Growing Hair on the extremal BTZBTZ black hole

We show that the nonlinear $\sigma-$model in an asymptotically $AdS_3$ space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear $\sigma-$model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear $\sigma-$model fields and changes the space-time metric, and it can be used to map an extremal $BTZ$ black hole to infinitely many hairy black hole solutions.Comment: 11 pages, 1 figure, minor corrections include

Gauged Nonlinear Sigma Model and Boundary Diffeomorphism Algebra

We consider Chern-Simons gauged nonlinear sigma model with boundary which has a manifest bulk diffeomorphism invariance. We find that the Gauss's law can be solved explicitly when the nonlinear sigma model is defined on the Hermitian symmetric space, and the original bulk theory completely reduces to a boundary nonlinear sigma model with the target space of Hermitian symmetric space. We also study the symplectic structure, compute the diffeomorphism algebra on the boundary, and find an (enlarged) Virasoro algebra with classical central term.Comment: 8 pages, Revte

Bosonic String in Affine-Metric Curved Space

The sigma model approach to the closed bosonic string on the affine-metric manifold is considered. The two-loop metric counterterms for the nonlinear two-dimensional sigma model with affine-metric target manifold are calculated. The correlation of the metric and affine connection is considered as the result of the ultraviolet finiteness (or beta-function vanishing) condition for the nonlinear sigma model. The examples of the nonflat nonRiemannian manifolds resulting in the trivial metric beta-function are suggested.Comment: 15 pages, LaTe

Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems

We review various connections between condensed matter systems with the Nambu-Jona Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Resent findings of a duality between the Nambu-Jona Lasinio model and the nonlinear sigma model enables us to investigate various properties underlying both theories. In this review we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu-Jona Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in the nonlinear sigma model owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.Comment: 24pages, 10 figures, Invited review paper commissioned by Symmetry. Comments warmly welcom

Dual Instantons

We show how to map the Belavin-Polyakov instantons of the O(3)-nonlinear $\sigma-$model to a dual theory where they then appear as nontopological solitons. They are stationary points of the Euclidean action in the dual theory, and moreover, the dual action and the O(3)-nonlinear $\sigma-$model action agree on shell.Comment: 13 page

Classically integrable boundary conditions for symmetric-space sigma models

We investigate boundary conditions for the nonlinear sigma model on the compact symmetric space $G/H$, where $H \subset G$ is the subgroup fixed by an involution $\sigma$ of $G$. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions in correspondence with involutions which commute with $\sigma$. Applied to $SO(3)/SO(2)$, the nonlinear sigma model on $S^2$, these yield the great circles as boundary submanifolds. Applied to $G \times G/G$, they reproduce known results for the principal chiral model.Comment: 8 pages. v2 has an introduction added and a few minor correction

The Noncommutative Supersymmetric Nonlinear Sigma Model

We show that the noncommutativity of space-time destroys the renormalizability of the 1/N expansion of the O(N) Gross-Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the subleading order in 1/N expansion, the noncommutative supersymmetric O(N) nonlinear sigma model becomes renormalizable in D=3. We also show that dynamical mass generation is restored and there is no catastrophic UV/IR mixing. Unlike the commutative case, we find that the Lagrange multiplier fields, which enforce the supersymmetric constraints, are also renormalized. For D=2 the divergence of the four point function of the basic scalar field, which in D=3 is absent, cannot be eliminated by means of a counterterm having the structure of a Moyal product.Comment: 15 pages, 7 figures, revtex, minor modifications in the text, references adde

Supersymmetric Nonlinear Sigma Model in AdS_5

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-Kahler 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.Comment: Latex, 7 pages. Published versio