Superconformal sigma models in higher than two dimensions (original) (raw)

Superconformal sigma models in three dimensions

Nuclear Physics B, 2010

We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N > 4 have necessarily flat targets, but the models with N ≤ 4 admit non-flat targets, which are cones with appropriate Sasakian base manifolds. Superconformal symmetry also requires that the three dimensional spacetimes admit conformal Killing spinors which we examine in detail. We present explicit results for the gauged superconformal theories for N = 1, 2. In particular, we gauge a suitable subgroup of the isometry group of the cone in a superconformal way. We finally show how these sigma models can be obtained from Poincaré supergravity. This connection is shown to necessarily involve a subset of the auxiliary fields of supergravity for N ≥ 2.

Off-shell superconformal nonlinear sigma-models in three dimensions

Journal of High Energy Physics, 2011

We develop superspace techniques to construct general off-shell N ≤ 4 superconformal sigma-models in three space-time dimensions. The most general N = 3 and N = 4 superconformal sigma-models are constructed in terms of N = 2 chiral superfields. Several superspace proofs of the folklore statement that N = 3 supersymmetry implies N = 4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N -extended superconformal groups act transitively and which include Minkowski space as a subspace. 7 Off-shell N = 3 superconformal sigma-models 33 7.

The geometry of supersymmetric non-linear sigma models in D≤ 2 dimensions

2008

After a review of the two-dimensional supersymmetric non-linear sigma models and the geometric constraints they put on the target space, I focus on sigma models in one dimension. The mathematical framework in terms of supersymmetry and complex geometry will also be studied and reviewed. The geometric constraints arising in D = 1 are more general than in D = 2, and can only after some assumptions be reduced to the well known geometries arising in the two dimensional case.

N= 2 nonlinear sigma models in N= 1 superspace: Four and five dimensions

2006

We formulate four-dimensional N = 2 supersymmetric nonlinear sigma models in N = 1 superspace. We show how to add superpotentials consistent with N = 2 supersymmetry. We lift our construction to higher-dimensional spacetime and write five-dimensional nonlinear sigma models in N = 1 superspace.

Quantizing the N=2 super sigma-model in two dimensions

Physics Letters B, 1986

A manifestly covariant background field formalism for the N = 2 supersymmetric non-linear o-model is presented. The formalism allows the symmetries of the model to be exploited to the full in the discussion of the ultraviolet divergences in the quantum theory. This proves the cohomological triviality of the metric counterterms at the l >/2 loop orders. The formalism confirms the finiteness of models with Ricci-flat metrics through the three-loop order. However, it seems unlikely that these cancellations will persist to higher orders. This general analysis is borne out by a study of the supercurrent structure. It is shown that while there is a component axial U(1) current which obeys an Adler-Bardeen theorem, this current is not in the supercurrent multiplet and its existence cannot therefore be used to prove conformal invariance at the quantum level.

Phase transition and 1/N expansion in (2+1)-dimensional supersymmetric sigma models

Letters in Mathematical Physics, 1981

Three-dimensional supersymmetric generalized non-linear sigma models are shown to exhibit second-order phase transition due to spontaneous breakdown of the internal symmetry below a critical value of the coupling constant. Supersymmetry remains unbroken in both phases. Supergraph diagram technique of the corresponding 1IN expansion and the particle spectrum are derived. 1 k k 5g(x, O) = Nla/T (z 1 k l (1) = +Msq~5, ~kl ~tk, 6 k l~l =O

N = 1 supersymmetric sigma model with boundaries, II

Nuclear Physics B, 2004

We study an N = 1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N = 1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures.

N = 1 Supersymmetric Sigma Model with Boundaries, I

Communications in Mathematical Physics, 2003

We study an N = 1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N = 1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures.