Null String Research Articles

Strings in strong gravitational fields

We study string propagation in curved space-time. In such a problem, the equations of motion and the string constraints are nonlinear and difficult to solve. We propose here a systematic expansion in c, the world-sheet speed of light, to solve the string dynamics. Since c is proportional to the string tension, this amounts to a large α' expansion. To zeroth order each point of the string moves along a null geodesic (null string), while the first order correction incorporates the string dynamics. As an illustration we apply our formalism to the Robertson-Walker geometry. In this case, it turns out that the string expands or contracts at the same rate as the whole universe.

Quantization of null spinning strings with U(1) gauge symmetry

The authors describe null spinning strings with U(1) gauge symmetry in terms of a phase-space Langrangian and then quantize it in the light-cone gauge. With normal ordering they come to the conclusion that the critical dimension is D=2.

BFV quantization for null strings

We calculate the propagator for null bosonic strings in a covariant way by using the Batalin-Fradkin-Vilkovisky formalism.

The tension as perturbative parameter in string theory

The author proposes an approach to string theory where the zero-order theory is the null string. An explicit form of the propagator for the null string in the momentum space is found. Considering the tension as a perturbative parameter, the perturbative series is completely summable and the propagator of the bosonic open string with tension T is found.

Null spinning strings

We quantize in detail the closed string with vanishing tension, the null closed string. For Weyl ordering of quantum operators, the spectrum is continuous and there is no critical dimension. For normal ordering, however, the usual critical dimension holds and the spectrum is finite: the field content is the same as in the field theory (infinite tension) limit of usual (closed) strings. The content of bosonic null strings is massless gravity. We carry through the local supersymmetrization of this system and find similar conclusions, normal ordered null spinning strings contain in their spectrum only the massless supergravity multiplet. However, normal ordered bosonic null strings do not have a consistent quantum interpretation, whereas null spinning strings do. It points to the likely origin of some spontaneous symmetry breakdown which generates a non-zero tension, and an infinite tower of massive states. We also consider the hamiltonian formalism for quantum null (super)strings.

Phase-space Lagrangians for null spinning strings

The striking fact that normal-ordered null strings have the same critical dimension as their usual non-zero tension siblings can be understood from the observation that one must, in the tensionless case, keep all the conjugate momenta as independent dynamical variables, thus doubling the number of physical degrees of freedom. The fermionic momenta give rise to a second-class constraint which cannot be solved covariantly, but can be successfully incorporated into the first-class constraint algebra after gauge-fixing. The ghost contributions to the anomaly consist oftwo b−c (and alsotwo β−γ systems in the supersymmetric case), of the single Virasoro sub(super)algebra for the closed null (spinning) string. In the appropriate gauge, the null (super)string is (super)chiral.

Statistical mechanics of null strings

In this paper we study the behaviour of a gas of null (tensionless) strings from the point of view of statistical mechanics. The interest in the study of null strings, apart from the intrinsic one, lies in the connection that can be made between null strings and strings at the Hagedorn temperature. We find that free energy and pressure can be defined, although, even in the microcanonical approach, temperature and entropy cannot be properly introduced. We also calculate the equation of state for a gas of null strings, and find it to be similar to the one of a gas of massless particles.

Interaction of null strings and null membranes with antisymmetric tensor fields

The interaction of null strings and null membranes with an arbitrary background T lm… n ( x) in (2 + 1) and (3 + 1) dimensions describes by Means of the Wess-Zumino-like actions are studied. Their equations of motion are exactly integrated. On the classical level it is shown that the contribution of antisymmetric fields to the equations of motion is compensated by the reparametrizations of the world hypersurfaces of null strings and null membranes.

Field theory of null strings and p-branes

In analogy with the Feynman-Landau propagator for the massless particle, we find expressions for the field theory propagators of null strings and p-branes, as well as the corresponding supersymmetric versions. These null propagators are presumably useful building blocks for the propagators of the “tensionful” theories, again in analogy with the massive particle.

FINITENESS AND DECOUPLING IN OPEN STRING THEORIES

Quantum consistency of open string theories is considered at the one-loop level, using a unified and consistent regularization of all divergences. Finiteness of all amplitudes with open string states is shown to be possible for any SO (n) or USp (n) gauge group. Two consequences of the nonunitarity of tachyonic theories are discussed; the presence of unphysical cuts in amplitudes and the nondecoupling of null states. If not for contributions of the open string tachyon, decoupling of all null open bosonic string states would be obtained for SO (2D/2) independently of the regularization, corresponding to vanishing tadpoles of unphysical closed string states.

Superstrings with zero tension

The superstring in the limit of vanishing tension is analyzed with the help of a phase space lagrangian. We show that our formulation is the supersymmetric extension of Schild's null string and that all the symmetries of the standard Green-Schwarz theory are maintained. The null superstring thus arises as a new theoretical laboratory, its complexity between the usual superstring and the massless superparticle. Its canonical quantization is carried through in detail.

Quantum null (super)strings

Null strings are the analog of massless particles, namely strings with zero tension or infinite slope. We present the supersymmetric extension of the null bosonic string constraint algebra and, in order to quantize covariantly, construct the corresponding BRST charge. We find that the null supersymmetric (bosonic) string is quantum consistent only in D = 10 (D = 26). The anomalies are generated only in the single Virasoro subalgebra associated to the tangenial direction.

Deviating congruences of null strings in a certain class of H-spaces of algebraic N type

A certain class of H-spaces of algebraic N type is studied with the main emphasis put onto the problem of deviating congruences of selfdual null strings. A detailed description of such congruences and the related objects is presented.

Double Kerr–Schild equivalence and hyperheavens

Double Kerr–Schild equivalence of hyperheavens is studied within a spinorial formalism based on the fact of the existence of a congruence of self-dual null strings. In particular, it is shown that a given hyperheavenly metric structure generates all members of the corresponding equivalence class in terms of a certain spinor field and the generalized key function subject to the generalized hyperheavenly equation. The treatment is manifestly covariant: no coordinates are employed. Finally, a link with the classical results on hyperheavens (Plebański and Robinson [J. F. Plebański and I. Robinson, Phys. Rev. Lett. 37, 493 (1976)] and Finley and Plebański [J. D. Finley, III and J. F. Plebański, J. Math. Phys. 17, 2207 (1976)]) is established.

On gauge fields with sources

It is shown that in an algebraically special space-time that admits a congruence of null strings, the Yang–Mills equations with sources reduce to a pair of nonlinear first-order differential equations for two matrices, provided that the gauge field is aligned with the congruence. In the case where the current is tangent to the null strings, the gauge field is determined by a matrix potential that has to satisfy a second-order differential equation with quadratic nonlinearities. As an example of this case, the Yang–Mills–Weyl equations are reduced, assuming that the multiplet of Weyl neutrino fields are also aligned with the congruence, and a reduced form of the Einstein–Yang–Mills–Weyl equations is also given.

Quantization of the null string and absence of critical dimensions

A null or Schild string is a string each point of which classically moves with the speed of light. We consider the problem of quantization of a free null string. Contrary to the case of known string theories, Lorentz invariance does not require any critical spacetime dimension for the null string. Nilpotency of the BRST charge confirms this result.

Null vectors, spinors, and strings

It is shown how, in the frame of the Cartan-conception of spinors, the old theorems onminimal surfaces, as generated from null-curves, formulated by Enneper-Weierstrass (1864–1866) for 3-dimensional ordinary space, and by Eisenhart (1911) for 4-dimensional space-time, may be reformulated in terms ofcomplex 2- and 4-component projective spinors respectively. For the correspondingreal (Majorana) spinors instead the same procedure naturally leads tostrings in 3-dimensional and 4-dimensional space-time (ℝ2, 1 and ℝ3, 1). It is suggested that this close connection with Cartan-spinors, and the corresponding (projective) null-geometry, may be the clue for understanding the fundamental nature of strings.

θ-vacua, fermions from bosons, solitons and Wess-Zumino terms in string models

String models are presented in a new formalation which shows that the conventional string admits the analogue of the QCD θ-vacuum and that Schild's null string can be quantized using either bosonic or fermionic states only. The latter is also shown to contain a soliton and to admit the analogue of a Wess-Zumino term. The new formulation reveals the possibility of several string models, permits their classification (in a way similar to the classification of point particles in representations of the Poincaré group) and suggests a novel description of spinning strings.

Gauge fields in algebraically special space-times

It is shown that in an algebraically special space-time which admits a congruence of null strings, a source-free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second-order differential equation with quadratic nonlinearities. The Einstein–Yang–Mills equations are then reduced to a scalar and two matrix equations. In the case of self-dual gauge fields in a self-dual space-time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Bäcklund transformations is demonstrated. All the results apply for an arbitrary gauge group.

The optics of null strings

The general ‘‘optical theory’’ of congruences of totally null strings is studied within complexified general relativity, employing the spinorial formalism, with the emphasis on the role of the Sommers vector. The results obtained yield a deeper geometric interpretation of the ‘‘complexified anatomy’’ of the fundamental Goldberg–Sachs theorem.