On M-theory fourfold vacua with higher curvature terms

We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kahler manifold with vanishing first Chern class. The metric solution, however, is non-Ricci-flat even when allowing for a conformal rescaling including the warp factor. This deviation is due to the possible non-harmonicity of the third Chern-form in the leading order Ricci-flat metric. We present a systematic derivation of the background solution by solving the Killing spinor conditions including higher curvature terms. These are translated into first-order differential equations for a globally defined real two-form and complex four-form on the fourfold. We comment on the supersymmetry properties of the described solutions.Comment: 14 page

The effective action of warped M-theory reductions with higher-derivative terms - Part II

We study the three-dimensional effective action obtained by reducing eleven-dimensional supergravity with higher-derivative terms on a background solution including a warp-factor, an eight-dimensional compact manifold, and fluxes. The dynamical fields are K\"ahler deformations and vectors from the M-theory three-form. We show that the potential is only induced by fluxes and the naive contributions obtained from higher-curvature terms on a Calabi-Yau background vanish once the back-reaction to the full solution is taken into account. For the resulting three-dimensional action we analyse the K\"ahler potential and complex coordinates and show compatibility with N=2 supersymmetry. We argue that the higher-order result is also compatible with a no-scale condition. We find that the complex coordinates should be formulated as divisor integrals for which a non-trivial interplay between the warp-factor terms and the higher-curvature terms allow a derivation of the moduli space metric. This leads us to discuss higher-derivative corrections to the M5-brane action.Comment: 26 page

On geometric corrections to effective actions of string theory

In this thesis we study geometric corrections to the low-energy effective actions of string theory. More concretely, we compute higher-derivative corrections to the couplings of three-dimensional, N = 2 supergravity theories and interpret the induced α′-corrections in N = 1, minimal supergravity theories in four dimensions, in the framework of F-theory. These allow for chiral spectra and are therefore phenomenological relevant. We analyzed higher-derivative corrections to M-theory, accessible through its low-energy effective theory, given by eleven-dimensional supergravity. The next to leading order terms to eleven-dimensional supergravity carry eight-derivatives, and are suppressed by lM6 compared to the classical terms, with lM being the eleven-dimensional Planck-Length - the only scale in eleven dimensions. These corrections are lifted from IIA supergravity corrections, which are derived from string scattering amplitudes. The common theme of this thesis is to compactify the bosonic sector of the eleven-dimensional supergravity action, including all known eight-derivative corrections, on a supersymmetric background to find a 3d, N = 2 theory, which then can be lifted to a 4d, N = 1 theory. This goal is approached in several steps. In the classical reduction of eleven-dimensional supergravity the metric background is a direct product of the external space, consisting of two space and one time dimension and the internal eight spacelike-dimensional Calabi-Yau manifold. However, when considering higher-derivative corrections the background has to be altered by introducing a dependence of the external space on the warp- factor, which is a function of the internal space. We find an explicit warped background solution to the eleven-dimensional E.O.M.’s including non-vanishing flux. To check the background for its supersymmetry features one would need to consider the eleven-dimensional gravitino variations at this order in lM . However, these are not known, which leads us to propose higher-order lM -corrected gravitino variations consistent with our background solution. As a next step we dimensionally reduce the bosonic sector of the eleven-dimensional supergravity action including all eight-derivative terms on this warped background and analyze the resulting three- dimensional theory. In this context the interplay of the warp-factor and the higher-derivative terms is of crucial importance. To identify the N = 2 properties of the resulting three-dimensional theory obtained by dimensional reduction, we compare it to the canonical from of three-dimensional N = 2 supergravtiy. We conclude that the reduced action is compatible with N = 2 supersymmetry and give a proposal for the K ̈ahler potential and the complex coordinates, which receive lM6 corrections. Besides a warp-factor contribution, the K ̈ahler potential receives a correction proportional to the third Chern- 2 form of the zeroth order internal background, being the Calabi-Yau fourfold. The complex coordinates are defined as divisor-integrals and are corrected by a warp-factor dependent term as well as one related to the non-harmonic part of the fourth Chern-form, of the zeroth order Calabi-Yau manifold. Thus the couplings of the resulting theory receive besides the warp-factor, in particular geometric corrections of order lM6 . In the first part of this thesis we study a simplified setup, only considering a subset of the relevant eight-derivative corrections in eleven dimensions. Furthermore, we do compactify on the classical background, consisting of the internal Calabi-Yau fourfold without warping and fluxes, to gain a three-dimensional theory. However, we use the M/F-theory duality to uplift the yielded corrections, which results in corrections to the couplings of the four-dimensional theory. In the weak coupling limit we find that these are sourced by the self-intersection curves of D7-branes

The influence of obesity on survival in early, high-risk breast cancer: results from the randomized SUCCESS A trial

Introduction: Obese breast cancer patients have worse prognosis than normal weight patients, but the level at which obesity is prognostically unfavorable is unclear. Methods: This retrospective analysis was performed using data from the SUCCESS A trial, in which 3754 patients with high-risk early breast cancer were randomized to anthracycline- and taxane-based chemotherapy with or without gemcitabine. Patients were classified as underweight/normal weight (body mass index (BMI) < 25.0), overweight (BMI 25.0–29.9), slightly obese (BMI 30.0–34.9), moderately obese (BMI 35.0–39.9) and severely obese (BMI ≥ 40.0), and the effect of BMI on disease-free survival (DFS) and overall survival (OS) was evaluated (median follow-up 65 months). In addition, subgroup analyses were conducted to assess the effect of BMI in luminal A-like, luminal B-like, HER2 (human epidermal growth factor 2)-positive and triple-negative tumors. Results: Multivariate analyses revealed an independent prognostic effect of BMI on DFS (p = 0.001) and OS (p = 0.005). Compared with underweight/normal weight patients, severely obese patients had worse DFS (hazard ratio (HR) 2.70, 95 % confidence interval (CI) 1.71–4.28, p < 0.001) and OS (HR 2.79, 95 % CI 1.63–4.77, p < 0.001), while moderately obese, slightly obese and overweight patients did not differ from underweight/normal weight patients with regard to DFS or OS. Subgroup analyses showed a similar significant effect of BMI on DFS and OS in patients with triple-negative breast cancer (TNBC), but not in patients with other tumor subtypes. Conclusions: Severe obesity (BMI ≥ 40) significantly worsens prognosis in early breast cancer patients, particularly for triple-negative tumors. Trial registration: Clinicaltrials.gov NCT02181101. Registered September 200

The influence of obesity on survival in early, high-risk breast cancer: results from the randomized SUCCESS A trial

Introduction Obese breast cancer patients have worse prognosis than normal weight patients, but the level at which obesity is prognostically unfavorable is unclear. Methods This retrospective analysis was performed using data from the SUCCESS A trial, in which 3754 patients with high-risk early breast cancer were randomized to anthracycline- and taxane-based chemotherapy with or without gemcitabine. Patients were classified as underweight/normal weight (body mass index (BMI) < 25.0), overweight (BMI 25.0–29.9), slightly obese (BMI 30.0–34.9), moderately obese (BMI 35.0–39.9) and severely obese (BMI ≥ 40.0), and the effect of BMI on disease-free survival (DFS) and overall survival (OS) was evaluated (median follow-up 65 months). In addition, subgroup analyses were conducted to assess the effect of BMI in luminal A-like, luminal B-like, HER2 (human epidermal growth factor 2)-positive and triple-negative tumors. Results Multivariate analyses revealed an independent prognostic effect of BMI on DFS (p = 0.001) and OS (p = 0.005). Compared with underweight/normal weight patients, severely obese patients had worse DFS (hazard ratio (HR) 2.70, 95 % confidence interval (CI) 1.71–4.28, p < 0.001) and OS (HR 2.79, 95 % CI 1.63–4.77, p < 0.001), while moderately obese, slightly obese and overweight patients did not differ from underweight/normal weight patients with regard to DFS or OS. Subgroup analyses showed a similar significant effect of BMI on DFS and OS in patients with triple-negative breast cancer (TNBC), but not in patients with other tumor subtypes. Conclusions Severe obesity (BMI ≥ 40) significantly worsens prognosis in early breast cancer patients, particularly for triple-negative tumors. Trial registration Clinicaltrials.gov NCT02181101. Registered September 2005