Macroscopoic Three-Loop Amplitudes and the Fusion Rules from the Two-Matrix Model

From the computation of three-point singlet correlators in the two-matrix model, we obtain an explicit expression for the macroscopic three-loop amplitudes having boundary lengths $\ell_{i}$ $(i = 1\sim 3)$ in the case of the unitary series $(p,q)= (m+1,m)$ coupled to two-dimensional gravity. The sum appearing in this expression is found to conform to the structure of the CFT fusion rules while the summand factorizes through a product of three modified Bessel functions. We briefly discuss a possible generalization of these features to macroscopic $n$-loop amplitudes.Comment: 9 pages, no figure, late

An integration of Euler's pentagonal partition

A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the coefficients result from a discrete integration of Euler's coefficients. Both a bijective proof and one based on generating functions show the equivalence of the subject recurrences.Comment: 22 pages, 2 figures. The recurrence investigated in this paper is essentially that proposed in Exercise 5.2.3 of Igor Pak's "Partition bijections, a survey", Ramanujan J. 12 (2006), but casted in a different form and, perhaps more interestingly, endowed with a bijective proof which arises from a construction by induction on maximal part

Eliminating ambiguities for quantum corrections to strings moving in AdS4×CP3AdS_4\times \mathbb{CP}^3

We apply a physical principle, previously used to eliminate ambiguities in quantum corrections to the 2 dimensional kink, to the case of spinning strings moving in $AdS_4\times \mathbb{CP}^3$, thought of as another kind of two dimensional soliton. We find that this eliminates the ambiguities and selects the result compatible with AdS/CFT, providing a solid foundation for one of the previous calculations, which found agreement. The method can be applied to other classical string "solitons".Comment: 18 pages, latex; references added, comments added at end of section 4, a few words changed; footnote added on page 1

The D^{2k} R^4 Invariants of N=8 Supergravity

The existence of a linearized SUSY invariant for N=8 supergravity whose gravitational components are usually called R^4 was established long ago by on-shell superspace arguments. Superspace and string theory methods have also established analogous higher dimensional D^{2k} R^4 invariants. However, very little is known about the SUSY completions of these operators which involve other fields of the theory. In this paper we find the detailed component expansion of the linearized R^4 invariant starting from the corresponding superamplitude which generates all component matrix elements of the operator. It is then quite straightforward to extend results to the entire set of D^{2k} R^4 operators.Comment: 17 page

The mechanics of a chain or ring of spherical magnets

Strong magnets, such as neodymium-iron-boron magnets, are increasingly being manufactured as spheres. Because of their dipolar characters, these spheres can easily be arranged into long chains that exhibit mechanical properties reminiscent of elastic strings or rods. While simple formulations exist for the energy of a deformed elastic rod, it is not clear whether or not they are also appropriate for a chain of spherical magnets. In this paper, we use discrete-to-continuum asymptotic analysis to derive a continuum model for the energy of a deformed chain of magnets based on the magnetostatic interactions between individual spheres. We find that the mechanical properties of a chain of magnets differ significantly from those of an elastic rod: while both magnetic chains and elastic rods support bending by change of local curvature, nonlocal interaction terms also appear in the energy formulation for a magnetic chain. This continuum model for the energy of a chain of magnets is used to analyse small deformations of a circular ring of magnets and hence obtain theoretical predictions for the vibrational modes of a circular ring of magnets. Surprisingly, despite the contribution of nonlocal energy terms, we find that the vibrations of a circular ring of magnets are governed by the same equation that governs the vibrations of a circular elastic ring

CP violation in sbottom decays

We study CP asymmetries in two-body decays of bottom squarks into charginos and tops. These asymmetries probe the SUSY CP phases of the sbottom and the chargino sector in the Minimal Supersymmetric Standard Model. We identify the MSSM parameter space where the CP asymmetries are sizeable, and analyze the feasibility of their observation at the LHC. As a result, potentially detectable CP asymmetries in sbottom decays are found, which motivates further detailed experimental studies for probing the SUSY CP phases.Comment: 29 pages, 7 figure