8 × 10-7). Both effects were confirmed in age-matched controls, and remained significant after correction for significant effects of age and axial globe length (P = 0.005).ConclusionsAlthough tethering and elongation of ON and sheath are normal in adduction, adduction is associated with abnormally great globe retraction in POAG without elevated IOP. Traction in adduction may cause mechanical overloading of the ON head and peripapillary sclera, thus contributing to or resulting from the optic neuropathy of glaucoma independent of IOP

G2 Hitchin functionals at one loop

We consider the quantization of the effective target space description of topological M-theory in terms of the Hitchin functional whose critical points describe seven-manifolds with G2 structure. The one-loop partition function for this theory is calculated and an extended version of it, that is related to generalized G2 geometry, is compared with the topological G2 string. We relate the reduction of the effective action for the extended G2 theory to the Hitchin functional description of the topological string in six dimensions. The dependence of the partition functions on the choice of background G2 metric is also determined.Comment: 58 pages, LaTeX; v2: Acknowledgments adde

Generalized Kahler Geometry from supersymmetric sigma models

We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.Comment: 18 page