Consistent 4-form fluxes for maximal supergravity

We derive new ansaetze for the 4-form field strength of D=11 supergravity corresponding to uplifts of four-dimensional maximal gauged supergravity. In particular, the ansaetze directly yield the components of the 4-form field strength in terms of the scalars and vectors of the four-dimensional maximal gauged supergravity---in this way they provide an explicit uplift of all four-dimensional consistent truncations of D=11 supergravity. The new ansaetze provide a substantially simpler method for uplifting d=4 flows compared to the previously available method using the 3-form and 6-form potential ansaetze. The ansatz for the Freund-Rubin term allows us to conjecture a `master formula' for the latter in terms of the scalar potential of d=4 gauged supergravity and its first derivative. We also resolve a long-standing puzzle concerning the antisymmetry of the flux obtained from uplift ansaetze.Comment: 20 pages + appendices; typos corrected; published versio

Filtrations in Dyson-Schwinger equations: next-to^{j} -leading log expansions systematically

Dyson-Schwinger equations determine the Green functions $G^r(\alpha,L)$ in quantum field theory. Their solutions are triangular series in a coupling constant $\alpha$ and an external scale parameter $L$ for a chosen amplitude $r$, with the order in $L$ bounded by the order in the coupling. Perturbation theory calculates the first few orders in $\alpha$. On the other hand, Dyson--Schwinger equations determine next-to$^{\{\mathrm{j}\}}$-leading log expansions, $G^r(\alpha,L) = 1 + \sum_{j=0}^\infty \sum_{\mathcal{M}} p_j^{\mathcal{M}}\alpha^j \mathcal{M}(u)$. $\sum_{\mathcal{M}}$ sums a finite number of functions $\mathcal{M}$ in $u = \alpha L/2$. The leading logs come from the trivial representation \mathcal{M}(u) = \begin{bsmallmatrix}\bullet\end{bsmallmatrix}(u) at $j=0$ with p_0^{\begin{bsmallmatrix}\bullet\end{bsmallmatrix}} = 1. All non-leading logs are organized by the suppression in powers $\alpha^j$. We describe an algebraic method to derive all next-to$^{\{\mathrm{j}\}}$-leading log terms from the knowledge of the first $(j+1)$ terms in perturbation theory and their filtrations. This implies the calculation of the functions $\mathcal{M}(u)$ and periods $p_j^\mathcal{M}$. In the first part of our paper, we investigate the structure of Dyson-Schwinger equations and develop a method to filter their solutions. Applying renormalized Feynman rules maps each filtered term to a certain power of $\alpha$ and $L$ in the log-expansion. Based on this, the second part derives the next-to$^{\{\mathrm{j}\}}$-leading log expansions. Our method is general. Here, we exemplify it using the examples of the propagator in Yukawa theory and the photon self-energy in quantum electrodynamics. The reader may apply our method to any (set of) Dyson-Schwinger equation(s) appearing in renormalizable quantum field theories.Comment: $2 pages, 1 Figure (typos corrected

An SO(3)×\timesSO(3) invariant solution of D=11D=11 supergravity

We construct a new SO(3)$\times$SO(3) invariant non-supersymmetric solution of the bosonic field equations of $D=11$ supergravity from the corresponding stationary point of maximal gauged $N=8$ supergravity by making use of the non-linear uplift formulae for the metric and the 3-form potential. The latter are crucial as this solution appears to be inaccessible to traditional techniques of solving Einstein's field equations, and is arguably the most complicated closed form solution of this type ever found. The solution is also a promising candidate for a stable non-supersymmetric solution of M-theory uplifted from gauged supergravity. The technique that we present here may be applied more generally to uplift other solutions of gauged supergravity.Comment: 33 pages + appendices, JHEP versio

Impact investments: a call for (re)orientation

Practitioners and academics have been using different terms to describe investments in the sustainability context. The latest inflationary term is impact investments—investments that focus on real-world changes in terms of solving social challenges and/or mitigating ecological degradation. At the core of this definition is an emphasis on transformational changes. However, the term impact investment is often used interchangeably for any investment that incorporates environmental, social, and governance (ESG) aspects. In the latter instance, achieving transformational change is not the main purpose of such investments, which therefore carries the risk of impact washing (akin to “green washing”). To offer (re-)orientation from an academic perspective, we derive a new typology of sustainable investments. This typology delivers a precise definition of what impact investments are and what they should cover. As one central contribution, we propose distinguishing between impact-aligned investments and impact-generating investments. Based on these insights, we hope to lay the foundation for future research and debates in the field of impact investing by practitioners, policymakers, and academics alike

Mesh structure-independent modeling of patient-specific atrial fiber orientation

The fiber orientation in the atria has a significant contribution to the electrophysiologic behavior of the heart and to the genesis of arrhythmia. Atrial fiber orientation has a direct effect on excitation propagation, activation patterns and the P-wave. We present a rule-based algorithm that works robustly on different volumetric meshes composed of either isotropic hexahedra or arbitrary tetrahedra as well as on 3-dimensional triangular surface meshes in patient-specific geometric models. This method fosters the understanding of general proarrhythmic mechanisms and enhances patient-specific modeling approaches

Left and Right Atrial Contribution to the P-wave in Realistic Computational Models

ECG markers derived from the P-wave are used frequently to assess atrial function and anatomy, e.g. left atrial enlargement. While having the advantage of being routinely acquired, the processes underlying the genesis of the P-wave are not understood in their entirety. Particularly the distinct contributions of the two atria have not been analyzed mechanistically. We used an in silico approach to simulate P-waves originating from the left atrium (LA) and the right atrium (RA) separately in two realistic models. LA contribution to the P-wave integral was limited to 30% or less. Around 20% could be attributed to the first third of the P-wave which reflected almost only RA depolarization. Both atria contributed to the second and last third with RA contribution being about twice as large as LA contribution. Our results foster the comprehension of the difficulties related to ECG-based LA assessment