Moduli Space Of D-branes Research Articles

\u21242 boundary twist fields and the moduli space of D-branes

We revisit the boundary conformal field theory of twist fields. Based on the equivalence between twisted bosons on a circle and the orbifold theory at the critical radius, we provide a bosonized representation of boundary twist fields and thus a free field representation of the latter. One advantage of this formulation is that it considerably simplifies the calculation of correlation functions involving twist fields. At the same time this also gives access to higher order terms in the operator product expansions of the latter which, in turn, allows to explore the moduli space of marginal deformation of bound states of D-branes. In the process we also generalize some results on correlation functions with excited twist fields.

A support theorem for Hilbert schemes of planar curves

Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve encodes the cohomology of {\em all} Hilbert schemes of points on the curve. Globally, it follows that a family of such curves with smooth relative compactified Jacobian ("moduli space of D-branes'') in an irreducible curve class on a Calabi-Yau threefold will contribute equally to the BPS invariants in the formulation of Pandharipande and Thomas, and in the formulation of Hosono, Saito, and Takahashi.

D-brane moduli spaces and superpotentials in a two-parameter model

We study D2-branes on the K3-fibration P^4_(11222)[8] using matrix factorizations at the Landau-Ginzburg point and analyze their moduli space and superpotentials in detail. We find that the open string moduli space consists of various intersecting branches of different dimensions. Families of D2-branes wrapping rational curves of degree one intersect with bound state branches. The influence of non-toric complex structure deformations is investigated in the Landau-Ginzburg framework, where these deformations arise as bulk moduli from the twisted sectors.

A relation between moduli space of D-branes on orbifolds and Ising model

We study D-branes transverse to an abelian orbifold 3/n × n. The moduli space of the gauge theory on the D-branes is analyzed by combinatorial calculation based on toric geometry. It is shown that the calculation is related to a problem to count the number of ground states of an antiferromagnetic Ising model. The lattice on which the Ising model is defined is a triangular one defined on the McKay quiver of the orbifold.

Instanton counting, Macdonald function and the moduli space ofD-branes

We argue the connection of Nekrasov's partition function in the \Omega background and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of N=2 SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant parameters \epsilon_1, \epsilon_2 of toric action on C^2 factorizes correctly as the character of SU(2)_L \times SU(2)_R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2-branes on (local) F_0. We also present an attempt at constructing a refined topological vertex in terms of the Macdonald function. The refined topological vertex with two parameters of T^2 action allows us to obtain the generating functions of equivariant \chi_y and elliptic genera of the Hilbert scheme of n points on C^2 by the method of topological vertex.

Baryon Spectra and AdS/CFT Correspondence

We provide a detailed map between wrapped D3-branes in Anti-de Sitter (AdS) backgrounds and dibaryon operators in the corresponding conformal field theory (CFT). The effective five dimensional action governing the dynamics of AdS space contains a $U(1)_R$ gauge field that mediates interactions between objects possessing R-charge. We show that the $U(1)_R$ charge of these wrapped D3-branes as measured by the gauge field matches the R-charge of the dibaryons expected from field theory considerations. We are able, through a careful probe brane calculation in an $AdS_5\times T^{1,1}$ background, to understand the exact relation between the mass of the wrapped D3-brane and the dimension of the corresponding dibaryon. We also make some steps toward matching the counting of dibaryon operators in the CFT with the ground states of a supersymmetric quantum mechanical system whose target space is the moduli space of D-branes. Finally, we discuss BPS excitations of the D3-brane and compare them with higher dimension operators in the CFT.

D-branes on group manifolds

Possible Dirichlet boundary states for WZW models with untwisted affine super Kac-Moody symmetry are classified for all compact simple Lie groups. They are obtained by inner- and outerautomorphisms of the group. The D-brane world-volume turns out to be a group manifold of a symmetric subgroup, so that the moduli space of D-branes is locally isomorphic to an irreducible Riemannian symmetric space. It is also clarified how these D-branes are transformed into each other under abelian T-duality of the WZW model. Our result implies, for example, that there is no D-particle on the compact simple group manifold. When the D-brane world-volume contains an S 1 factor, the D-brane moduli space becomes locally isomorphic to a hermitian symmetric space and open string world-sheet instantons are allowed.

Mirror symmetry in three-dimensional gauge theories, [formula omitted] and D-brane moduli spaces

We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N = 4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL(2, Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane world-volume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping 5-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.