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We show that in a four-dimensional space–time a complex scalar field can be associated with a one-dimensionally extended object, called a charged string. The string is said to be charged because the complex scalar field describing it interacts with an electromagnetic field. A charged string is characterized by an extension of the symmetry group of the charge space to a group of stretch rotations. We propose relativistically invariant and gauge-invariant equations describing the interaction of a complex scalar field with an electromagnetic field, and each solution of them corresponds to a charged string. We achieve this by introducing the notion of a charged string index, which, as verified, takes only integer values. We establish equations from which it follows that charged strings fit naturally into the framework of the Maxwell–Dirac electrodynamics.

The fermionic Neveu–Schwartz–Ramond string has a hidden N=2 superconformal symmetry on the worldsheet. Using an isomorphism of the N=2 superconformal algebra, we show how to obtain a subspace of physical string states on which the super-Poincare group acts. The proposed construction is an alternative to the GSO projection in string theory.

We review papers on a new method for quantizing the Yang-Mills field applicable both in perturbation theory and beyond it. We show that in the modified formulation of the Yang-Mills theory leading to a formal perturbation theory that coincides with the standard one, there exist soliton solutions of the classical equations of motion.

We discuss the possibility of applying a purely ghost kinetic operator in open string field theory from the perspective of a modern analytic method based on the KBc subalgebra. A purely ghost kinetic operator is obtained as a result of gauge fixing string field theory around the identity-based tachyon vacuum solution. We show that the obtained kinetic operator is not equivalent to the midpoint insertion of a conformal ghost, to which an extensive literature is devoted. We also show that the equation of motion does not admit nontrivial solutions.

We obtain regularized adelic formulas for gamma and beta functions for fields of rational numbers and the one-class quadratic fields and arbitrary quasicharacters (ramified or not). We consider applications to four-tachyon tree string amplitudes, generalized Veneziano amplitudes (open string), perturbed Virasoro amplitudes (closed string), massless four-particle tree open and closed superstring amplitudes, Ramond-Neveu-Schwarz superstring amplitudes, and charged heterotic superstring amplitudes. We establish certain relations between different string and superstring amplitudes.

We discuss a new, simple analytic solution for tachyon condensation in open string field theory. In particular, the new solution requires no regularization or “phantom term,” and the proof of Sen’s first conjecture requires only a few lines of calculation.

We review recent achievements and open questions in string field theory. We comment on the history of the construction of the covariant gauge-invariant string field formulation and briefly consider possible applications of string field theory in D-brane physics and cosmology.

We construct a sequence of new nilpotent BRST charges in the Ramond-Neveu-Schwarz superstring theory based on the hierarchy of found local gauge symmetries. These gauge symmetries are in turn related to global α-symmetries in the space-time forming a noncommutative ring. The constructed BRST charges are presumably connected with the superstring dynamics in a curved space-time with an AdS-type geometry.

Special perturbative pure gauge solutions parameterized by a pair of wedge states are parts of the nontrivial (not purely gauge) tachyon solutions of the cubic fermionic string field theory describing the non-BPS brane true vacuum. We demonstrate explicitly that for the large parameter of the perturbation expansion, these pure gauge configurations are no longer solutions of the equations of motion. We show that this problem is solved by adding an extra term that is just the term needed for the first Sen conjecture to hold.

We demonstrate that vacuum solutions in the Neveu-Schwarz field theory of a fermionic string incorporating the GSO(−) sector are naturally related to the zero-curvature representation in a graded space of special form. We use the same representation to describe the equivalence of the cubic and nonpolynomial theories with the GSO(−) sector also taken into account.

Field theories which violate the null energy condition (NEC) are of interest for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter $w, Comment: 13 pages, Latex, 1 figure

We construct a dark energy model with a phantom scalar field, a standard scalar field, and a polynomial potential inspired by string field theory. We find a two-parameter set of exact solutions of the Friedmann equations. We find a potential satisfying the conditions obtained from the string theory and such that at large times, some of the exact solutions correspond to the state parameter wDE > −1 while the others correspond to wDE < −1. We demonstrate that the superpotential method is very effective for seeking new exact solutions.

We investigate the anomalous dimensions of (super)conformal Wilson operators in the weak-and strong-coupling regimes using the integrability symmetry on both sides of the gauge/string correspondence. We study the origin of the single-logarithmic asymptotic behavior of long operators/strings in the limit of large Lorentz spin.

We reexamine the oscillator level truncation method in the bosonic String Field Theory (SFT) by calculation the descent relation =Z_3, Comment: 21 pages, 10 figures, Latex

We find asymptotic expansions in the “string mass” μ for μ-deformed Γ-functions and Neumann coefficients characterizing the three-string vertex in the light-cone gauge of the field theory of open superstrings on a maximally supersymmetric pp-wave background.

We take one more step in formulating the theory of non-Abelian two-tensor fields: we find gauge transformation rules and the curvature tensor for them. To define the theory, we use the surface exponential. We derive a differential equation for the exponential and attempt to formulate its definition as a matrix model. We discuss applications of our construction to the Yang-Baxter equation for integrable models and to string field theory.

We investigate arbitrary small perturbations of the uniform rotation of a rectilinear relativistic string with massive ends. Two classes of such perturbations with different spectra of eigenfrequencies have the form of stationary waves and correspond to string oscillations in the rotation plane and in the orthogonal direction. These states are represented by the Fourier series used to quantize string excitations in the linear neighborhood of the classical rotation. These string oscillations can be used to describe daughter Regge trajectories in the framework of the considered model.

We assume that QCD can be effectively described with stringlike variables and that this string is approximately represented by a Nambu–Goto or Polyakov string in some energy region. But to overcome the long-standing problems with the behavior of hadronic string amplitudes at low energies, the string is built over the correct (chirally noninvariant) QCD vacuum using a boundary interaction with background chiral fields associated with pions. Making this interaction compatible with the conformal symmetry of the string and with the unitarity constraint on chiral fields, we reconstruct the equations of motion for the latter and, furthermore, recover the Lagrangian of a nonlinear sigma model of pion interactions. We obtain the chiral structural constants of Gasser and Leutwyler in the next-to-leading order in the derivative expansion. The estimated coefficients fit the phenomenological values well.

We find all independent classical solutions for the three-mode Nambu–Goto string. We investigate the geometry of the closed curves obtained. Canonical quantization is performed for a part of the solutions obtained. We consider the spectrum of the quantum states obtained. It is consistent with the experimental masses and quantum numbers of mesons corresponding to glueballs. The leading Regge trajectory of the obtained states is consistent with the available data on the Pomeron trajectory.

We discuss the derivation of string effective actions for tachyons and massless modes within the sigma-model approach. We mostly consider the open string case, demonstrating that the renormalized partition function of the boundary sigma model gives the effective action for the massless vector and tachyon in the derivative expansion. We give a manifestly gauge-invariant definition of Z(T,A) in the non-Abelian Neveu–Schwarz–Ramond (NSR) open string theory and verify that its derivative reproduces the tachyon beta function in a particular scheme. We also comment on the derivation of similar actions for tachyons and massless modes in the closed bosonic and the NSR string theories.

Classical three-dimensional relativistic string theory is considered in terms of world sheet quadratic forms. Taking the second quadratic form, not only the first one, into account is essential. A system of nonlinear evolution equations describing the string dynamics at the surface of primary constraints in a conformally invariant manner is derived. The results are generalized to the four-dimensional case.

The bosonic string is investigated using the approach to 4D string dynamics previously proposed by the author. The physical states and the mass spectrum are constructed. The scale invariance of the theory results in the linear dependence of the squared mass μ2 on the “spin” $$\hbar \sqrt {s(s + 1)}$$ .

In this paper, consideration is given to a baryon model in which three material points (quarks) are pairwise connected by relativistic strings forming a curvilinear triangle. For this model, we found and studied classical solutions corresponding to a uniform rotation of the system in a plane about the center of mass. Along with the simplest state—a rotating curvilinear triangle with smooth sides—there can be more complicated configurations characterized by the motion, at the velocity of light, of some interior massless points of the string. In the limit, the closed string takes the form of a rotating hypocycloid as the quark masses tend to zero.

A new formulation for the action of the Nambu-Goto string moving in curved space-time is studied. The action contains a two-dimensional “cosmological” world-sheet term multiplied by a tension parameter. It is shown that when treating this cosmological term as a perturbation, nonlinear equations for the string can be linearized. It is argued that in the zeroth-order approximation with respect to the tension, strings and membranes can be considered as dominant gravitation sources for the Friedmann universe with κ=0.

In the phase space of an open bosonic string, finite-dimensional submanifolds that admit anomaly-free quantization in d=4 are studied.

The general scheme for covariant quantization of the string theory in the previously introduced nonstandard Hamiltonian formulation is proposed. The particular case of a bosonic string is studied in detail and the Regge spectrum is found.

The quantum string theory in the indefinite (pseudo-Hilbert) Fock representation is considered. It is shown that all anomalies in the four-dimensional theory of an open bosonic string are canceled for a particular choice of the vacuum state. Then the algebra of the reparametrization symmetry (in the covariant approach) and the algebra of rotations (in the light-cone gauge) become closed. The indefiniteness of the space of states leads to some nonphysical properties of the theory. Modifications of the model under consideration, which are necessary to construct a more realistic theory, are discussed.

A description of the motions of a relativistic string with massive ends (for the model with a finite mass on the first end and an infinite mass on the second end) is proposed. This approach uses the expansion of the string world surface into a series that is not reduced to the ordinary Fourier series due to the nonlinearity of the problem. The state equation of the string is derived from the mass shell condition for its end. The string motions are classified, allowing linearization of the boundary condition by a natural parametrization of the trajectory of the moving end. The set of such world surfaces is shown to be limited; for the special cases of 2+1 - and 3+1-dimensional Minkowski spaces, all of them reduce to a helicoid.

In this paper, the classical dynamics of a D=1+3 string with spin degree of freedom is described in terms of nonstandard Hamiltonian variables.

A relativistic quantum model is suggested in which the Regge trajectories can grow faster than linearly. The model is a rigid string with a Lagrangian given by an exponential function of the string world-sheet curvature. Exactly solvable generalizations of the model are considered.

A closed bosonic string in a curved affine—metric spacetime is considered as an example of dissipative quantum field theory. The conformal anomaly of the trace of the energy—momentum tensor for the string on the affine—metric manifold is investigated. The two-loop metric beta function for the two-dimensional nonlinear dissipative sigma model is calculated. Examples of nonflat manifolds that lead to ultraviolet-finite sigma models are found.

A consistent scheme for quantizing anomalous theories that takes into account explicitly a procedure of ultraviolet regularization is proposed. Chiral electrodynamics in two and four dimensions and string theory are considered in the framework of this scheme.