Supergravity in $2+\epsilon$ Dimensions

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effective action constructed in the configuration space contains two super-Liouville actio...

We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations. Some of them are shown to be equivalent to the introduction of $2+\epsilon$-dimensional terms into the initially 2-dimensional theory. We also argue that the $\beta$-function for the Einstein constant has a non-trivial ultraviolet stable point beyond two dimensions.

I will report on a top-down approach relating N=2, D=4 pure supergravity with non-trivial boundary behavior to a (2+1)-dimensional analog model which is able to describe the electronic properties of graphene-like materials. This is obtained, in a special asymptotic limit, by imposing an unconventional realization of supersymmetry in the D=3 boundary model.

We offer a guide to dimensional reduction (DRED) in theories with anomaly mediated supersymmetry breaking. Evanescent operators proportional to epsilon arise in the bare Lagrangian when it is reduced from d=4 to d= (4-2 epsilon) dimensions. In the course of a detailed diagrammatic calculation, we show that inclusion of these operators is crucial. The evanescent operators conspire to drive the supersymmetry-breaking parameters along anomaly-mediation trajectories across heavy ...

Quantum gravitational effects on the renormalization group equation are studied in the $(2+\epsilon)$-dimensional approach. Divergences in a matter one-loop effective action do not receive gravitational radiative corrections. The renormalization factor for beta functions recently found by Klebanov, Kogan and Polyakov is obtained by using the renormalized cosmological constant to define the physical scale transformation.

We propose a new gauge prepotential $\Upsilon_i$ describing the four-dimensional ${\mathcal N}=2$ superconformal gravitino multiplet. The former naturally arises via a superspace reduction of the ${\mathcal N}=3$ conformal supergravity multiplet. A locally superconformal chiral action for $\Upsilon_i$, which is gauge-invariant in arbitrary conformally-flat backgrounds, is derived. This construction readily yields a new superprojector, which maps an isospinor superfield $\Psi_...

Standard superspace Feynman diagram rules give one estimate of the onset of ultraviolet divergences in supergravity and super Yang-Mills theories. Newer techniques motivated by string theory but which also make essential use of unitarity cutting rules give another in certain cases. We trace the difference to the treatment of higher-dimensional gauge invariance in supersymmetric theories that can be dimensionally oxidized to pure supersymmetric gauge theories.

We argue that the observed UV finiteness of the 3-loop extended supergravities may be a manifestation of a hidden local superconformal symmetry of supergravity. We focus on the SU(2,2|4) dimensionless superconformal model. In Poincare gauge where the compensators are fixed to phi^2= 6 M_P^2 this model becomes a pure classical N=4 Einstein supergravity. We argue that in N=4 the higher-derivative superconformal invariants like phi^{-4}W^2 \bar W^2 and the consistent local anoma...

Quantum theory of dilaton gravity coupled to a nonlinear sigma model with a maximally symmetric target space is studied in $2+\epsilon$ dimensions. The ultraviolet stable fixed point for the curvature of the nonlinear sigma model demands a new fixed point theory for the dilaton coupling function. The fixed point of the dilaton coupling is a saddle point similarly to the previous case of the flat target space.

Using the harmonic superspace background field formulation for general D=4, N=2 super Yang-Mills theories, with matter hypermultiplets in arbitrary representations of the gauge group, we present the first rigorous proof of the N=2 non-renormalization theorem; specifically, the absence of ultraviolet divergences beyond the one-loop level. Another simple consequence of the background field formulation is the absence of the leading non-holomorphic correction to the low-energy ef...