Janos Balog

Toda Theory and W-Algebra from a Gauged WZNW Point of View

A new formulation of Toda theories is proposed by showing that they can be regarded as certain gauged Wess-Zumino-Novikov-Witten (WZNW) models. It is argued that the WZNW variables are the proper ones for Toda theory, since all the physically permitted Toda solutions are regular when expressed in these variables. A detailed study of classical Toda theories and their W-algebras is carried out from this unified WZNW point of view. We construct a primary field basis for the w-algebra for any group, we obtain a new method for calculating the W-algebra and its action on the Toda fields by constructing its Kac-Moody implementation, and we analyse the relationship between w-algebras and Casimir algebras. The w-algebra of G2 and the Casimir algebras for the classical groups are exhibited explicitly.

Liouville and Toda theories as conformally reduced WZNW theories

It is shown that Liouville theory can be regarded as an SL(2, o) Wess-Zumino-Novikov-Witten theory with conformal invariant constraints and that Polyakovs SL(2, o) 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.

Consistency of string propagation on curved spacetimes. An SU(1, 1) based counterexample

String propagation on non-compact group manifolds is studied as an exactly solvable example of propagation on more general curved spacetimes. It is shown that for the only viable group SU(1, 1) × Gc string propagation is consistent classically but not quantum mechanically (unitarity is violated). This shows that conformal invariance of the corresponding σ-model (vanishing of the β-functions) is not sufficient to guarantee unitarity.

5-loop Konishi from linearized TBA and the XXX magnet

Using the linearized TBA equations recently obtained in arXiv:1002.1711 we show analytically that the 5-loop anomalous dimension of the Konishi operator agrees with the result obtained previously from the generalized Lüscher formulae. The proof is based on the relation between this linear system and the XXX model TBA equations.

Kac-Moody realization of W-algebras

Abstract By realizing the W -algebras of Toda field-theories as the algebras of gauge-invariant polynomials of constrained Kac-Moody systems we obtain a simple algorithm for constructing W -algebras without computing the W -generators themselves. In particular this realization yields an identification of a primary field basis for all the W -algebras, quadratic bases for the A, B, C-algebras, and the relation of W -algebras to Casimir algebras. At the quantum level it yields the general formula for the Virasoro centre in terms of the KM level.

Classical r-matrix and exchange algebra in WZNW and Toda theories

Abstract It is shown that the fundamental Poisson brackets in the chiral sectors of WZNW theory and its Liouville-Toda reduction are of the r -matrix form. In general, the r -matrix is monodromy dependent, but in the case of A l Lie algebras, and only then, this monodromy dependence can be “gauged away” by choosing appropriate representatives in the conjugacy classes of the monodromy. The resulting non-trivial solution of the classical Yang-Baxter equation is the classical limit of the quantum R -matrix of A l Toda theory found recently by Cremmer and Gervais.

The Bajnok-Janik formula and wrapping corrections

We write down the simplified TBA equations of the AdS5 ×S5 string σ-model for minimal energy twist-two operators in the sl(2) sector of the model. By using the linearized version of these TBA equations it is shown that the wrapping corrected Bethe equations for these states are identical, up to O(g8), to the Bethe equations calculated in the generalized Lüscher approach (Bajnok-Janik formula). Applications of the Bajnok-Janik formula to relativistic integrable models, the nonlinear O(n) sigma models for n = 2, 3, 4 and the SU(n) principal sigma models, are also discussed.

A new family of SU(2) symmetric integrable sigma models

Abstract Local Lagrangians are derived for a class of SU (2) invariant sigma models admitting two commuting Kac-Moody algebras at the level of Poisson brackets. The one-loop renormalizability of these models is established. Some hueristic arguments are presented in favour of their quantum integrability.

TBA equations for excited states in the O(3) and O(4) nonlinear σ-model

TBA integral equations are proposed for one-particle states in the sausage and SS models and their σ-model limits. Combined with the ground-state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear σ-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.

AdS5×S5 mirror TBA equations from Y-system and discontinuity relations

Using the recently proposed set of discontinuity relations we translate the AdS/CFT Y-system to TBA integral equations and quantization conditions for a large subset of excited states from the