相关论文: Equivariant Kaehler Geometry and Localization in t…

When $G$ is a complex reductive algebraic group and $G/K$ is a reductive symmetric space, the decomposition of $\C[G/K]$ as a $K$-module was obtained (in a non-constructive way) by Richardson, generalizing the celebrated result of…

We consider models with a noncompact symmetry in the framework of $\mathcal{N}=1$ supersymmetry. Contrary to the conventional approach, the noncompact symmetry is realized linearly on all fields without constraints. The models are…

The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide…

Let G be a compact Lie group. Let M be a smooth G-manifold and V --> M be an oriented G-equivariant vector bundle. One defines the spaces of equivariant forms with generalized coefficients on V and M. An equivariant Thom form $\theta$ on V…

The general theory of N = 1 supergravity with supermatter is studied using a canonical approach. The supersymmetry and gauge constraint generators are found. The framework is applied to the study of a Friedmann minisuperspace model. We…

N=(2,2), d=2 supersymmetric non-linear sigma-models provide a physical realization of Hitchin's and Gualtieri's generalized Kaehler geometry. A large subclass of such models are comprised by WZW-models on even-dimensional reductive group…

We develop the theory of nilpotent $G$-spaces and their localisations, for $G$ a compact Lie group, via reduction to the non-equivariant case using Bousfield localisation. One point of interest in the equivariant setting is that we can…

Equivariant localization expresses global invariants in terms of local invariants, and many of them appearing in equivariant index theory, (holomorphic) Morse theory, geometric quantization and supersymmetric localization can be…

We first retell in the K-theoretic context the heuristics of $S^1$-equivariant Floer theory on loop spaces which gives rise to $D_q$-module structures, and in the case of toric manifolds, vector bundles, or super-bundles to their explicit…

We extend the results of hep-th/0310137 to show that a general classical action for D=2, N=2 sigma models on a non(anti)commutative superspace is not standard and contains infinite number of terms, which depend on the determinant of the…

We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver…

We present a review of supersymmetry, supergravity, and the non-perturbative dynamics of gauge theories, tracing a path from the supersymmetry algebra to moduli stabilisation and de~Sitter vacua in string theory. Representations of the…

We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general…

In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein…

A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative…

We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group G on a space E. We…

The geometry of the target space of an N=(2,2) supersymmetry sigma-model carries a generalized Kahler structure. There always exists a real function, the generalized Kahler potential K, that encodes all the relevant local differential…

We prove a localization formula for group-valued equivariant de Rham cohomology of a compact G-manifold. This formula is a non-trivial generalization of the localization formula of Berline-Vergne and Atiyah-Bott for the usual equivariant de…

This thesis considers one and two dimensional supersymmetric nonlinear sigma models. First there is a discussion of the geometries of one and two dimensional sigma models, with rigid supersymmetry. For the one-dimensional case, the…

Quillen's localization theorem is well known as a fundamental theorem in the study of algebraic K-theory. In this paper, we present its arithmetic analogue for the equivariant K-theory of arithmetic schemes, which are endowed with an action…