Lukas W. Lindwasser

A bstract: Scalar field theories in (A)dS ₂ with integer scaling dimensions ∆ = k + 1 are characterised by the existence of a pair of (anti-)holomorphic higher-spin currents. We explore the consequences of this to describe their quantisation and subsets of their linear and non-linear symmetries, taking care to treat AdS ₂ and dS ₂ separately. In particular, we point out that the theories admit mode expansions reminiscent of standard two-dimensional conformal field theories in complex coordinates, with which we are able to construct a large set of symmetry transformations which includes Virasoro symmetry. We further leverage holomorphicity of the currents to show that the significant subset of the full symmetries of theories with k > 0 is captured by a chiral algebra, which is a subalgebra of the one in the k = 0 (massless) theory. This allows us to identify integrable deformations for k ∈ {0 , 1 , 2}. We finally observe that a lack of integrable deformations for k > 2 is a consequence of a known conjecture.

The Lie algebra of symmetries generated by the left-moving current j = ∂ − ϕ in the two-dimensional (2D) single scalar conformal field theory is infinite dimensional, exhibiting mutually commuting subalgebras. The infinite-dimensional mutually commuting subalgebras define integrable deformations of the 2D single scalar conformal field theory that preserve the Poisson bracket structure. We study these mutually commuting subalgebras, finding general properties that the generators of such a subalgebra must satisfy. Along the way, we derive constraints on integrable equations of the Korteweg–de Vries type. We also confirm that the recently found [ j ] = 0 , − 1 , − 2 mutually commuting subalgebras are infinite dimensional.

A bstract: We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond with the symmetry algebra of 2 d integrable models. These Lie algebras are defined by the set of infinitesimal, nonlinear, and higher derivative symmetry transformations present in theories with a left(right)-moving or (anti)-holomorphic current. We study a large class of such Lagrangian theories. We study the commuting subalgebras of the 2 d free massless scalar, and find the symmetries of the known integrable models such as sine-Gordon, Liouville, Bullough-Dodd, and Korteweg-de Vries. Along the way, we find several new sequences of commuting charges, which we conjecture are charges of integrable models which are new deformations of a single scalar. After quantizing, the Lie algebra is deformed, and so are their commuting subalgebras.

A bstract: Consistent interactions with electromagnetism and gravity for mass m particles of any spin are obtained. This is done by finding interactions which preserve the covariantized massive gauge symmetry present in recently constructed massive particle actions. This gauge principle is sufficient for finding consistent completions of minimal as well as non-minimal couplings of any type. For spins s ≥ 3/2, consistency requires infinitely many interaction terms in the action, including arbitrarily high order derivatives of electromagnetic and gravitational curvatures, with correspondingly high powers of 1/ m . These interactions may be formally resummed and expressed in terms of non-local operators. Finally, although the interactions appear non-local, evidence is presented for the existence of a field redefinition which makes the interacting action local. This work provides the first explicit realization of an exactly gauge invariant formulation of massive particles interacting with electromagnetism and gravity.

We analyze so-called generalized Veneziano and generalized Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an over-determined set of non-linear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a two-parameter family which includes the Veneziano amplitude, the one-parameter family of Coon amplitudes, and a larger two-parameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum.

We analyze so-called generalized Veneziano and generalized Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an over-determined set of non-linear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a two-parameter family which includes the Veneziano amplitude, the one-parameter family of Coon amplitudes, and a larger two-parameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum.

We detail the properties of the Veneziano, Virasoro, and Coon amplitudes. These tree-level four-point scattering amplitudes may be written as infinite products with an infinite sequence of simple poles. Our approach for the Coon amplitude uses the mathematical theory of q-analysis. We interpret the Coon amplitude as a q-deformation of the Veneziano amplitude for all q ≥ 0 and discover a new transcendental structure in its low-energy expansion. We show that there is no analogous q-deformation of the Virasoro amplitude.