Dilogarithm Identities in Conformal Field Theory and Group Homology

Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all $2 \times 2$ real matrices viewed as a {\it discrete} group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic $K$-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all $2 \times 2$ real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with the summary of a number of open conjectures on the mathematical side.Comment: 20 pages, 2 figures not include

Superpotentials for M-theory on a G_2 holonomy manifold and Triality symmetry

For $M$-theory on the $G_2$ holonomy manifold given by the cone on {\bf S^3}\x {\bf S^3} we consider the superpotential generated by membrane instantons and study its transformations properties, especially under monodromy transformations and triality symmetry. We find that the latter symmetry is, essentially, even a symmetry of the superpotential. As in Seiberg/Witten theory, where a flat bundle given by the periods of an universal elliptic curve over the $u$-plane occurs, here a flat bundle related to the Heisenberg group appears and the relevant universal object over the moduli space is related to hyperbolic geometry.Comment: 58 pages, latex; references adde

An algebraic proof of Bogomolov-Tian-Todorov theorem

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L-infinity algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.Comment: 20 pages, amspro

Obstruction theory on 8-manifolds

This note gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. We give necessary and sufficient cohomological critera for the existence of almost complex and almost quaternionic structures on the tangent bundle and for the reduction of the structure group to U(3) by the homomorphism U(3) --> O(8) given by the Lie algebra representation of PU(3).Comment: 19 page

Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivariant de Rham cohomology in terms of derived functors developed earlier for the special case where the Lie groupoid is an ordinary Lie group, viewed as a Lie groupoid with a single object; in that theory over a Lie group, the ordinary Bott-Dupont-Shulman-Stasheff complex arises as an a posteriori object. We prove that, given a locally trivial Lie groupoid G and a smooth G-manifold f over the space B of objects of G, the resulting G-equivariant de Rham theory of f boils down to the ordinary equivariant de Rham theory of a vertex manifold relative to the corresponding vertex group, for any vertex in the space B of objects of G; this implies that the equivariant de Rham cohomology introduced here coincides with the stack de Rham cohomology of the associated transformation groupoid whence this stack de Rham cohomology can be characterized as a relative derived functor. We introduce a notion of cone on a Lie-Rinehart algebra and in particular that of cone on a Lie algebroid. This cone is an indispensable tool for the description of the requisite monads.Comment: 47 page

Curvature effects on the surface thickness and tension at the free interface of 4^4He systems

The thickness $W$ and the surface energy $\sigma_A$ at the free interface of superfluid $^4$He are studied. Results of calculations carried out by using density functionals for cylindrical and spherical systems are presented in a unified way, including a comparison with the behavior of planar slabs. It is found that for large species $W$ is independent of the geometry. The obtained values of $W$ are compared with prior theoretical results and experimental data. Experimental data favor results evaluated by adopting finite range approaches. The behavior of $\sigma_A$ and $W \sigma_A$ exhibit overshoots similar to that found previously for the central density, the trend of these observables towards their asymptotic values is examined.Comment: 35 pages, TeX, 5 figures, definitive versio

Time-of-flight and activation experiments on 147Pm and 171Tm for astrophysics

The neutron capture cross section of several key unstable isotopes acting as branching points in the s-process are crucial for stellar nucleosynthesis studies, but they are very challenging to measure due to the difficult production of sufficient sample material, the high activity of the resulting samples, and the actual (n,γ) measurement, for which high neutron fluxes and effective background rejection capabilities are required. As part of a new program to measure some of these important branching points, radioactive targets of 147Pm and 171Tm have been produced by irradiation of stable isotopes at the ILL high flux reactor. Neutron capture on 146Nd and 170Er at the reactor was followed by beta decay and the resulting matrix was purified via radiochemical separation at PSI. The radioactive targets have been used for time-of-flight measurements at the CERN n-TOF facility using the 19 and 185 m beam lines during 2014 and 2015. The capture cascades were detected using a set of four C6D6 scintillators, allowing to observe the associated neutron capture resonances. The results presented in this work are the first ever determination of the resonance capture cross section of 147Pm and 171Tm. Activation experiments on the same 147Pm and 171Tm targets with a high-intensity 30 keV quasi-Maxwellian flux of neutrons will be performed using the SARAF accelerator and the Liquid-Lithium Target (LiLiT) in order to extract the corresponding Maxwellian Average Cross Section (MACS). The status of these experiments and preliminary results will be presented and discussed as well

Characterization of the n-TOF EAR-2 neutron beam

The experimental area 2 (EAR-2) at CERNs neutron time-of-flight facility (n-TOF), which is operational since 2014, is designed and built as a short-distance complement to the experimental area 1 (EAR-1). The Parallel Plate Avalanche Counter (PPAC) monitor experiment was performed to characterize the beam prole and the shape of the neutron 'ux at EAR-2. The prompt γ-flash which is used for calibrating the time-of-flight at EAR-1 is not seen by PPAC at EAR-2, shedding light on the physical origin of this γ-flash