Classical and Quantized Tensionless Strings

{}From the ordinary tensile string we derive a geometric action for the tensionless ($T=0$) string and discuss its symmetries and field equations. The Weyl symmetry of the usual string is shown to be replaced by a global space-time conformal symmetry in the $T\to 0$ limit. We present the explicit expressions for the generators of this group in the light-cone gauge. Using these, we quantize the theory in an operator form and require the conformal symmetry to remain a symmetry of the quantum theory. Modulo details concerning zero-modes that are discussed in the paper, this leads to the stringent restriction that the physical states should be singlets under space-time diffeomorphisms, hinting at a topological theory. We present the details of the calculation that leads to this conclusion.Comment: 34 pages, Latex, USITP 93-1

Schild's Null Strings in Flat and Curved Backgrounds

Schild's null (tensionless) strings are discussed in certain flat and curved backgrounds. We find closed, stationary, null strings as natural configurations existing on the horizons of spacetimes which possess such null hypersurfaces. Examples of these are obtained in Schwarzschild and Rindler spacetimes. A dynamic null string is also identified in Rindler spacetime. Furthermore, a general prescription (with explicit examples) is outlined by means of which null string configurations can be obtained in a large class of cosmological backgrounds.Comment: RevTex 3.0, 14 Pages, no figure

Null Branes in Curved Backgrounds

We consider null bosonic p-branes in curved space-times. Some exact solutions of the classical equations of motion and of the constraints for the null membrane in general stationary, axially symmetrical, four dimensional, gravity background are found.Comment: 19 pages, LaTeX, no figures. Extended version. To appear in Phys. Rev.

Tree-Level Unitarity Constraints on the Gravitational Couplings of Higher-Spin Massive Fields

We analyse the high-energy behavior of tree-level graviton Compton amplitudes for particles of mass m and arbitrary spin, concentrating on a combination of forward amplitudes that will be unaffected by eventual cross- couplings to other, higher spins. We first show that for any spin larger than 2, tree-level unitarity is already violated at energies well below the Planck scale M, if m << M. We then restore unitarity to this amplitude up to M by adding non-minimal couplings that depend on the curvature and its derivatives, and modify the minimal description - including particle gravitational quadrupole moments - at scales O(1/m).Comment: 12 pages (Latex file, needs FEYNMAN macros), IASSNS-HEP-94/63, NYU-TH-94/05/01, CERN-TH.7388/9

Space-Time Symmetries of Quantized Tensionless Strings

The tensionless limit of the free bosonic string is space-time conformally symmetric classically. Requiring invariance of the quantum theory in the light cone gauge tests the reparametrization symmetry needed to fix this gauge. The full conformal symmetry gives stronger constraints than the Poincar\'e subalgebra. We find that the symmetry may be preserved in any space-time dimension, but only if the spectrum is drastically reduced (part of this reduction is natural in a zero tension limit of the ordinary string spectrum). The quantum states are required to be symmetric ({\it i.e.} singlets) under space-time diffeomorphisms, except for the centre of mass wave function.Comment: 15pp, plain latex, USITP-92-

String Tension and the Generation of the Conformal Anomaly

The origin of the string conformal anomaly is studied in detail. We use a reformulated string Lagrangian which allows to consider the string tension $T_{0}$ as a small perturbation. The expansion parameter is the worldsheet speed of light c, which is proportional to $T_{0}$ . We examine carefully the interplay between a null (tensionless) string and a tensionful string which includes orders $c^{2}$ and higher. The conformal algebra generated by the constraints is considered. At the quantum level the normal ordering provides a central charge proportional to $c^{2}$. Thus it is clear that quantum null strings respect conformal invariance and it is the string tension which generates the conformal anomaly.Comment: More references are included. Final version, to appear in Phys.Rev.D. 6 pages, LaTex, no figure

Null Branes in String Theory Backgrounds

We consider null bosonic p-branes moving in curved space-times and develop a method for solving their equations of motion and constraints, which is suitable for string theory backgrounds. As an application, we give an exact solution for such background in ten dimensions.Comment: 11 pages, LaTeX. Final version, to appear in Phys. Rev.

Small E8E_8 Instantons and Tensionless Non-critical Strings

T-duality is used to extract information on an instanton of zero size in the $E_8\times E_8$ heterotic string. We discuss the possibility of the appearance of a tensionless anti-self-dual non-critical string through an implementation of the mechanism suggested by Strominger of two coincident 5-branes. It is argued that when an instanton shrinks to zero size a tensionless non-critical string appears at the core of the instanton. It is further conjectured that appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions in much the same way as massless particles do in four dimensions.Comment: 22 pages, Latex, two figures added, reference added, We also added a discussion on new phase transitions in six dimensions. The appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions similarly to the appearance of massless particles at special points in the moduli space in four dimensional theorie