Derived Brackets from Super-Poisson Brackets

The relation between Poisson brackets in supersymmetric one or two-dimensional sigma-models and derived brackets is summarized.Comment: 2 pages, to appear in the proceedings (Nuclear Physics B -- Proceedings Supplements) of the Cargese summer school 2006 on strings and brane

A Projection to the Pure Spinor Space

This article is based on a talk given at the Memorial Conference for Maximilian Kreuzer at the ESI in Vienna and contains a compact summary of a recent collaboration with P.A. Grassi. A non-linear projection from the space of SO(10) Weyl spinors to the space of pure spinors is presented together with some of its particular properties. This projection can be used to remove the constraints from Berkovits' pure spinor superstring while introducing additional gauge symmetries. This should allow to make transitions to equivalent formulations which might shed light on the origin of the pure spinor ghosts. It might also be useful in the context of path integral measures for the pure spinor string.Comment: 9 page

Superstrings in General Backgrounds

The thesis divides into three parts. The first is devoted to a careful study of very convenient superspace conventions which are a basic tool for the second part. A theorem is formulated that gives a clear statement about when the signs of a superspace calculation can be omitted. The second part describes the type II superstring using Berkovits' pure spinor formalism. The derivation of the supergravity constraints from classical BRST invariance of Berkovits and Howe is carefully reviewed and new aspects are added. The present derivation uses a covariant variation principle and stays throughout in the Lagrangian formalism. A new result is the explicit form of the BRST transformation of the worldsheet fields for type II. By further deriving the form of the local supersymmetry transformations of the fermionic fields, a connection is established to the starting point of those supergravity calculations, which derive generalized Calabi Yau conditions from effective four-dimensional supersymmetry. Generalized complex geometry is in turn the motivation for the last part, which is based on the author's paper on derived brackets from sigma models and the relation to integrability of generalized complex structures. Finally there are detailed appendices on geometric brackets, generalized complex geometry, Noether's theorem, Bianchi identities, supergauge transformations and the WZ gauge, gamma-matrices and on some aspects of structure group connections.Comment: PhD-thesis, TU-Vienna 2007, 246 pages. Contains hyperlinks and thesis-index (This time really! Last time it got lost during upload). Corrections in section 5.9 and 5.10 and additional appendix section E.4. Equation and section numbers remained the same. Possible future corrections will be only added as errat

Sharing the fiscal burden of the crisis: A Pandemic Solidarity Instrument for the EU. Bertelsmann Stiftung Policy Paper April 2020.

The debate over how Europe should cope with the fiscal costs of the COVID-19 pan- demic is in full swing. Adversaries and opponents of “Coronabonds” seem suddenly back in the trenches of the euro crisis. Our proposal attempts to build a bridge bet- ween the two camps: We do not propose a full-on Eurobond or any mutualisation of existing debt, as this is not how we should overcome the unique challenges of this crisis. Instead, we propose a Pandemic Solidarity Instrument that is tailored speci- fically to this crisis. The EU does not need another layer of market-access insurance, as the European Central Bank and the European Stability Mechanism are already in place for this. What it needs is an instrument to share the costs of the crisis. The main problem the EU faces now is that some member states have entered this crisis in a much weaker economic position and with higher debt levels than others. At the same time, all countries have a vital interest in all other countries being able to spend as much as necessary to fight the economic fallout of the pandemic. To ensure that this happens, we need a burden sharing of the fiscal costs of this crisis. The Pandemic Solidarity Instrument delivers this burden sharing. It should be set up as an EU instrument: The EU would borrow 440 billion euros in the market, ba- cked by the EU budget and by guarantees of the member states. As this would be EU debt, it would not count as debt of individual member states. The bonds issued by the EU would have long maturities and could be refinanced in the market at the end of their terms; otherwise, they would be repaid once they come due according to the future state of economic strength of member states. The funds would be used for four purposes: • Grants to member states to partially cover health-related costs; • Guarantees to the European Investment Bank to provide liquidity to European companies; • Subsidies to member states so that they can fund short-time work schemes and short-term unemployment benefits; • Co-financing of national stimulus packages once confinement measures have been lifted. The Instrument would be based on Article 122 of the Treaty on the Functioning of the European Union. This article gives the EU wide discretion to act in emergency situations. In our legal analysis, we show how this article allows the EU to bor- row in this specific context and why our proposal does not conflict with the EU’s no-bailout clause

Sharing the fiscal burden of the crisis - A Pandemic Solidarity Instrument for the EU

EU member states must share the burden of the fiscal costs of the COVID-19 pandemic. The Pandemic Solidarity Instrument delivers such burden sharing: The EU would borrow 440 billion euros in the market and would give it as grants to member states for specific spending in areas such as health care, short-time works schemes or stimulus packages; it would also give guarantees to the European Investment Bank to provide liquidity to European companies

Brackets, Sigma Models and Integrability of Generalized Complex Structures

It is shown how derived brackets naturally arise in sigma-models via Poisson- or antibracket, generalizing a recent observation by Alekseev and Strobl. On the way to a precise formulation of this relation, an explicit coordinate expression for the derived bracket is obtained. The generalized Nijenhuis tensor of generalized complex geometry is shown to coincide up to a de-Rham closed term with the derived bracket of the structure with itself, and a new coordinate expression for this tensor is presented. The insight is applied to two known two-dimensional sigma models in a background with generalized complex structure. Introductions to geometric brackets on the one hand and to generalized complex geometry on the other hand are given in the appendix.Comment: 48 pages (27 without appendix), created with LyX, based on LaTeX, including hyperrefs. Typos in (2.162)-(2.167) and in (3.15) fixed. Content agrees with JHEP-Version. Page numbers and equation numbers agree with old version but not with JHEP version

Schwinger–Fronsdal Theory of Abelian Tensor Gauge Fields

This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor gauge fields. The theory describes the propagation of free massless gauge bosons of integer helicities and their interaction with external currents. Self-consistency of its equations requires only the traceless part of the current divergence to vanish. The essence of the theory is given by the fact that this weaker current conservation is enough to guarantee the unitarity of the theory. Physically this means that only waves with transverse polarizations are propagating very far from the sources. The question whether such currents exist should be answered by a fully interacting theory. We also suggest an equivalent representation of the corresponding action