2D Principal Chiral Field at Large N as a Possible Solvable 2D String Theory

The SU($N$) principal chiral model is asymptotically free and integrable in $1+1$ dimensions. In the large-$N$ limit, there is no scattering, but correlation functions are {\em not} those of a free field theory. We briefly review the derivation of form factors for local operators. Two-point functions for such operators are known exactly. The two-point function of scaling-field operators has the short-distance behavior expected from the renormalization group. We briefly discus...

After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no {\it explicit} gravitational dressing factor, analogue to the Liouville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, ...

Second-order equations of motion on a group manifold that appear in a large class of so-called chiral theories are presented. These equations are presented and explicitely solved for cases of semi-simple, finite-dimensional Lie groups. With three figures avaliable from the authors upon request.

Following a recent proposal for integrable theories in higher dimensions based on zero curvature, new Lorentz invariant submodels of the principal chiral model in 2+1 dimensions are found. They have infinite local conserved currents, which are explicitly given for the su(2) case. The construction works for any Lie algebra and in any dimension, and it is given explicitly also for su(3). We comment on the application to supersymmetric chiral models.

We examine the precise structure of the loop algebra of `dressing' symmetries of the Principal Chiral Model, and discuss a new infinite set of abelian symmetries of the field equations which preserve a symplectic form on the space of solutions.

Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected to be a large discrete subgroup of the hidden symmetry group. With this motivation, we explore the hidden symmetries of principal chiral models and symmetric space models.

Two dimensional $N=\infty$ lattice chiral models are investigate by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the point of showing asymptotic scaling (within 5\%).

The finite form of the $N=2$ super-Weyl transformations in the chiral and twisted-chiral irreducible formulations of the two-dimensional $N=2$ superfield supergravity are found in $N=2$ superspace. The super-Weyl anomaly of the $N=2$ extended fermionic string theory is computed in terms of the $N=2$ superfields, by using a short time expansion of the $N=2$ chiral heat kernel. The super-Weyl invariant $N=2$ superconformal structure is introduced, and a new definition of the $N...

We present results for the large-$N$ limit of the (1+1)-dimensional principal chiral sigma model. This is an asymptotically-free $N\times N$ matrix-valued field with massive excitations. All the form factors and the exact correlation functions of the Noether-current operator and the energy-momentum tensor are found, from Smirnov's form-factor axioms. We consider (2+1)-dimensional $SU(\infty)$ Yang-Mills theory as an array of principal chiral models with a current-current inte...

We describe some recent progress in understanding and formulating string theory which is based on extensive studies of strings in lower (D=2) dimension. At the center is a large $W_{\infty}$ symmetry that appears most simply in the matrix model picture. In turn the symmetry defines the dynamics giving Ward identities and the complete S-matrix. The integrability aspect where nonlinear string phenomena emerges from linear matrix model dynamics is emphasized. Extensions involvin...