A bosonic model for relativistic spinors

In an 11-dimensional manifold with topology ⁷ ×S ⁷ (Minkowski-space times 7-dimensional sphere) we construct a completely antisymmetrical 8-rank tensor field (equivalent to the Pauli matrices) performing a symmetry breaking so that a Lorentz-transformation must be linked with a rotation of the internal spaceS ⁷. Certain scalar fields are then described as and have the same transformation properties as relativistic 4-dimensional spinor fields.Research supported by the Commission of the European Communities (Directorate General for Science, Research and Development-Joint Research Center).     

Integrability conditions for Killing spinors

The conditions for the existence of solutions ofD _µ=±c_µ are discussed. In general, it is not sufficient to consider only the first integrability condition [D _µ,D _v ]=–2c ²_{µv}; in particular, the second integrability condition is needed to explain why, in certain cases, only for one choice of sign does a solution exist. The Killing spinor-tensors, as defined by Walker and Penrose, are shown to be the spinorial equivalent of conformal Killing tensors. Their relationship to the Killing spinors and spinor-vectors used in supergravity, is given.On leave from the Institute for Theoretical Physics of the State University of New York at Stony BrookWork supported in part by the U.S. Department of Energy under Contract No. DEAC-03-81-ER 40050 and Weingart Fellowship     

N-string,g-loop vertex for the bosonic string

We construct the N-string, g-loop vertex V_N,g for the orbital degrees of freedom of the bosonic string in terms of the first abelian differentials, the period matrix and the prime form. We also build the |g> vacuum recently discussed by many people in the framework of an operator formalism on an arbitrary Riemann surface; our expression also contains the measure that takes into account the ghost contribution.     

BRST invariant mixed string vertex for the bosonic string

We construct a BRST invariant (N + M)-string vertex including both open and closed string states. When we saturate it with N open string and M closed string physical states it reproduces their corresponding scattering amplitude. As a particular case we obtain a BRST invariant vertex for the open-closed string transition.     

Multiloop amplitudes for the bosonic Polyakov string

We provide a simple formula for multiloop amplitudes of the bosonic, closed oriented Polyakov string (in d = 26) as integrals over moduli space with respect to the Weil-Petersson measure. The integrand consists of Green functions and the determinants of laplacians acting on functions and vectors. We compute these determinants in terms of the lengths of the closed geodesics on the surface. They are finite and different from zero. The one on functions equals the derivative at 1 of the Selberg zeta function. A discussion of lengths of closed geodesics and coordinates for Teichmueller space is given.     

Tensors,spinors, and functions on the unit sphere

A representation of tensors and spinors at a point of space-time as spin and conformally weighted functions on the unit sphere is derived. Methods for performing algebraic operations on tensors and spinors in this representation are discussed.Supported in part by grants Nos. GP-35773X1 and MPS74-18020 from the National Science Foundation.     

Conformal gravity and the bosonic string

We show that the Callan et al. effective equations of motion for the bosonic closed string in a non-trivial background may not be derived only from the bosonic part of theN=1 supergravity action of Manton and Chapline, but also from just a general conformally invariant theory of gravity. In our scheme the invariance under gauge transformations of the antisymmetric tensor field turns out to be a consequence of the metricity condition.     

Modifying the bosonic string vacuum

A nontrivial string vacuum can induce effects in open bosonic string theories which can be interpreted in terms of nonlocality of the mapping of the string world sheet into spacetime. This is achieved by modifying the sum over Riemann surfaces to include boundaries on which the bosonic fields satisfy a Dirichlet condition, as well as holes with the usual Neumann condition and crosscaps. Such effects profoundly alter the large-angle behaviour of string amplitudes. With suitable normalization, they also lead to a cancellation of the one-loop divergence associated with the vacuum emission of a soft dilaton.     

Non-commutative geometry and the closed bosonic string

We propose an action for an interacting closed bosonic string. Our formalism relies heavily on ideas discussed by Witten for the open bosonic string. We also obtain the gauge fixed quantum action for the fully interacting open bosonic string.     

Pseudo-supergravity extension of the bosonic string

We construct a “pseudo-supersymmetric” fermionic extension of the effective action of the bosonic string in arbitrary spacetime dimension D. The theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order, which is sufficient in order to be able to derive Killing spinor equations in bosonic backgrounds, and hence to define BPS type solutions determined by a system of first-order equations. The pseudo-supersymmetric theory can be extended by coupling it to a Yang-Mills pseudo-supermultiplet. This also allows us to construct “α^′ corrections” involving quadratic curvature terms. An exponential dilaton potential term, associated with the conformal anomaly for a bosonic string outside its critical dimension, can also be pseudo-supersymmetrised.     

Spin content of the bosonic string

A new form is derived for the generating function, χ^[λ](x) = Σ_n=0^∞xⁿχ_n^[λ], which counts the number of times, χ_n^[λ], that the irreducible O(D − 1) rotation group representation [λ] appears at the nth mass level for the bosonic string. The derivation goes through for arbitrary old spatial dimensions, D − 1 = 2v + 1. Simplifications of the results are noted for large v and the relation to a previously obtained formula for χ^[λ](x) is explained.     

Ghost vertices for the bosonic string using the group-theoretic approach to string theory

The N-string tree-level scattering vertices for the bosonic string are extended to include anticommuting (ghost) oscillators. These vertices behave correctly under the action of the BRST charge Q and reproduce the known results for the scattering of physical states. This work is an application of the group-theoretic approach to string theory.     

Off-shell string amplitudes and singular states in bosonic string theory

The off-shell amplitudes with N external scalar particles are investigated. The dependence of the momenta is emphasized.     

Symmetries of the interacting gauge-covariant bosonic string

We derive in detail the local gauge transformations and interaction lagrangian of the second-quantized bosonic string. We verify at lowest non-trivial order in the coupling constant the gauge invariance of the interacting action, and the closure of the field transformations. This gives the structure constants of the corresponding local gauge group. This group has its generators labelled by all the string states of the theory. We show that the fermionic part of the interaction is just the overlap condition for the ghost coordinates of the three strings, multiplied by an appropriate extra ghost at the point common to the three strings. Our treatment is based on an extensive use of Goto-Naka-type overlap equations. It avoids the use of ill-defined infinite matrices or series, and can be straightforwardly extended to other string theories. We explicitly derive the conformal transformation relating the gauge-covariant three-point function to the old Caneschi-Schwimmer-Veneziano vertex. We also deal with the closed bosonic string.     

A superadditive time coordinate for the closed bosonic string

The possibility of using the moduli of ringlike domains on the world sheet to define a conformal invariant notion of time intervals for closed bosonic strings is investigated. It is demonstrated that time intervals for neighboring domains on the world sheet defined in this way in general do not add up, rather they behave superadditive.