Matching the (DR4)-R-6 interaction at two-loops

The coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is included.Comment: 40 pages, various typos and coefficients corrected in version

Modular properties of two-loop maximal supergravity and connections with string theory

The low-momentum expansion of the two-loop four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a circle and a two-torus is considered up to terms of order S^6R^4 (where S is a Mandelstam invariant and R is the linearized Weyl curvature). In the case of the toroidal compactification the coefficient of each term in the low energy expansion is generically a sum of a number of SL(2,Z)-invariant functions of the complex structure of the torus. Each such function satisfies a separate Poisson equation on moduli space with particular source terms that are bilinear in coefficients of lower order terms, consistent with qualitative arguments based on supersymmetry. Comparison is made with the low-energy expansion of type II string theories in ten and nine dimensions. Although the detailed behaviour of the string amplitude is not generally expected to be reproduced by supergravity perturbation theory to all orders, for the terms considered here we find agreement with direct results from string perturbation theory. These results point to a fascinating pattern of interrelated Poisson equations for the IIB coefficients at higher orders in the momentum expansion which may have a significance beyond the particular methods by which they were motivated.Comment: 79 pages, 4 figures. Latex format. v2: Small corrections made, version to appear in JHE

On Schwinger Pair Creation in Gravity and in Closed Superstring Theory

We investigate the Schwinger pair creation process in the context of gravitational models with the back reaction of the electric field included in the geometry. The background is also an exact solution of type II superstring theory, where the electric field arises by Kaluza-Klein reduction. We obtain a closed formula for the pair creation rate that incorporates the gravitational back reaction. At weak fields it has the same structure as the general Schwinger formula, albeit pairs are produced by a combination of Schwinger and Unruh effect, the latter due to the presence of a Rindler horizon. In four spacetime dimensions, the rate becomes constant at strong electric fields. For states with mass of Kaluza-Klein origin, the rate has a power-like dependence in the electric field, rather than the familiar (non-perturbative) exponential dependence. We also reproduce the same formula from the string partition function for winding string states. Finally, we comment on the generalization to excited string states.Comment: 21 page

Body image perception and body composition: assessment of perception inconsistency by a new index

BACKGROUND: A correct perception of the body image, as defined by comparison with actual anthropometric analyses, is crucial to ensure the best possible nutritional status of each individual. Bioimpedance analysis (BIA) represents a leading technique to assess body composition parameters and, in particular, the fat mass. This study examined the self-perception of body image at various levels of adiposity proposing a new index. METHODS: We investigated 487 young Italian adults (mean age of males: 21.9 ± 2.4 years; mean age of females: 21.0 ± 2.2 years). Each subject could choose, on the Contour Drawing Rating Scale, the silhouette that he/she considered most resembling his/her perceived body image as well as his/her ideal body image. On each subject, we performed anthropometric measurements and determined the values of Fat mass and  út with BIA. A new index, FAIFAT (Feel fat status minus Actual fat status Inconsistency), was developed to evaluate possible fat status perception inconsistencies by BIA. RESULTS: Based on ideal and feel body image comparison, women showed higher dissatisfaction than men and preferred slimmer silhouettes. FAIFAT values indicated that the fat status perception was correct in the majority of the examined individuals and only three subjects showed a serious misperception. CONCLUSIONS: Our findings suggest that FAIFAT is an appropriate index for assessing the perceived fat status from the body image when compared with data obtained by BIA. In a population, the use of this index will allow the correct identification of groups at risk for eating disorders

Structural properties and quasiparticule energies of cubic SrO, MgO and SrTiO3

The structural properties and the band structures of the charge-transfer insulating oxides SrO, MgO and SrTiO3 are computed both within density functional theory in the local density approximation (LDA) and in the Hedin's GW scheme for self-energy corrections, by using a model dielectric function, which approximately includes local field and dynamical effects. The deep valence states are shifted by the GW method to higher binding energies, in very good agreement with photoemission spectra. Since in all of these oxides the direct gaps at high-symmetry points of the Brillouin zone may be very sensitive to the actual value of the lattice parameter a, already at the LDA level, self-energy corrections are computed both at the theoretical and the experimental a. For MgO and SrO, the values of the transition energies between the valence and the conduction bands are improved by GW corrections, while for SrTiO3 they are overestimated. The results are discussed in relation to the importance of local field effects and to the nature of the electronic states in these insulating oxides.Comment: 3 figures, accepted in J. Phys.: Condens. Matte

Eisenstein series for higher-rank groups and string theory amplitudes

Scattering amplitudes of superstring theory are strongly constrained by the requirement that they be invariant under dualities generated by discrete subgroups, E_n(Z), of simply-laced Lie groups in the E_n series (n<= 8). In particular, expanding the four-supergraviton amplitude at low energy gives a series of higher derivative corrections to Einstein's theory, with coefficients that are automorphic functions with a rich dependence on the moduli. Boundary conditions supplied by string and supergravity perturbation theory, together with a chain of relations between successive groups in the E_n series, constrain the constant terms of these coefficients in three distinct parabolic subgroups. Using this information we are able to determine the expressions for the first two higher derivative interactions (which are BPS-protected) in terms of specific Eisenstein series. Further, we determine key features of the coefficient of the third term in the low energy expansion of the four-supergraviton amplitude (which is also BPS-protected) in the E_8 case. This is an automorphic function that satisfies an inhomogeneous Laplace equation and has constant terms in certain parabolic subgroups that contain information about all the preceding terms.Comment: Latex. 38 pages. 1 figure. v2: minor changes and clarifications. v3: minor corrections, version to appear in Communications in Number Theory and Physics. v4: corrections to table