Muon g-2 through a flavor structure on soft SUSY terms

In this work we analyze the possibility to explain the muon anomalous magnetic moment discrepancy within theory and experiment through lepton flavor violation processes. We propose a flavor extended MSSM by considering a hierarchical family structure for the trilinear scalar Soft-Supersymmetric terms of the Lagranagian, present at the SUSY breaking scale. We obtain analytical results for the rotation mass matrix, with the consequence of having non-universal slepton masses and the possibility of leptonic flavour mixing. The one-loop supersymmetric contributions to the leptonic flavour violating process $\tau \to \mu\gamma$ are calculated in the physical basis, with slepton flavour mixed states, instead of using the well known Mass Insertion Method. We present the regions in parameter space where the muon g-2 problem is either entirely solved or partially reduced through the contribution of these flavor violating processes.Comment: 21 pages, 7 figures. Changes on version 3: In order to obtain the complete result for muon g-2 in the limit of non-flavor violation we added the terms given in the appendix. We redid the graphics and numerical analysis including these changes. We also corrected some typos and changed the order of figure

An Invitation to Higher Gauge Theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry at the 2009 Corfu Summer Institut

A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.Comment: 22 pages, latex, amsfonts, Xypic. Version 3: improved presentation. Version 2 is a major revision with explicit formulae included for the evaluation of relativistic spin networks and the computation of examples which have finite value

Self-referential Monte Carlo method for calculating the free energy of crystalline solids

A self-referential Monte Carlo method is described for calculating the free energy of crystalline solids. All Monte Carlo methods for the free energy of classical crystalline solids calculate the free-energy difference between a state whose free energy can be calculated relatively easily and the state of interest. Previously published methods employ either a simple model crystal, such as the Einstein crystal, or a fluid as the reference state. The self-referential method employs a radically different reference state; it is the crystalline solid of interest but with a different number of unit cells. So it calculates the free-energy difference between two crystals, differing only in their size. The aim of this work is to demonstrate this approach by application to some simple systems, namely, the face centered cubic hard sphere and Lennard-Jones crystals. However, it can potentially be applied to arbitrary crystals in both bulk and confined environments, and ultimately it could also be very efficient

2-Vector Spaces and Groupoids

This paper describes a relationship between essentially finite groupoids and 2-vector spaces. In particular, we show to construct 2-vector spaces of Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding to functors between groupoids in both a covariant and contravariant way, which are ambidextrous adjoints. This is used to construct a representation--a weak functor--from Span(Gpd) (the bicategory of groupoids and spans of groupoids) into 2Vect. In this paper we prove this and give the construction in detail.Comment: 44 pages, 5 figures - v2 adds new theorem, significant changes to proofs, new sectio

Numerical treatment of spin systems with unrestricted spin length S: A functional renormalization group study

We develop a generalized pseudofermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case S=1/2 to the classical limit S→∞. Within this framework, spins of magnitude S are realized by implementing M=2S copies of spin-1/2 degrees of freedom on each lattice site. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudofermion constraint in previous spin-1/2 PFFRG studies. We apply this method to the antiferromagnetic J1−J2 honeycomb Heisenberg model with nearest-neighbor J1>0 and second-neighbor J2>0 interactions. Mapping out the phase diagram in the J2/J1−S plane, we find that upon increasing S, quantum fluctuations are rapidly decreasing. In particular, already at S=1 we find no indication for a magnetically disordered phase. In the limit S→∞, the known phase diagram of the classical system is exactly reproduced. More generally, we prove that for S→∞ the PFFRG approach is identical to the Luttinger-Tisza method

On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables

We discuss various features and details of two versions of the Barrett-Crane spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian model and second of the SL(2,C)-symmetric Lorentzian version in which all tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a causal structure into the Lorentzian Barrett--Crane model from which one can construct a path integral that corresponds to the causal (Feynman) propagator. We show how to obtain convergent integrals for the 10j-symbols and how a dimensionless constant can be introduced into the model. We propose a `Wick rotation' which turns the rapidly oscillating complex amplitudes of the Feynman path integral into positive real and bounded weights. This construction does not yet have the status of a theorem, but it can be used as an alternative definition of the propagator and makes the causal model accessible by standard numerical simulation algorithms. In addition, we identify the local symmetries of the models and show how their four-simplex amplitudes can be re-expressed in terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible numerical simulations, we express the matrix elements that are defined by the model, in terms of the continuous connection variables and determine the most general observable in the connection picture. Everything is done on a fixed two-complex.Comment: 22 pages, LaTeX 2e, 1 figur

Discreteness of the volume of space from Bohr-Sommerfeld quantization

A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.Comment: 4 pages, 4 figures; v2, to appear in PR