D-brane World-volume Theory Research Articles

Tachyon field theory description of (thermo)dynamics in dS space

In this work, we present a few pieces of evidence in support of a possible connection of the gravitational theory in dS space to the worldvolume theory of unstable D-branes. We show that the action describing the geodesic motion of a massive particle (or point-like object) in static dS space turns out to be the same as that of the tachyon field theory for an unstable particle. The motion along the radial direction from the origin, a locally Minkowski spacetime, to the horizon, a locally Rindler space times a sphere, represents just the tachyon condensation process, therefore providing a geometric picture of tachyon condensation. We further study a scalar in global or flat dS and the tachyon fluctuations in a homogeneous tachyon background, representing either the full or half S-brane, on unstable D-branes and find that certain dynamics of the dS universe corresponds to that of the homogeneous full or half S-brane. The thermal temperature of tachyon radiation is found to agree with that felt by any timelike observer in dS space. In string theory context, this temperature is just the Hagedorn one, signaling a phase transition to closed strings. An understanding of this transition in the bulk dS space is also given.

Decaying D-branes and moving mirrors

We present an exact time-dependent solution to the effective D-brane world-volume theory which describes an inhomogeneous decay of a brane-antibrane system. We compute the quantum energy flux induced by the particle creation in this inhomogeneous and time-dependent background. We find that this calculation is essentially equivalent to that of the moving mirror system. In the initial stage, the energy flux turns out to be thermal with the temperature given by the inverse of the distance between the brane and the antibrane. Later it changes its sign and becomes a negative energy flux. Our result may be relevant for the (p)reheating process or/and the evolution of cosmic string network after stringy brane inflation.

Ghost D-branes

We define a ghost D-brane in superstring theories as an object that cancels the effects of an ordinary D-brane. The supergroups U(N|M) and OSp(N|M) arise as gauge symmetries in the supersymmetric world-volume theory of D-branes and ghost D-branes. A system with a pair of D-brane and ghost D-brane located at the same location is physically equivalent to the closed string vacuum. When they are separated, the system becomes a new brane configuration. We generalize the type I/heterotic duality by including n ghost D9-branes on the type I side and by considering the heterotic string whose gauge group is OSp(32+2n|2n). Motivated by the type IIB S-duality applied to D9- and ghost D9-branes, we also find type II-like closed superstrings with U(n|n) gauge symmetry.

Computation of Superpotentials for D-Branes

We present a general method for the computation of tree-level superpotentials for the world-volume theory of B-type D-branes. This includes quiver gauge theories in the case that the D-brane is marginally stable. The technique involves analyzing the A-infinity structure inherent in the derived category of coherent sheaves. This effectively gives a practical method of computing correlation functions in holomorphic Chern-Simons theory. As an example, we give a more rigorous proof of previous results concerning 3-branes on certain singularities including conifolds. We also provide a new example.

Noncommutative gauge theories from deformation quantization

We construct noncommutative gauge theories based on the notion of the Weyl bundle, which appears in Fedosov's construction of deformation quantization on an arbitrary symplectic manifold. These correspond to D-brane worldvolume theories in non-constant B-field and curved backgrounds in string theory. All such theories are embedded into a “universal” gauge theory of the Weyl bundle. This shows that the combination of a background field and a noncommutative field strength has universal meaning as a field strength of the Weyl bundle. We also show that the gauge equivalence relation is a part of such a “universal” gauge symmetry.

Phase structure of non-commutative field theories and spinning brane bound states

General spinning brane bound states are constructed, along with their near-horizon limits which are relevant as dual descriptions of non-commutative field theories. For the spinning D-brane world volume theories with a B-field a general analysis of the gauge coupling phase structure is given, exhibiting various novel features, already at the level of zero angular momenta. We show that the thermodynamics is equivalent to the commutative case at large N and we discuss the possibility and consequences of finite N. As an application of the general analysis, the range of validity of the thermodynamics for the NCSYM is discussed. In view of the recently conjectured existence of a 7-dimensional NCSYM, the thermodynamics of the spinning D6-brane theory, for which a stable region can be found, is presented in detail. Corresponding results for the spinning M5-M2 brane bound state, including the near-horizon limit and thermodynamics, are given as well.

D3-branes on partial resolutions of abelian quotient singularities of Calabi–Yau threefolds

We investigate field theories on the world-volume of a D3-brane transverse to partial resolutions of a Z 3× Z 3 Calabi–Yau threefold quotient singularity. We deduce the field content and Lagrangian of such theories and present a systematic method for mapping the moment map levels characterizing the partial resolutions of the singularity to the Fayet–Iliopoulos parameters of the D-brane world-volume theory. As opposed to the simpler cases studied before, we find a complex web of partial resolutions and associated field-theoretic Fayet–Iliopoulos deformations. The analysis is performed by toric methods, leading to a structure which can be efficiently described in the language of convex geometry. For the world-volume theory, the analysis of the moduli space has an elegant description in terms of quivers. As a by-product, we present a systematic way of extracting the birational geometry of the classical moduli spaces, thus generalizing previous work on resolution of singularities by D-branes.

Multiple D0-branes in weakly curved backgrounds

We investigate further our recent proposal for the form of the matrix theory action in weak background fields. Using Seiberg's scaling argument we relate the matrix theory action to a low-energy system of many D0-branes in an arbitrary but weak NS-NS and R-R background. The resulting multiple D0-brane action agrees with the known Born-Infeld action in the case of a single brane and gives an explicit formulation of many additional terms which appear in the multiple brane action. The linear coupling to an arbitrary background metric satisfies the non-trivial consistency condition suggested by Douglas that the masses of off-diagonal fields are given by the geodesic distance between the corresponding pair of D0-branes. This agreement arises from combinatorial factors which depend upon the symmetrized trace ordering prescription found earlier for higher moments of the matrix theory stress-energy tensor. We study the effect of a weak background metric on two graviton interactions and find that our formalism agrees with the results expected from supergravity. The results presented here can be T-dualized to give explicit formulae for the operators in any D-brane world-volume theory which couple linearly to bulk gravitational fields and their derivatives.

D-branes on three-dimensional nonabelian orbifolds

We study D-branes on a three complex dimensional nonabelian orbifold ${\bf C}^3/\Gamma$ with $\Gamma$ a finite subgroup of SU(3). We present general formulae necessary to obtain quiver diagrams which represent the gauge group and the spectrum of the D-brane worldvolume theory for dihedral-like subgroups $\Delta(3n^2)$ and $\Delta(6n^2)$. It is found that the quiver diagrams have a similar structure to webs of branes.

BPS ANALYSIS OF THE CHARGED SOLITON SOLUTIONS OF D-BRANE WORLD VOLUME THEORY FROM THE VIEWPOINT OF TARGET-SPACE SUPERSYMMETRY

We investigate BPS properties of the charged soliton solutions of D-brane world volume theory, which is described by the supersymmetric Dirac–Born–Infeld action, by means of the N=2 target-space supersymmetry algebra. Our results agree with those obtained previously. We also extend our BPS analysis to the case where axion background exists.

String junction transitions in the moduli space of N = 2 SYM

The string theory description of BPS states in D-brane world-volume field theories may undergo transitions from open strings to string webs, as well as between different string webs, as one moves in the field theory moduli space. These transitions are driven by the string creation phenomenon. We demonstrate such transitions in the D3-brane realization of N = 2 SU(2) Super-Yang-Mills theory.

D-branes and the noncommutative torus

We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a physical derivation of the identification proposed by Connes, Douglas and Schwarz of Matrix theory compactification on the noncommutative torus with M theory compactification with constant background three-form tensor field.

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.