Light-cone quantisation of the Liouville and Toda field theories

The Toda field is a multicomponent field in two space-time dimensions satisfying a generalisation of the Liouville equation ?²? + exp ? = 0. We define the quantum field theory, and solve for the fields in terms of their initial values on a forward light-cone, demonstrating that our solution is regular. We give an explicit result for the Liouville equation which is the quantum version of the well-known classical solution. We also discuss the energy-momentum spectrum, and the conformal properties of the theory.     

Open M5-branes

We show how, in heterotic M theory, an M5-brane in the 11-dimensional bulk may end on an "M9-brane" boundary, the M5-brane boundary being a Yang-monopole 4-brane. This possibility suggests various novel 5-brane configurations of heterotic M theory, in particular, a static M5-brane suspended between the two M9-brane boundaries, for which we find the asymptotic heterotic supergravity solution.     

On characteristic integrals of Toda field theories

Characteristic integrals of Toda field theories associated to general simple Lie algebras are constructed using systematic techniques, and complete mathematical proofs are provided. Plenty of examples illustrating the results are presented in explicit forms.     

Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality

We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus ${\mathbb{T}}^n(n\ge 2)$, by a noncommutative ${\mathbb{T}}^n$-deformation of the M5-brane. The ingredients of the noncommutative action and equations of motion include the deformed Hodge duality, deformed wedge product, and the noncommutative integral over the noncommutative space obtained by strict deformation quantization. As an application we then introduce a variant model with an enhanced action in which we show that the corresponding partition function is a modular form, which is a purely noncommutative geometry phenomenon since the usual theory only has a ${\mathbb{Z}}_2$-symmetry. In particular, S-duality in this 6-dimensional higher abelian gauge theory model is shown to be, in this sense, on par with the usual 4-dimensional case.     

On non-linear action of multiple M2-branes

A non-linear SO(8)$\mathit{SO}(8)$ invariant BF type Lagrangian for describing the dynamics of N M2-branes in flat spacetime has been proposed recently in the literature which is an extension of the non-abelian DBI action of N   D2-branes. This action includes only terms with even number of the totally antisymmetric tensor MIJK$M^{IJK}$. We argue that the action should contain terms with odd number of MIJL$M^{IJL}$ as well. We modify the action to include them.     

Chern-Simons solitons,Toda theories and the chiral model

The two-dimensional self-dual Chern-Simons equations are equivalent to the conditions for static, zero-energy solutions of the (2+1)-dimensional gauged nonlinear Schrödinger equation with Chern-Simons matter-gauge dynamics. In this paper we classify all finite chargeSU(N) solutions by first transforming the self-dual Chern-Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck-Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between theSU(N) Toda andSU(N) chiral model solutions.This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069, and NSF grant #87-08447     

Reflection amplitudes of boundary Toda theories and thermodynamic Bethe ansatz

We study the ultraviolet asymptotics in A_n affine Toda theories with integrable boundary actions. The reflection amplitudes of non-affine Toda theories in the presence of conformal boundary actions have been obtained from the quantum mechanical reflections of the wave functional in the Weyl chamber and used for the quantization conditions and ground-state energies. We compare these results with the thermodynamic Bethe ansatz derived from both the bulk and (conjectured) boundary scattering amplitudes. The two independent approaches match very well and provide the non-perturbative checks of the boundary scattering amplitudes for Neumann and (+) boundary conditions.     

Mass deformation of the multiple M2-branes theory

Based on recent developments, in this paper we study the one parameter deformation of 2+1-dimensional gauge theories with scale invariance and N = 8mathcal{N} = 8 supersymmetry, which is expected to be the field theory living on a stack of M2-branes. The deformed gauge theory is defined by the Lagrangian and is based on an infinite set of novel 3-algebras constructed by relaxing the assumption that the invariant metric is positive definite. Under the Higgs mechanism, we can develop the D-branes world volume theory in the presence of background fluxes.     

Solving Toda field theories and related algebraic and differential properties

Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld–Sokolov gauge is used. The main objective of this paper is to carry out this approach of solving the Toda field theories for the classical Lie algebras, following Balog et al. (1990) [5]. In this process, we discover and prove some algebraic identities for principal minors of special matrices. The known elegant solutions of Leznov (1980) [10] fit in our scheme in the sense that they are the general solutions to our conditions discovered in this solving process. To prove this, we find and prove some differential identities for iterated integrals. It can be said that altogether our paper gives complete mathematical proofs for Leznov’s solutions.     

Solitons and vertex operators in twisted affine Toda field theories

Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields display interesting patterns in their masses and coupling which have recently been shown to extend to the classical soliton solutions arising when the couplings are imaginary. Here these results are extended from the untwisted to the twisted algebras. The new soliton solutions and their masses are found by a folding procedure which can be applied to the affine Kac-Moody algebras themselves to provide new insights into their structures. The relevant foldings are related to inner automorphisms of the associated finite dimensional Lie group which are calculated explicitly and related to what is known as the twisted Coxeter element. The fact that the twisted affine Kac-Moody algebras possess vertex operator constructions emerges naturally and is relevant to the soliton solutions.