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In this paper, we present the proof of a no-ghost theorem for the bosonic string in Nappi–Witten spacetime by the BRST-technology. The key point in this proof is to compare the characters with the signature functions, where traces are taken over the whole state space. It includes the states of Nappi–Witten string, the states of some extra unitary CFT and the conformal ghost states. Only the signature function of the Nappi–Witten string part is not trivial. Here we obtain it in a new complete basis for the states space of Nappi–Witten string. For all real number b, which is a parameter of the Nappi–Witten metric, the characters and the signature functions are exactly equivalent. Then we can state that the physical string states in Nappi–Witten group are all of non-negative norm.

The tremendous progress achieved through the study of black holes and branes suggests that their time dependent generalizations called Spacelike branes (S-branes) may prove similarly useful. An example of an established approach to S-branes is to include a string boundary interaction and we first summarize evidence for the death of open string degrees of freedom for the homogeneous rolling tachyon on a decaying brane. Then, we review how to extract the flat S-brane worldvolumes describing the homogeneous rolling tachyon and how large deformations correspond to creation of lower dimensional strings and branes. These S-brane worldvolumes are governed by S-brane actions which are on equal footing to D-brane actions, since they are derived by imposing conformality on the string worldsheet, as well as by analyzing fluctuations of time dependent tachyon configurations. As further examples we generalize previous solutions of the S-brane actions so as to describe multiple decaying and nucleating closed fundamental strings. Conceptually S-brane actions are therefore different from D-brane actions and can provide a description of time dependent strings/branes and possibly their interactions., Comment: 15 pages, 7 eps figures; invited review for Modern Physics Letters A, including new solutions for S-brane actions. v2 published version, minor typos corrected

In this paper some properties of the superstring with noncommutative worldsheet are studied. We study the noncommutativity of the spacetime, generalization of the Poincar\'e symmetry of the superstring, the changes of the metric, antisymmetric tensor and dilaton., Comment: 11 pages, Latex, no figure, a new action and some references have been added

Conformal field theory of the D1/D5 system and superstrings on AdS3 × S3 × T4 is studied with particular attention to the worldsheet fields corresponding to the T4 part. A solution to the space–time N = 4 superconformal symmetry doubling and other problems is proposed. It is argued that the relevant space–time symmetry should be based on the middle N = 4 superconformal algebra. It is discussed as to why this superconformal structure has been missed so far.

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein-like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for space–time gravity, even in the absence of other matter fields.

We attempt to construct new superstring actions with a $D$-plet of Majorana fermions $\psi^{\cal B}_A$, where ${\cal B}$ is the $D$ dimensional space-time index and $A$ is the two dimensional spinor index, by deforming the Schild action. As a result, we propose three kinds of actions: the first is invariant under N=1 (the world-sheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some non-locality because of bilinear terms of $\psi^{\cal B}_A$. The reasons why completing a Schild type superstring action with $\psi^{\cal B}_A$ is difficult are finally discussed., Comment: 12 pages, Latex, both title and abstract are changed, discussion of some relations among our results, Nambu-Goto string and super Yang-Mills theories, added. Results unchanged

Making use of the duality transformation, we derive in the Londons' limit of the Abelian Higgs model string representation for the 't Hooft loop average defined on the string worldsheet, which yields the values of two coefficient functions parametrizing the bilocal correlator of the dual field strength tensors. The asymptotic behaviors of these functions agree with the ones obtained within the method of vacuum correlators in QCD in the lowest order of perturbation theory. We demonstrate that the bilocal approximation to the method of vacuum correlators is an exact result in the Londons' limit, i.e. all the higher cumulants in this limit vanish. We also show that at large distances, apart from the integration over metrics, the obtained string effective theory (which in this case reduces to the nonlinear massive axionic sigma model) coincides with the low energy limit of the dual version of 4D compact QED, the so-called universal confining string theory. We derive string tension of the Nambu–Goto term and the coupling constant of the rigidity term for the obtained string effective theory and demonstrate that the latter is always negative, which means the stability of strings, while the positiveness of the former is confirmed by the present lattice data. These data enable us to find the Higgs boson charge and the vacuum expectation value of the Higgs field, which well-described QCD. We also study dynamics of the weight factor of the obtained string representation for the 't Hooft average in the loop space. In conclusion, we obtain string representation for the partition function of the correlators of an arbitrary number of Higgs currents, by virtue of which we rederive the structure of the bilocal correlator of the dual field strength tensors, which yields the surface term in the string effective action.

We construct a locally supersymmetric action for the scalar particle, and study its relation with the usual reparametrization invariant action. The mechanisms at work are similar to those employed in the embedding of the bosonic string into the fermionic one, originally due to Berkovits and Vafa in their search for a universal string. The simpler algebraic structure present in the particle case provides us with a guide on how to prove in a simple way, without the need of fixing the superconformal gauge, that the supersymmetric formulation of the bosonic string is equivalent to the usual one, where reparametrization invariance is the only world-sheet gauge symmetry., Comment: 8 pages, REVTEX

We examine the change induced in the worldsheet geometry of a relativistic membrane under a conformal rescaling of the spacetime metric. As the induced transformation of the intrinsic geometry is obvious, the extrinsic geometry can be transformed nontrivially. By identifying the worldsheet scalars which transform multiplicatively, we can construct actions for extended objects which are conformally invariant.

Superstring models on Weyl orbifolds are investigated in [Formula: see text] heterotic string theories. Some of the Weyl orbifold models are shown to be consistent with worldsheet supersymmetry, N=1 spacetime supersymmetry and modular invariance. Two ways of embedding in [Formula: see text] are studied and residual gauge groups are classified.

We describe a scenario for inflation in the framework of non-critical string theory, which does not employ an inflaton field. There is an exponential expansion of the volume of the Universe, induced by enormous entropy production in the early stages of cosmological evolution. This is associated with the loss of information carried by global string modes that cross the particle horizon. It is the same loss of information that induces irreversible time flow when target time is identified with the world-sheet Liouville mode. The resulting scenario for inflation is described by a string analogue of the Fokker-Planck equation that incorporates diffusion and dissipative effects. Cosmological density perturbations are naturally small., Comment: 17 pages LATEX

As an example of our noncritical string approach to microscopic black hole dynamics, we exhibit some string contributions to the [Formula: see text] matrix relating in- and out-state density matrices that do not factorize as a product of S and S† matrices. They are associated with valley trajectories between topological defects on the string worldsheet, that appear as quantum fluctuations in the space-time foam. Through their uv renormalization scale dependences these valleys cause non-Hamiltonian time evolution and suppress off-diagonal entries in the density matrix at large times. Our approach is a realization of previous formulations of nonequilibrium quantum statistical mechanics with an arrow of time.

It is known that Nambu–Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri (Rh) equation for membranes to determine if there are cusps and kinks in the worldsheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu–Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.

Exact and explicit string solutions propagating in 2+1 dimensional de Sitter spacetime are presented and physically analized. (In this case the string equations reduce to a sinh-Gordon model.) Strings generically tend to inflate or either to collapse. The world-sheet time τ interpolates between the cosmic (τ→±∞) and conformal (τ→0) times. For τ→0, the typical string instability is found, while for τ→±∞, a new string behavior appears. In that regime, the string expands (or contracts) but not with the same rate as the universe does. The string constraints select periodic solutions of the sinh-Gordon equation associated to the lower boundary of the allowed zone, therefore excluding elliptic solutions.

T-Duality invariant worldsheet string actions, recently written down by Schwarz and Sen, are coupled to the worldsheet gauge fields. It is shown that the integration of the dual coordinates gives the conventional, vector, axial and chiral, gauged string actions for the appropriate choice of the gauged isometries. Alternatively, the gauge field integration is shown to give a T-duality invariant action which matches with the corresponding results known earlier., Comment: (minor mixup in notations have been corrected), 15 pages, IP/BBSR/93-32

We have made a modification of a very heuristic relationship available in the literature between the parameter space distance and the embedding space distance on the string worldsheet. This modification along with the input of numerically determined values of the fractal dimension of the fermionic worldsheet and of the Wilson scaling dimensions of conventional ψ2 and ψ4-field theories enables a numerical calculation of the critical exponents α and β of the 3D Ising model. These values are in very good agreement with the experimental and other theoretical values.

We present a geometric interpretation for the torsion constraints in (2,0) supergravity using G-structures. This leads to a classification of the constraints as given by Ref. 1. We also present the essential torsion constraints for (p,q) geometry.

We study the properties of amplitudes in the closed string theory based on the N=2 worldsheet supergravity. The one-loop correction to the three-point amplitude is computed and compared to the effective field theory result. We discuss the peculiar kinematics arising from the (2, 2) signature of the space-time and its role in the factorization properties of the amplitudes.

We consider strings with an N=2 local superconformal symmetry on the worldsheet. The critical dimension for this theory is four (two complex dimensions) with the signature (2, 2). A Kähler function giving rise to self-dual gravity is the only physical degree of freedom of this theory. Some miraculous symmetries are observed corresponding to the exchange of worldsheet and target moduli. The open and heterotic versions of this string theory correspond to self-dual Yang-Mills fields coupled to self-dual gravity in four dimensions.

Sine-square deformation, a recently found modulation of the coupling strength in certain statistical models, is discussed in the context of two-dimensional conformal field theories, with particular attention to open/closed string duality. This deformation is shown to be non-trivial and leads to a divergence in the worldsheet metric. The structure of the vacua of the deformed theory is also investigated. The approach advocated here may provide an understanding of string duality through the worldsheet dynamics., Comment: 15 pages, 4 figures

The question "What lies beyond the Quantized String or Superstring Theory?" and the question "What lies beyond Quantum Mechanics itself?" might have one common answer: a discretized, classical version of string theory, which lives on a lattice in Minkowski space. The size a of the meshes on this lattice in Minkowski space is determined by the string slope parameter, α′.

We consider circular spinning string solutions in AdS5×T1, 1 and calculate the quantum corrections to the energy at one-loop on worldsheet. The fluctuations are given as a set of harmonic oscillators and we calculate their normal mode frequency in closed form. The sum of frequency is equal to the one-loop string energy, which through AdS/CFT correspondence corresponds to the leading order correction of the conformal dimension for long operators in Klebanov–Witten conifold gauge field theory.

It is shown that the bosonic non-linear sigma model with torsion may be reinterpreted as a non-linear sigma model formulated on an algebraically extended two-dimensional worldsheet. The torsion term arises naturally as a consequence of the extended geometry. The two models, while locally equivalent, have distinct global features.