Gauging the Wess-Zumino term of a sigma model with boundary

We investigate the gauging of the Wess-Zumino term of a sigma model with boundary. We derive a set of obstructions to gauging and we interpret them as the conditions for the Wess-Zumino term to extend to a closed form in a suitable equivariant relative de Rham complex. We illustrate this with the two-dimensional sigma model and we show that the new obstructions due to the boundary can be interpreted in terms of Courant algebroids. We specialise to the case of the Wess-Zumino-Witten model, where it is proved that there always exist suitable boundary conditions which allow gauging any subgroup which can be gauged in the absence of a boundary. We illustrate this with two natural classes of gaugings: (twisted) diagonal subgroups with boundary conditions given by (twisted) conjugacy classes, and chiral isotropic subgroups with boundary conditions given by cosets.Comment: 18 pages (minor changes in response to referee report

Penrose limits of Lie Branes and a Nappi--Witten braneworld

Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy classes. We determine the (twisted and untwisted) symmetric D-branes in the plane wave background and we prove the existence of a space-filling D5-brane and, separately, of a foliation by D3-branes with the geometry of the Nappi--Witten spacetime which can be understood as the Penrose limit of the AdS_2 x S^2 D3-brane in AdS_3 x S^3. Parenthetically we also derive a simple criterion for a symmetric plane wave to be isometric to a lorentzian Lie group. In particular we observe that the maximally supersymmetric plane wave in IIB string theory is isometric to a lorentzian Lie group, whereas the one in M-theory is not.Comment: 21 pages (v2: references added

A Gravitational Wave Background from Reheating after Hybrid Inflation

The reheating of the universe after hybrid inflation proceeds through the nucleation and subsequent collision of large concentrations of energy density in the form of bubble-like structures moving at relativistic speeds. This generates a significant fraction of energy in the form of a stochastic background of gravitational waves, whose time evolution is determined by the successive stages of reheating: First, tachyonic preheating makes the amplitude of gravity waves grow exponentially fast. Second, bubble collisions add a new burst of gravitational radiation. Third, turbulent motions finally sets the end of gravitational waves production. From then on, these waves propagate unimpeded to us. We find that the fraction of energy density today in these primordial gravitational waves could be significant for GUT-scale models of inflation, although well beyond the frequency range sensitivity of gravitational wave observatories like LIGO, LISA or BBO. However, low-scale models could still produce a detectable signal at frequencies accessible to BBO or DECIGO. For comparison, we have also computed the analogous gravitational wave background from some chaotic inflation models and obtained results similar to those found by other groups. The discovery of such a background would open a new observational window into the very early universe, where the details of the process of reheating, i.e. the Big Bang, could be explored. Moreover, it could also serve in the future as a new experimental tool for testing the Inflationary Paradigm.Comment: 22 pages, 18 figures, uses revtex

Global Aspects of T-Duality, Gauged Sigma Models and T-Folds

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.Comment: Minor corrections and addition

Supersymmetric exact sequence, heat kernel and super KdV hierarchy

We introduce the free N=1 supersymmetric derivation ring and prove the existence of an exact sequence of supersymmetric rings and linear transformations. We apply necessary and sufficient conditions arising from this exact supersymmetric sequence to obtain the essential relations between conserved quantities, gradients and the N=1 super KdV hierarchy. We combine this algebraic approach with an analytic analysis of the super heat operator.We obtain the explicit expression for the Green's function of the super heat operator in terms of a series expansion and discuss its properties. The expansion is convergent under the assumption of bounded bosonic and fermionic potentials. We show that the asymptotic expansion when $t\to0^+$ of the Green's function for the super heat operator evaluated over its diagonal generates all the members of the N=1 super KdV hierarchy.Comment: 20 pages, to be published in JM

Strain in epitaxial MnSi films on Si(111) in the thick film limit studied by polarization-dependent extended x-ray absorption fine structure

We report a study of the strain state of epitaxial MnSi films on Si(111) substrates in the thick film limit (100-500~\AA) as a function of film thickness using polarization-dependent extended x-ray absorption fine structure (EXAFS). All films investigated are phase-pure and of high quality with a sharp interface between MnSi and Si. The investigated MnSi films are in a thickness regime where the magnetic transition temperature $T_\mathrm{c}$ assumes a thickness-independent enhanced value of $\geq$43~K as compared with that of bulk MnSi, where $T_\mathrm{c} \approx 29~{\rm K}$. A detailed refinement of the EXAFS data reveals that the Mn positions are unchanged, whereas the Si positions vary along the out-of-plane [111]-direction, alternating in orientation from unit cell to unit cell. Thus, for thick MnSi films, the unit cell volume is essentially that of bulk MnSi --- except in the vicinity of the interface with the Si substrate (thin film limit). In view of the enhanced magnetic transition temperature we conclude that the mere presence of the interface, and its specific characteristics, strongly affects the magnetic properties of the entire MnSi film, even far from the interface. Our analysis provides invaluable information about the local strain at the MnSi/Si(111) interface. The presented methodology of polarization dependent EXAFS can also be employed to investigate the local structure of other interesting interfaces.Comment: 11 pages, 10 figure

The return of the four- and five-dimensional preons

We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged supergravities by explicitly constructing them as smooth quotients of the AdS_4 and AdS_5 maximally supersymmetric backgrounds, respectively. This result illustrates how the spacetime topology resurrects a fraction of supersymmetry previously ruled out by the local analysis of the Killing spinor equations.Comment: 10 pages (a minor imprecision has been corrected

On the maximal superalgebras of supersymmetric backgrounds

In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund-Rubin backgrounds, and propose a geometric construction extending the well-known construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric Freund-Rubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS_4 x S^7 and find that is isomorphic to osp(1|32). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS_4 x S^7 and we test this proposal by computing the maximal superalgebra of the M2-brane in its two maximally supersymmetric limits, finding agreement.Comment: 17 page