Einstein Supergravity and New Twistor String Theories

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. The theories include one with the spectrum of N=8 supergravity, another with the spectrum of N=4 supergravity coupled to N=4 super-Yang-Mills, and a family with $N\ge 0$ supersymmetries with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills. The non-supersymmetric string with N=0 gives self-dual gravity coupled to self-dual Yang-Mills and a scalar. A three-graviton amplitude is calculated for the N=8 and N=4 theories and shown to give a result consistent with the cubic interaction of Einstein supergravity.Comment: LaTeX, 69 pages, no figures; v2: minor corrections made, footnotes and references adde

Space-Time Supersymmetry, IIA/B Duality and M-Theory

The connection between IIA superstring theory compactified on a circle of radius R and IIB theory compactified on a circle of radius 1/R is reexamined from the perspective of N=2, D=9 space-time supersymmetry. We argue that the consistency of IIA/B duality requires the BPS states corresponding to momentum and winding of either of the type-II superstrings to transform as inequivalent supermultiplets. We show that this is indeed the case for any finite compactification radius, thus providing a nontrivial confirmation of IIA/B duality. From the point of view of N=2, D=9 supergravity, one is naturally led to an SL(2,Z) invariant field theory that encompasses both the M-theory torus and the Kaluza-Klein states of the IIB theory.Comment: LaTeX, 14 pages; v2:one reference added and extended discussion of the BPS mass formula; v3: minor changes, to appear in PL

Sigma models with non-commuting complex structures and extended supersymmetry

We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.Comment: 11 pages. Talk presented by U.L. at "30th Winter School on Geometry and Physics" Srni, Czech Republic January 2010

The Gauged (2,1) Heterotic Sigma-Model

The geometry of (2,1) supersymmetric sigma-models with isometry symmetries is discussed. The gauging of such symmetries in superspace is then studied. We find that the coupling to the (2,1) Yang-Mills supermultiplet can be achieved provided certain geometric conditions are satisfied. We construct the general gauged action, using an auxiliary vector to generate the full non-polynomial structure.Comment: LaTeX, 25 pages, no figures; version to appear in Nuclear Physics

A Chiral Perturbation Expansion for Gravity

A formulation of Einstein gravity, analogous to that for gauge theory arising from the Chalmers-Siegel action, leads to a perturbation theory about an asymmetric weak coupling limit that treats positive and negative helicities differently. We find power counting rules for amplitudes that suggest the theory could find a natural interpretation in terms of a twistor-string theory for gravity with amplitudes supported on holomorphic curves in twistor space.Comment: 11 pages, LaTeX, no figures; v2: one reference adde

Comments on the Energy-Momentum Tensor in Non-Commutative Field Theories

In a non-commutative field theory, the energy-momentum tensor obtained from the Noether method needs not be symmetric; in a massless theory, it needs not be traceless either. In a non-commutative scalar field theory, the method yields a locally conserved yet non-symmetric energy-momentum tensor whose trace does not vanish for massless fields. A non-symmetric tensor also governs the response of the action to a general coordinate transformation. In non-commutative gauge theory, if translations are suitably combined with gauge transformations, the method yields a covariantly constant tensor which is symmetric but only gauge covariant. Using suitable Wilson functionals, this can be improved to yield a locally conserved and gauge invariant, albeit non-symmetric, energy-momentum tensor.Comment: LaTeX, 10 pages, no figures; v2: minor changes made, a summary added, version to appear in PL

Dynamics of Wilson Observables in Non-Commutative Gauge Theory

An equation for the quantum average of the gauge invariant Wilson loop in non-commutative Yang-Mills theory with gauge group U(N) is obtained. In the 't Hooft limit, the equation reduces to the loop equation of ordinary Yang-Mills theory. At finite $N$, the equation involves the quantum averages of the additional gauge invariant observables of the non-commutative theory associated with open contours in space-time. We also derive equations for correlators of several gauge invariant (open or closed) Wilson lines. Finally, we discuss a perturbative check of our results.Comment: 12 pages, typo in formula (32) correcte

Radiation from Accelerated Branes

The radiation emitted by accelerated fundamental strings and D-branes is studied within the linear approximation to the supergravity limit of string theory. We show that scalar, gauge field and gravitational radiation is generically emitted by such branes. In the case where an external scalar field accelerates the branes, we derive a Larmor-type formula for the emitted scalar radiation and study the angular distribution of the outgoing energy flux. The classical radii of the branes are calculated by means of the corresponding Thompson scattering cross sections. Within the linear approximation, the interaction of the external scalar field with the velocity fields of the branes gives a contribution to the observed gauge field and gravitational radiation.Comment: LaTeX, 25 pages, 2 figures; v2: added comments on the validity of the linear approximation, minor changes; version to appear in Physical Review