Collective String Field Theory Research Articles

RECENT DEVELOPMENTS IN D=2 STRING FIELD THEORY

We review the recent developments in the construction of string field theory in two dimensions. We analyze the bewildering number of string field theories that have been proposed, all of which correctly reproduce the correlation functions of two-dimensional string theory. These include (1) free fermion field theory, (2) collective string field theory, (3) temporal gauge string field theory and (4) nonpolynomial string field theory. We will analyze discrete states, the ω(∞) symmetry, and correlation functions in terms of these different string field theories. We will also comment on the relationship between these field theories, which is still not well understood.

Integrable extensions of the rational and trigonometric AN Calogero-Moser potentials

We describe the R-matrix structure associated with integrable extensions, containing both one-body and two-body potentials, of the A N Calogero-Moser N-body systems. We construct non-linear, finite dimensional Poisson algebras of observables. Their N → ∞ limits realize the infinite Lie algebras Sdiff( R × S 1) in the trigonometric case and Sdiff( R 2) in the rational case. It is then isomorphic to the algebra of observables constructed in the two-dimensional collective string field theory.

MARINARI–PARISI AND SUPERSYMMETRIC COLLECTIVE FIELD THEORY

A field theoretic formulation of the Marinari–Parisi supersymmetric matrix model is established and shown to be equivalent to a recently proposed supersymmetrization of the bosonic collective string field theory. It also corresponds to a continuum description of super-Calogero models. The perturbation theory of the model is developed and, in this approach, an infinite sequence of vertices is generated. A class of potentials is identified for which the spectrum is that of a massless boson and Majorana fermion. For the harmonic oscillator case, the cubic vertices are obtained in an oscillator basis. For a rather general class of potentials it is argued that one cannot generate from Marinari–Parisi models a continuum limit similar to that of the d = 1 bosonic string.

PERTURBATIVE RESULTS OF COLLECTIVE STRING FIELD THEORY

We present a summary of perturbative results obtained in the framework of collective string field theory. We discuss computations of tree-level scattering amplitudes, loop corrections to tachyon self-energy, ground state energy and finite temperature free energy. A comparison with results obtained in different approaches is given. We also discuss the physical implications of our results.

Scattering amplitudes and loop corrections in collective string field theory (II)

Abstract Using collective field theory we compute the scattering of one-dimensional strings. The amplitude is determined and seen to have a contribution from the tachyon as well as from an infinite sequence of discrete states. It is not proportional to the length of the space and is finite. We then consider the issue of higher-loop corrections in collective string field theory. The two-loop diagrams are evaluated and the correction to the ground-state energy is found to be in exact agreement with the finite value obtained previously from matrix model calculations. We also point to the origin of the large-order behavior in collective field theory.

Quantum integrability and exact eigenstates of the collective string field theory

Abstract The quantum w∞ algebra associated with the collective string theory is used to construct exact discrete eigenstates of the cubic hamiltonian. Imaginary-eigenvalued creation/annihilation operators are constructed which build a F ⊗ F - graded algebra . Real-eigenvalued operators are formally obtained as combinations of discrete eigenvalued ones and vice versa.

Scattering amplitudes and loop corrections in collective string field theory

Using collective field theory we compute the scattering of one-dimensional strings. The amplitude is determined and seen to have a contribution from the tachyon as well as from an infinite sequence of discrete states. It is not proportional to the length of the space and is finite. We then consider the issue of higher-loop corrections in collective string field theory. The two-loop diagrams are evaluated and the correction to the ground-state energy is found to be in exact agreement with the finite value obtained previously from matrix model calculations. We also point to the origin of the large-order behavior in collective field theory.

Classical integrability and higher symmetries of collective string field theory

We demonstrate the complete integrability of classical collective field theory. An exact equivalence to the classical N-body problem of Calogero type is described. A Lax pair is constructed for the general continuum collective equations. A form of background independence is pointed out. An infinite set of commuting currents is constructed in the general case. A large symmetry algebra is discovered and shown to take the form of a W ∞ algebra.