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We investigate the topological theory obtained by twisting the N=(2,2) supersymmetric nonlinear sigma model with target a bihermitian space with torsion. For the special case in which the two complex structures commute, we show that the action is a Q-exact term plus a quasi-topological term. The quasi-topological term is locally given by a closed two-form which corresponds to a flat gerbe-connection and generalises the usual topological term of the A-model. Exponentiating it gives a Wilson surface, which can be regarded as a generalization of a Wilson line. This makes the quantum theory globally well-defined.
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We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.
A Symmetry Principle has been shown to augment unambiguously the Einstein Field Equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a non-relativistic limit, and derive the stringy augmentation of Newton Gravity: [ begin{array}{lll} {bf{ abla}^{2}Phi}=4pi G rho+bf{H}{bf{cdot}}bf{H},, quad&qquadbf{ abla}bf{cdot}bf{H}=0,, quad&qquad {bf{ abla}bf{times}bf{H}}=4pi G, bf{K},. end{array} ] Not only the mass density $rho$ but also the current density $mathbf{K}$ is intrinsic to matter. Sourcing $mathbf{H}$ which is of NS-NS $H$-flux origin, $mathbf{K}$ is nontrivial if the matter is `stringy. $mathbf{H}$ contributes quadratically to the Newton potential, but otherwise is decoupled from the point particle dynamics, i.e. $bf{ddot{x}}=-bf{ abla}Phi$. We define `stringization analogous to magnetization and discuss regular as well as monopole-like singular solutions.
We examine topological terms of $(2+1)$d sigma models and their consequences in the light of classifications of invertible quantum field theories utilizing bordism groups. In particular, we study the possible topological terms for the $U(N)/U(1)^N$ flag-manifold sigma model in detail. We argue that the Hopf-like term is absent, contrary to the expectation from a nontrivial homotopy group $pi_3(U(N)/U(1)^N)=mathbb{Z}$, and thus skyrmions cannot become anyons with arbitrary statistics. Instead, we find that there exist ${N(N-1)over 2}-1$ types of Chern-Simons terms, some of which can turn skyrmions into fermions, and we write down explicit forms of effective Lagrangians.
We find a geometric description of interacting $betagamma$-systems as a null Kac-Moody quotient of a nonlinear sigma-model for systems with varying amounts of supersymmetry.
Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure of supersymmetric models in four dimensional space-time in which metric singularities occur. For this purpose we study a simple anomaly-free extension of the supersymmetric CP^1 model from a classical point of view. We show that the metric singularities can be regularized by the addition of a soft supersymmetry-breaking mass parameter.
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