We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

https://iopscience.iop.org/article/10.1088/1126-6708/1999/09/032/pdf

String theory and noncommutative geometry

We describe two constructions of hyperkahler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinear σ-models, but can be described entirely geometrically. In this general setting, we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry, along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience.

/pdf/hyperkahler-metrics-and-supersymmetry-4al39d7k9z.pdf

Hyperkahler Metrics and Supersymmetry

https://pure.rug.nl/ws/files/3235480/1997NuclPhysBBergshoeff1.pdf

Super D-branes

Soft supersymmetry breaking in KKLT flux compactification

We review and elaborate on some aspects of Born-Infeld action and its supersymmetric generalizations in connection with string theory. Contents: BI action from string theory; some properties of bosonic D=4 BI action; N=1 and N=2 supersymmetric BI actions with manifest linear D=4 supersymmetry; four-derivative terms in N=4 supersymmetric BI action; BI actions with `deformed' supersymmetry from D-brane actions; non-abelian generalization of BI action; derivative corrections to BI action in open superstring theory.

Born-Infeld action, supersymmetry and string theory

The partial spontaneous breaking of rigid $N=2$ supersymmetry implies the existence of a massless $N=1$ Goldstone multiplet. In this paper we show that the spin-$(1/2,1)$ Maxwell multiplet can play this role. We construct its full nonlinear transformation law and find the invariant Goldstone action. The spin-$1$ piece of the action turns out to be of Born-Infeld-type, and the full superfield action is duality invariant. This leads us to conclude that the Goldstone multiplet can be associated with a D-brane solution of superstring theory for $p=3$. In addition, we find that $N=1$ chirality is preserved in the presence of the Goldstone-Maxwell multiplet. This allows us to couple it to $N=1$ chiral and gauge field multiplets. We find that arbitrary K\"ahler and superpotentials are consistent with partially broken $N=2$ supersymmetry.

New Goldstone multiplet for partially broken supersymmetry

This paper concludes the formulation of N=2 supergravity in harmonic superspace. The authors generalize the approach to include conformal supergravity. The superconformal group is then compensated by coupling to a Maxwell and various matter multiplets. All the previously known versions of N=2 Einstein supergravity are reproducible in this way. The authors give one example (with the non-linear multiplet as a compensator). Their main result is a new version of N=2 Einstein supergravity which involves an off-shell complex hypermultiplet with its infinitely many auxiliary fields. They believe this version to be fundamental.

$N=2$ Supergravity in Superspace: Different Versions and Matter Couplings

The most general unconstrained superfield action for self-interactingN=2 matter hypermultiplets in analyticN=2 superspace is argued to produce a most generalN=2 hyper-Kahler σ-model after eliminating an infinite set of auxiliary fields. This suggests a new possibility of classifying hyper-Kahler metrics according to theN=2 analytic superfield self-interactions and provides an effective tool to compute these metrics explicitly. As the simplest example the U(2)-invariant quartic self-coupling of a singleq-hypermultiplet is analyzed and is shown to yield the familiar Taub-NUT metric. To see the geometric pattern directly in terms ofN=2 superfields we introduce a new on-shell representation ofq-hypermultiplets inN=2 harmonic superspace similar to the τ-description ofN=2 gauge theories. For the U(2)-example this formulation is checked to coincide with that by Sierra and Townsend.

/pdf/hyper-kahler-metrics-and-harmonic-superspace-3fuo9pirwf.pdf

Hyper-Kähler metrics and harmonic superspace

Harmonic Superspace: Hyper-Kähler geometry in harmonic space

We propose a new formulation of the heterotic [ital D]=10 Green-Schwarz superstring whose world sheet is a superspace with two even and eight odd coordinates. The action is manifestly invariant under both target-space supersymmetry and a world-sheet reparametrization supergroup. It contains only a finite set of auxiliary fields. The key ingredients are the commuting spinor (twistor) variables, which naturally arise as world-sheet superpartners of the target-space Grassmann coordinates. These spinors parametrize the sphere [ital S][sup 8] regarded as a coset space of the [ital D]=10 Lorentz group. The sphere is associated with the lightlike vector of one of the string Virasoro cosntraints. The origin of the on-shell [ital D]=10 fermionic [kappa] symmetry of the standard Green-Schwartz formulation is explained. An essential and unusual feature is the appearance of the string tension only on shell as an integration constant.

A. Galperin

Papers

New Goldstone multiplet for partially broken supersymmetry

$N=2$ Supergravity in Superspace: Different Versions and Matter Couplings

Hyper-Kähler metrics and harmonic superspace

Harmonic Superspace: Hyper-Kähler geometry in harmonic space

Twistor formulation of the heterotic D=10 superstring with manifest (8,0) world-sheet supersymmetry.