(8,0) Locally supersymmetric sigma models with conformal invariance in two dimensions (original) (raw)

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.

Heterotic σ-models and conformal supergravity in two dimensions

The (1, 0) and (2, 0) type heterotic a-models with Wess-Zumino term are coupled to conformal supergravity in two dimensions. There are no new restrictions on the o-model manifolds in addition to those which arise in the globally supersymmetric cases. In the (1, 0) case possible isometries of the scalar manifold are gauged. A derivation of d = 2 conformal supergravity based on the super Lie algebra aSp(2, N)~OSp(2, N) (N = 1, 2) is given.

Generalized supersymmetric non-linear sigma models

Physics Letters B, 2004

We rewrite the N = (2, 2) non-linear sigma model using auxiliary spinorial superfields defining the model on T ⊕ * T , where T is the tangent bundle of the target space M. This is motivated by possible connections to Hitchin's generalized complex structures. We find the general form of the second supersymmetry compatible with the known one for the original model.

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.

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.

Supersymmetric nonlinear sigma model

2016

We construct the supersymmetric nonlinear sigma model in a fixed AdS 5 background. We use component fields and find that the complex bosons must be the coordinates of a hyper-Kähler manifold that admits a Killing vector satisfying an inhomogeneous tri-holomorphic condition. We propose boundary conditions that map the on-shell bulk hypermultiplets into off-shell chiral multiplets on 3-branes that foliate the bulk. The supersymmetric AdS 5 isometries reduce to superconformal transformations on the brane fields.

The geometry of supersymmetric sigma-models

We review non-linear σ-models with (2,1) and (2,2) supersymmetry. We focus on off-shell closure of the supersymmetry algebra and give a complete list of (2, 2) superfields. We provide evidence to support the conjecture that all N = (2, 2) non-linear σ-models can be described by these fields. This in its turn leads to interesting consequences about the geometry of the target manifolds. One immediate corollary of this conjecture is the existence of a potential for hyper-Kähler manifolds, different from the Kähler potential, which does not only allow for the computation of the metric, but of the three fundamental twoforms as well. Several examples are provided: WZW models on SU (2) × U (1) and SU (2) × SU (2) and four-dimensional special hyper-Kähler manifolds.