Selecting Finite Unified Theories with Current Data

Fitting and selecting scattering data

The main purpose of scattering experiments is to unveil the underlying structure of the colliding particles and their interaction. Typically one measures scattering observables (cross sections and polarizations) at discrete angles and energies and mutually consistent data may validate or falsify proposed theories or models. However, the accumulation of data from different laboratories while potentially improves the statistical significance it may sometimes generate mutually inconsistent data as a side-effect. Thus, some decision has to be made on what are the maximal amount of data which are m…

Current OPEs in Superconformal Theories

It's well known that in conformal theories the two- and three-point functions of a subset of the local operators-the conformal primaries-suffice, via the operator product expansion (OPE), to determine all local correlation functions of operators. It's less well known that, in superconformal theories, the OPE of superdescendants is generally undetermined from those of the superprimaries, and there is no universal notion of superconformal blocks. We recall these and related aspects of 4d (S)CFTs, and then we focus on the super operator product expansion (sOPE) of conserved currents in 4d N=1 SCF…

Lattice field theories with an energy current

We investigate a lattice scalar field theory in the presence of a bias favouring the establishment of an energy current, as a model for stationary nonequilibrium processes at low temperature in a non-integrable system. There is a transition at a finite value of the bias to a gapless modulated phase which carries a classical current; however, unlike in similar, integrable, models, quantum effects also allow for a non-zero current at arbitrarily small bias. The transition is second order in the magnetically disordered phase, but is pre-empted by a first-order transition in the ferromagnetic case…

Current Directions in String Theory and Abstract Supersymmetry

I discuss some current thoughts on how low-energy measurements and consistency constrain theories at high energies with emphasis on string theory. I also discuss some recent work on the dynamics of supersymmetric gauge theories.

Is There Scale Invariance in N=1 Supersymmetric Field Theories ?

In two dimensions, it is well known that the scale invariance can be considered as conformal invariance. However, there is no solid proof of this equivalence in four or higher dimensions. We address this issue in the context of 4d $\mathcal{N}=1$ SUSY theories. The SUSY version of dilatation current for theories without conserved $R$ symmetry is constructed through the FZ-multiplet. We discover that the scale-invariant SUSY theory is also conformal when the real superfield in the dilatation current multiplet is conserved. Otherwise, it is only scale-invariant, despite of the transformation of …

Current Renormalization in Finite Volume

For finite volume field theories with discrete translational invariance, conserved currents can be additively renormalized by infrared effects. We demonstrate this for pions using chiral perturbation theory coupled to electromagnetism in a periodic box. Gauge invariant single particle effective theories are constructed to explain these results. In such theories, current renormalization arises from operators involving the zero mode of the gauge field. No contradictions with Ward identities, or low-energy theorems are encountered.

Notes on Operator Equations of Supercurrent Multiplets and the Anomaly Puzzle in Supersymmetric Field Theories

Recently, Komargodski and Seiberg have proposed a new type of supercurrent multiplet which contains the energy-momentum tensor and the supersymmetry current consistently. In this paper we study quantum properties of the supercurrent in renormalizable field theories. We point out that the new supercurrent gives a quite simple resolution to the classic problem, called the anomaly puzzle, that the Adler-Bardeen theorem applied to an R-symmetry current is inconsistent with all order corrections to $β$ functions. We propose an operator equation for the supercurrent in all orders of perturbation the…

诺特定理与量子规范理论中的能量动量张量

Noether's theorems and the energy-momentum tensor in quantum gauge theories

本文通过诺特定理第二定理，在量子电动力学和量子色动力学中推导出自动对称且具有预期对称性的能量动量张量。