Duiliu-Emanuel Diaconescu

D-branes, monopoles and Nahm equations

Abstract We study the correspondence between 11b solitonic 1-branes and monopoles in the context of the 3-brane realization of D = 4 N = 4 super Yang-Mills theory. We show that a bound state of 1-branes stretching between two separated 3-branes exhibits a family of supersymmetric ground states that can be identified with the ADHMN construction of the moduli space of SU(2) monopoles. This identification is supported by the construction of the monopole gauge field as a space-time coupling in the quantum mechanical effective action of a 1-brane used as a probe. The analysis also reveals an intriguing new aspect of the 1-brane theory: the transverse oscillations of the 1-branes in the ground states are described by non-commuting matrix valued fields which develop poles at the boundary. Finally, the construction is generalized to SU(n) monopoles with arbitrary n > 2.

The Coulomb branch of (4,4) supersymmetric field theories in two dimensions

We study (4,4) supersymmetric field theories in two dimensions with a one dimensional Coulomb branch. These theories have applications in string theory. Our analysis explains the known relation between A−D−E groups and modular invariants of affine SU(2).

Nonrenormalization theorem for the d=1, N=8 vector multiplet

Sigma models describing low energy effective actions on D0-brane probes with N=8 supercharges are studied in detail using a manifestly d=1, N=4 superspace formalism. Two (0+1)-dimensional N=4 multiplets together with their general actions are constructed. We derive the condition for these actions to be N=8 supersymmetric and apply these techniques to various D-brane configurations. We find that if in addition to N=8 supersymmetry the action must also have Spin(5) invariance, the form of the {sigma} model metric is uniquely determined by the one-loop result and is not renormalized perturbatively or nonperturbatively. {copyright} {ital 1997} {ital The American Physical Society}

Gauge-mediated supersymmetry breaking in string compactifications

We provide string theory examples where a toy model of a SUSY GUT or the MSSM is embedded in a compactification along with a gauge sector which dynamically breaks supersymmetry. We argue that by changing microscopic details of the model (such as precise choices of flux), one can arrange for the dominant mediation mechanism transmitting SUSY breaking to the Standard Model to be either gravity mediation or gauge mediation. Systematic improvement of such examples may lead to top-down models incorporating a solution to the SUSY flavor problem.

Localization and gluing of topological amplitudes

We develop a gluing algorithm for Gromov-Witten invariants of toric Calabi-Yau threefolds based on localization and gluing graphs. The main building block of this algorithm is a generating function of cubic Hodge integrals of special form. We conjecture a precise relation between this generating function and the topological vertex at fractional framing.

Moduli of ADHM sheaves and the local Donaldson–Thomas theory

Abstract The ADHM construction establishes a one-to-one correspondence between framed torsion free sheaves on the projective plane and stable framed representations of a quiver with relations in the category of complex vector spaces. This paper studies the geometry of moduli spaces of representations of the same quiver with relations in the abelian category of coherent sheaves on a smooth complex projective curve X . In particular it is proven that this moduli space is virtually smooth and related by relative Beilinson spectral sequence to the curve counting construction via stable pairs of Pandharipande and Thomas. This yields a new conjectural construction for the local Donaldson–Thomas theory of curves as well as a natural higher rank generalization.

Large N Duality, Lagrangian Cycles, and Algebraic Knots

We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.

Geometric transitions and integrable systems

Abstract We consider B-model large N duality for a new class of noncompact Calabi–Yau spaces modeled on the neighborhood of a ruled surface in a Calabi–Yau threefold. The closed string side of the transition is governed at genus zero by an A 1 Hitchin integrable system on a genus g Riemann surface Σ. The open string side is described by a holomorphic Chern–Simons theory which reduces to a generalized matrix model in which the eigenvalues lie on the compact Riemann surface Σ. We show that the large N planar limit of the generalized matrix model is governed by the same A 1 Hitchin system therefore proving genus zero large N duality for this class of transitions.

A D-brane landscape on Calabi-Yau manifolds

We explore the dynamics of nonsupersymmetric D-brane configurations on Calabi-Yau orientifolds with fluxes. We show that supergravity D-terms capture supersymmetry breaking effects predicted by more abstract ?-stability considerations. We also investigate the vacuum structure of such configurations in the presence of fluxes. Based on the shape of the potential, we argue that metastable nonsupersymmetric vacua can be in principle obtained by tuning the values of fluxes.

Black string entropy and Fourier-Mukai transform

We propose a microscopic description of black strings in F-theory based on string duality and Fourier-Mukai transform. These strings admit several different microscopic descriptions involving D-brane as well as M2 or M5-brane configurations on elliptically fibered Calabi-Yau threefolds. In particular our results can also be interpreted as an asymptotic microstate count for D6-D2-D0 configurations in the limit of large D2-charge on the elliptic fiber. The leading behavior of the microstate degeneracy in this limit is shown to agree with the macroscopic entropy formula derived from the black string supergravity solution.