Strings in the pp-wave background from membrane

In this Letter we study strings with quantized masses in the pp-wave background. We obtain these strings from the membrane theory. For achieving to this, one of the membrane and one of the spacetime directions will be identified and wrapped. From the action of strings in the pp-wave background, we obtain its mass-dual action. Some properties of the closed and open strings in this background will be studied.     

Evolution of Nielsen-Olesen''''s String from Chern-Simons Field Theory

We study the topology of Nielsen-Olesen's local field theory of single dual string. Based on the Chern-Simons field theory in three dimensons, we find many strings that can form world sheets in four dimensions. These strings have important relation to the zero point of the complex scalar field. These world sheets of strings can be expressed by the topological invariant number, Hopf index, and Brower degree. Nambu-Goto's action is obtained from the Nielsen's action definitely by using o-mapping theory.     

Evolution of Nielsen-Olesen's String from Chern-Simons Field Theory

We study the topology of Nielsen-Olesen's local field theory of single dual string. Based on the Chern-Simons field theory in three dimensons, we find many strings that can form world sheets in four dimensions. These strings have important relation to the zero point of the complex scalar field. These world sheets of strings can be expressed by the topological invariant number, Hopf index, and Brower degree. Nambu-Goto's action is obtained from the Nielsen's action definitely by using φ-mapping theory.     

Spacelike brane actions

We derive effective actions for "spacelike branes" (S-branes) and find a solution describing the formation of fundamental strings in the rolling tachyon background. The S-brane action is a Dirac-Born-Infeld action for Euclidean world volumes defined in the context of time-dependent tachyon condensation of non-BPS (Bogomol'nyi-Prasad-Sommerfield) branes. It includes gauge fields and, in particular, a scalar field associated with translation along the time direction. We show that the BIon spike solutions constructed in this system correspond to the production of a confined electric flux tube (a fundamental string) at late time of the rolling tachyon.     

A model regularizing gauge fields in the strong coupling region

We propose a model using an effective lagrangian for bilocal gauge extended fields, looking somehow as an average over all open strings with fixed end points. The locality of the action is retrieved as a range parameter, which acts as a regulator, shrinks, and the Yang-Mills theory is recovered in this limit. The system is invariant by rotation and translation, generalizes lattice gauge theories and allows regularized strong coupling expansions for Yang-Mills field theory.     

An Area-Preserving Action of the Modular Group on Cubic Surfaces and the Painlevé VI Equation

We construct an area-preserving action of the modular group on a general 4-parameter family of affine cubic surfaces. We present a geometrical background behind this construction, that is, a natural symplectic structure on a moduli space of rank two linear monodromy representations over the 2-dimensional sphere with four punctures, and a natural symplectic action upon it of the braid group on three strings. Studying this action as a discrete dynamical system will be important in discussing the monodromy of the Painlevé VI equation.     

Non-commutative geometry and string field theory

An attempt is made to interpret the interactions of bosonic open strings as defining a non-cummulative, associative algebra, and to formulate the classical non-linear field theory of such strings in the language of non-commulative geometry. The point of departure is the BRST approach to string field theory. A setting is given in which there is a unique gauge invariant action, whose linearized approximation reproduces the conventional Veneziano spectrum. A derivation of conventional Veneziano model amplitudes from this gauge invariant action is sketched. Some brief comments are made about attempts to extend these results to open superstrings and to closed strings.     

Four-dimensional heterotic strings and conformal field theory

The techniques of (super) conformal field theory are applied to 4-dimensional heterotic string theories. We discuss certain aspects of 4-dimensional strings in the framework of the bosonic lattice approach such as the realization of superconformal symmetry, character valued partition functions, construction of vertex operators and ghost picture changing. As an application we compute all possible 3- and 4-point tree amplitudes of the massless fields and derive from them the low energy effective action of the massless modes. Some effects for the massless spectrum due to one-loop string effects are also mentioned.     

Noncommutative Dp-Brane in General Background Fields

We investigate the noncommutativity of open strings, attached to a Dp-brane, in the presence of the linear dilaton, tachyon, U(1) gauge field as well as constant antisymmetric B-field backgrounds. The Noncommutativity parameter, open string metric, and some special cases will be studied. The Mode-dependent noncommutativity, inspired by the tachyon field, will be discussed in detail.     

General covariance and open string interactions

It has been suggested that Witten's open string cubic interaction is independent of the background geometry. We investigate this suggestion in detail with a view to understanding the rôle of closed strings in Witten's open string field theory. The standard oscillator formulation of the vertex requires the use of a metric, if it is to be generally covariant, indicating that closed string interactions are required. However by changing to variables better suited to treating the midpoint, we show explicitly that it is possible to transform away all reference to the background metric. This supports the assertion that the cubic action (of Horowitz, Lykken, Rohm and Strominger) can also describe closed strings.     

Worldsheet instantons and a null string limit of Born–Infeld theory

For a superstring theory in four spacetime dimensions, we propose a modification of the Born–Infeld action that possesses a well-defined tensionless limit. We interpret this as describing the effective target space dynamics of null strings on a D3-brane. We argue that such a modification can be induced by nonperturbative contributions from instantons in the worldsheet σ-model describing string propagation on the brane.     

A FIELD THEORY MODEL FOR CLOSED BOSONIC STRINGS

Besed on the BRST approach to the first quantization of closed bosonic strings, we propose a gauge covariant field theory model for both free and interacting closed bosonic strings. The action is of the Chexn-Simons type and coincides with the cohomology of the BRST operators.     

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.     

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.     

A geometrical framework for dyons in the presence of the dilaton and the axion in four dimensions

The action of the bosonic sector of the effective field theory induced by heterotic strings in four dimensions, which is relevant (for instance) to the study of dyons (Shapere et al. in Mod Phys Lett A6: 2677, 1991), is re-interpreted geometrically by using the new concept of ‘D-Differentiation’. This extends the authors’ geometrical unification of the Einstein–Maxwell theory.     

The gravitational interaction of conical strings

Up to now calculations of the interaction of cosmic strings have neglected gravity. We consider the purely gravitational interactions that occur at large distances, using the conical line singularity for the gravitational field of a string. We construct spaces with multiple intersecting conical strings, that are exactly consistent with General Relativity, and which can be covered in a single Minkowski coordinate patch, using a Regge calculus type construction. We show that after two such strings pass through each other they remain connected by another string, and we derive the branching rules which govern the junction of three strings. These rules apply to conical type strings in any smoothly curved background, whether they are straight or curved, moving or stationary, and they show that, at the junction, the three strings must be as coplanar as is possible in such a space. For these results to be matched onto the short range results of Field Theory calculations, it is suggested that gravitational radiation must be introduced. This would mean that gravitation is not negligible in these interactions.     

Fine structure of strings

We show that the critical behavior of the string tension and most other important qualitative properties of strings are driven by a term in the action containing extrinsic curvatures, which is necessary to add to the Nambu-Goto term. Depending on the renormalization-group structure, strings can be “creased” (with non-zero surface tension at the critical point) or “smooth”. Candidates for both possibilities and their physical relevance are discussed.     

String picture for a model of frustrated quantum magnets and dimers

We study the effect of quantum dynamics on geometrically frustrated magnets for a transverse field Ising model at finite temperatures. We develop a microscopic derivation of the Landau-Ginzburg-Wilson action for this model and show that it can be interpreted as the free energy of a 3D elastic lattice of noncrossing strings. As a first application, we quantitatively predict the phase diagram and correlations, confirming excellently a key prediction of recent simulations about the existence of unusual phase transitions and an ordered phase. We discuss the implications of our string picture for the understanding of the effect of quenched disorder in such quantum frustrated systems.     

Nonsupersymmetric string solitons

We begin a search for nonsupersymmetric/supersymmetric dual string pairs by constructing candidate critical nonsupersymmetric strings as solitons in supersymmetric string theories. Using orbifold techniques, one can construct cosmic string solutions which lie in supersymmetric vacua but which do not fall in supermultiplets. We discuss two three-dimensional examples in detail. The effective worldsheet actions for the soliton strings have (0,2) and (1,1) supersymmetry and the correct numbers of massless bosons and fermions to be critical heterotic and type II strings, respectively.