Closed bosonic strings in a covariant phase space

In a covariant phase space the Poisson bracket Lie algebra of (1+1)-dimensional diffeomorphisms has a three-parameter family of Lorentz- and translation-invariant local string representations. In the second-quantized string theory these parameters appear in the Schwinger term of the commutator algebra and modify the critical dimension, and in the lagrangian formulation they contribute to frame anomalies associated with functional determinants.     

On the dilaton vertex in the covariant formulation of strings

We investigate the dilaton vertex operator in the covariant formulation of strings. We find that the Faddeev-Popov ghosts play an essential role to construct conformal fields.     

Gauge fixing in fully gauge-invariant field theory of closed bosonic and Neveu-Schwarz strings

The gauge fixing procedure is reanalyzed in our fully gauge-invariant closed bosonic and Neveu-Schwarz string field theory which does not have any constraint on string functionals and gauge parameters. The relations to other formulations are clarified; in particular, it is shown that our theory recovers other formulation with constraints L₊ − L₋ = 0 after partial gauge fixing but without any truncation. Complete gauge fixing is also made and the expected propagator is obtained. The constraint L₊ − L₋ = 0 appears as a field equation in our formulation.     

The interacting gauge covariant bosonic string

The interaction of the gauge covariant open bosonic string is presented in oscillator form, and in functional form. In the latter form, the string is described by commuting and anticommuting coordinates. The interaction is essentially the condition that the strings should overlap.     

On gauge invariant bosonic strings

Following Witten, an associative product is constructed for fields on open strings, with BRST ghosts, which has the same topological structure as that in the light-cone gauge. The product is shown to be well defined on a certain class of string functionals. The corresponding action is that of Chern-Simons. The relation of this product to that of others is discussed.     

Gauge covariant formulation of the generating operator. 1. The Zakharov-Shabat system

A gauge covariant formulation of the generating operator Λ, related to the Zakharov-Shabat system L is proposed. The operator Λ̃, corresponding to $\text{L}\text{?}\text{= ψ}{}_0{}^{\mathrm{?1}}\text{Lψ}{}_0$ in the pole gauge is explicitly calculated. Thus the unified approach to the higher nonlinear Schrödinger equations, based on Λ is automatically reformulated with Λ̃ for the higher Heisenberg ferromagnet equations.     

The geometry of open bosonic strings

The coordinate conditions usually used to describe the open string and its boundary conditions are intrinsically singular at the boundary. As a result, the boundary conditions are difficult to understand or interpret geometrically. The physical requirement that the variation of the string at the boundary yield a vanishing contribution to the variation of the action may be accomplished by the requirement that the induced metric, in non-singular coordinates, have signature (0, — 1) at the boundary and that the metric be C¹ on the boundary. These geometrically simple by analytically somewhat complicated requirements are equivalent to the usual boundary conditions. Lastly it is shown that the open string is, in a strict sense, a special case of the closed string. Some of the peculiar behavior of characteristic curves on the open string becomes clear in this context.     

TheC*-algebra of bosonic strings

We give a rigorous definition of Witten'sC ^*-string-algebra. To this end we present a new construction ofC ^*-algebras associated to special geometric situations (Kähler foliations) and generalize this later construction to the string case. Through this we get a natural geometrical interpretation of the string of semi-infinite forms as well as the fermionic algebra structure. Using the (non-commutative) geometric concepts for investigating the string algebra we get a natural Fredholm module representation of dimension 26+.Work partially supported by the DFG (under contract MU 75712.3)     

Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space

In this work we develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and a method of deriving the BRST operator for such an algebra is proposed. A general procedure of Lagrangian construction, describing the dynamics of a bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2, containing the total set of auxiliary fields and gauge symmetries.     

Regularized bosonic strings need extrinsic curvature

We show that the string tension in a class of triangulated random surface models with gaussian action does not tend to zero at the critical point. This rules out the existence of a non-trivial continuum limit of these models. Furthermore, the proof seems to lead to the conclusion that the most natural (if not the only) way to avoid this feature of random surface models is by introducing asymptotically free interactions depending e.g. on the extrinsic curvature of the surface.     

Gauge covariant formulation of the generating operator. 2. Systems on homogeneous spaces

A gauge covariant approach to the operator Λ, generating the n-wave type equations on homogeneous spaces is proposed. The operator Λ̃ for the gauge equivalent equations is explicitly constructed. The main results (such as conservation laws, hierarchies of hamiltonian structures, etc.) for the n-wave type equations and their gauge equivalent ones are formulated in terms of Λ and Λ̃ respectively.     

Monte Carlo simulations of regularized bosonic strings

The world sheet of the bosonic string is regularized by triangulation. The corresponding statistical theory of triangulated random surfaces is simulated by Monte Carlo methods and the critical exponent γ for the susceptibility determined. A careful analysis of the systematic and statistical errors reveals that we have to wait for the next generation of computers before a high-precision measurement of γ is possible.     

Open bosonic strings in general background fields

We discuss the renormalization properties of the 2 dim. field theory describing an open bosonic string in the background fields corresponding to its massless excitations. The relevant β-functions are calculated for gravitational, antisymmetric tensor and Yang-Mills background on 1-loop level, for pure Yang-Mills background an 2-loop level and in the Abelian case up to 3 loops. We find a renormalization scheme dependence starting at 2 loop order. Putting β to zero yields the equation of motion for the non-linear electrodynamics of Fradkin and Tseytlin.     

Closed bosonic strings in background gauge fields

The coupling to abelian background gauge fields of closed bosonic strings compactified on a torus is considered. There exist specific field configurations for which the theory cannot be defined consistently, in spite of the fact that the field equations of motion are then solved exactly. This critical behaviour is related to a breakdown of local and global world-sheet symmetries, as well as of spacetime unitarity. A physical interpretation of this phenomenon is proposed. The issue of spacetime duality is also discussed. This symmetry is shown to be partially broken for generic background field configurations.     

The construction of the sh-Lie-algebra of closed bosonic strings

We present a construction of the closed string algebra in terms of Gaussian processes and crossed products. Also we give a purely functional analytical prove of the sh-Lie-structure.     

Modular invariance for interacting bosonic strings at finite temperature

We study the finite temperature string path integral introduced by Polchinski [1]. It is shown that on an arbitrary genus world sheet all windings of the fields around the compact time direction can be rotated into a single cycle. The modular invariance of this result is demonstrated.