Kac-Moody Symmetry Research Articles

Kac-Moody algebra, nonlocal symmetries, and backlund transformation for KdV equation

Gauge transformation of the Lax eigenfunction through the explicit use of Lie group generators is seen to generate a two-parameter Backlund transformation. Explicit integration of this in two particular cases leads to sech2θ type and rational solutions starting from the trivial one. A method is indicated to generate infinitesimal transformations aroundu in the sense of Steudel, which in this case leads to a nonlocal structure of transformations.

Liouville and Toda theories as conformally reduced WZNW theories

It is shown that Liouville theory can be regarded as an SL(2, ø) Wess-Zumino-Novikov-Witten theory with conformal invariant constraints and that Polyakov's SL(2, ø) Kac-Moody symmetry of induced two-dimensional gravity is just one side of the WZNW current algebra. Analogously, Toda field theories can be regarded as conformal-invariantly constrained WZNW theories for appropriate (maximally non-compact) groups.

SOME SPECIAL POINTS IN THE MODULI SPACE OF c=N CONFORMAL FIELD THEORY

We point out a generalized Frenkel-Kac point for the c=N conformal field theories in fermion language. The critical value, [Formula: see text], of the modular parameter for the c=1 case is generalized to [Formula: see text] for c=N, where R is a parameter in the moduli space which can be used to continuously deform a conformal field theory with SO (2N)L× SO (2N)R Kac-Moody symmetry to one with SU (N+1)L× SU (N+1)R symmetry. Similar deformation from [Formula: see text] to SO (N+1)L×SO(N+1)R is also shown to occur at [Formula: see text].

Hamiltonian reduction and conformal symmetries in two dimensions

We construct chiral operator of two-dimensional conformal field using the method of hamiltonian reduction for affine Kac-Moody symmetries. The relevance of this formalism to the problem of induced quantum gravity is also discussed.

Generalization of the Hauser-Ernst formalism for two-dimensional reduced Einstein abelian gauge field equations

Recently the Hauser-Ernst formalism has played an important role in the discussion of the Virasoro symmetry in the two-dimensional reduced gravity theory. In this Letter we generalize the Hauser-Ernst formalism to the Einstein abelian gauge field equations when the spacetime possesses two commuting Killing vectors. Using this formalism, it is effective to investigate the Kac-Moody symmetry and, in particular, the Virasoro symmetry, which can be used to induced new solutions from the old one. We then provide an example concerning the derivation of a six-parameter generalization of a three-parameter family of colliding wave solutions found by Ernst, García and Hauser.

The Virasoro and Kac-Moody symmetries for the principal chiral model

For the principal chiral model, two hierarchies of symmetries and the related Virasoro and Kac-Moody algebras are derived by using a recursion operator.

Operator content of the four-state Potts quantum chain with Z3-boundary conditions

The four-state Potts quantum chain with a toroidal boundary condition leaving a global Z3 symmetry of the Hamiltonian is investigated. At the critical point, the infinite system shows SU(2) Kac-Moody symmetry. The conjectured operator content is confirmed by numerical finite-size calculations.

Heterotic superstrings in auxiliary field background and extended spacetime supersymmetry

We introduce the superstring vertices of the auxiliary connections of extended supergravity and elucidate the relation between the internal symmetry of the spacetime superconformal algebra and the Kac-Moody symmetry of the 2D superconformal algebra. The microscopic computation of effective lagrangians is outlined: it turns out that the low-energy effective lagrangians for 4D heterotic superstrings are of a standard supergravity form.

Global symmetries in maximal supergravities from compactified superstrings

Maximal ungauged supergravities in ten or fewer dimensions can be viewed as field-theory limits of toroidally compactified type-II superstrings. The symmetries of the spectra can then be constructed in terms of vertex operators, and it is shown here how this can be done to obtain the global and composite local symmetries previously discovered in supergravity lagrangians. This formulation reveals the common origin of the symmetries in different dimensions and indicates possible extensions to Kac-Moody symmetries.

Action of the loop group on the self dual Yang-Mills equation

Recently Kac-Moody symmetry has played an important role in mathematical physics. Dolan and Chau, Ge and Wu discovered an infinitesimal action of the Kac-Moody Lie algebra on the space of solutions of SDYM. We have discovered an action of the loop group on the space of generalized solutions of SDYM, which exponentiates the Kac-Moody action. The group acts by adding a special type of source onto the solution. The action is a geometric construction using the twistor picture.

A new symmetry group of real self-dual Yang-Mills theory

A new infinite parameter symmetry group is found for real self-dual Yang-Mills theory in four euclidean dimensions. Whereas the gauge potentials transform under a group including local gauge transformations and Kac-Moody-like transformations, the gauge invariant object tr P exp(∮ A·d ξ) is seen to carry a representation of the Kac-Moody symmetry. Four-dimensional Polyakov loop-space currents restricted to the self-dual sector are constructed from this algebra.