Non-commutative World-volume Research Articles

Noncommutative field theory on homogeneous gravitational waves

We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and analyse quantum field theories defined thereon. Various star-products are derived in closed explicit form and the Hopf algebra of twisted isometries of the plane wave is constructed. Scalar field theories are defined using explicit forms of derivative operators, traces and noncommutative frame fields for the geometry, and various physical features are described. Noncommutative worldvolume field theories of D-branes in the pp-wave background are also constructed.

Open Wilson Lines as States of Closed String

System of a D-brane in bosonic string theory on a constant $B$ field background is studied in order to obtain further insight into the bulk-boundary duality. Boundary states which describe arbitrary numbers of open-string tachyons and gluons are given. UV behaviors of field theories on the non-commutative world-volume are investigated by using these states. We take zero-slope limits of generating functions of one-loop amplitudes of gluons (and open-string tachyons) in which the region of the small open-string proper time is magnified. Existence of $B$ field allows the limits to be slightly different from the standard field theory limits of closed-string. They enable us to capture world-volume theories at a trans-string scale. In this limit the generating functions are shown to be factorized by two curved open Wilson lines (and their analogues) and become integrals on the space of paths with a Gaussian distribution around straight lines. These indicate a possibility that field theories on the non-commutative world-volume are topological at such a trans-string scale. We also give a proof of the Dhar-Kitazawa conjecture by making an explicit correspondence between the closed-string states and the paths. Momentum eigenstates of closed-string or momentum loops also play an important role in these analyses.

The Atick–Witten free energy, closed tachyon condensation and deformed Poincaré symmetry

The dependence of the free energy of string theory on the temperature at T⪢ T Hag was found long ago by Atick and Witten and is F( T)∼ ΛT 2, where Λ diverges because of a tachyonic instability. We show that this result can be understood assuming that, above the Hagedorn transition, Poincaré symmetry is deformed into a quantum algebra. Physically this quantum algebra describes a non-commutative spatial geometry and a discrete Euclidean time. We then show that in string theory this deformed Poincaré symmetry indeed emerges above the Hagedorn temperature from the condensation of vortices on the world-sheet. This result indicates that the endpoint of the condensation of closed string tachyons with non-zero winding is an infinite stack of space-like branes with a given non-commutative world-volume geometry. On a more technical side, we also point out that T-duality along a circle with antiperiodic boundary conditions for space–time fermions is broken by world-sheet vortices, and the would-be T-dual variable becomes non-compact.

T-duality and actions for noncommutative D-branes

We show how the T-duality is realized for D-branes with noncommutative world-volume coordinates. We discuss D-branes wrapped on tori and the result is that the recently found noncommutative actions form a consistent collection due to the T-duality mapping between noncommutative D-branes and rotated commutative D-branes on deformed tori.

CURVED D-BRANE GEOMETRY AND ZERO MODES

We present a path integral formalism to review the effective dynamics of an arbitrary and curved Dirichlet p-brane (Dp-brane) in open bosonic string and subsequently in type I superstring theory. We obtain the perturbative corrections to the Dirac–Born–Infeld dynamics up to [Formula: see text] in the presence of an antisymmetric two-form B field. A part of the corrections can be seen to be associated with an ultraviolet divergence. Renormalization of the Dp-brane collective coordinates is performed to show that the residual corrections lead to a noncommutative description on the world volume. The Dp-brane modes are analyzed and we show that its zero modes play a vital role in noncommutative geometry. Our analysis facilitates the noncommutative world volume description for an arbitrary B field.

Chern-Simons terms on noncommutative branes

We write down couplings of the fields on a single BPS Dp-brane with noncommutative world-volume coordinates to the RR-forms in type II theories, in a manifestly background independent way. This generalises the usual Chern-Simons action for a commutative Dp-brane. We show that the noncommutative Chern-Simons terms can be mapped to Myers terms on a collection of infinitely many D-instantons. We also propose Chern-Simons couplings for unstable non-BPS branes, and show that condensation of noncommutative tachyons on these branes leads to the correct Myers terms on the decay products.

Non-commutative vs. commutative descriptions of D-brane BIons

The U(1) gauge theory on a D3-brane with non-commutative worldvolume is shown to admit BIon-like solutions which saturate a BPS bound on the energy. The mapping of these solutions to ordinary fields is found exactly, namely non-perturbatively in the non-commutativity parameters. The result is precisely an ordinary supersymmetric BIon in the presence of a background B -field. We argue that the result provides evidence in favour of the exact equivalence of the non-commutative and the ordinary descriptions of D-branes.

Non-commutative worldvolume geometries: D-branes on SU(2) and fuzzy spheres

The geometry of D-branes can be probed by open string scattering. If the background carries a non-vanishing B-field, the world-volume becomes non-commutative. Here we explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB. Using exact and generally applicable methods from boundary conformal field theory, we study the example of open strings in the SU(2) Wess-Zumino-Witten model, and establish a relation with fuzzy spheres or certain (non-associative) deformations thereof. These findings could be of direct relevance for D-branes in the presence of Neveu-Schwarz 5-branes; more importantly, they provide insight into a completely new class of world-volume geometries.