Generalization of general relativity to the space of closed strings

A geometrical string field theory is constructed on the space of bosonic closed strings. Einstein gravity is reproduced in a part of the massless sector at the level of the classical lagrangian.     

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.     

Quantum gravitational bremsstrahlung: massless versus massive gravity

The massive spin-2 quantum gauge theory previously developed is applied to calculate gravitational bremsstrahlung. It is shown that this theory is unique and free from defects. In particular, there is no strong coupling if the graviton mass becomes small. The cross sections go over smoothly into the ones of the massless theory in the limit of vanishing graviton mass. The massless cross sections are calculated for the full tensor theory.     

On the conjectured transition of black holes into strings

It is argued that if black holes change into strings in the last stage of their evaporation, as has been conjectured, they will go into massless strings directly rather than via an intermediate state containing a massive string.     

Nondecoupling of maximal supergravity from the superstring

We consider the conditions necessary for obtaining perturbative maximal supergravity in d dimensions as a decoupling limit of type II superstring theory compactified on a (10-d) torus. For dimensions d=2 and d=3, it is possible to define a limit in which the only finite-mass states are the 256 massless states of maximal supergravity. However, in dimensions d>or=4, there are infinite towers of additional massless and finite-mass states. These correspond to Kaluza-Klein charges, wound strings, Kaluza-Klein monopoles, or branes wrapping around cycles of the toroidal extra dimensions. We conclude that perturbative supergravity cannot be decoupled from string theory in dimensions>or=4. In particular, we conjecture that pure N=8 supergravity in four dimensions is in the Swampland.     

Heterotic string theory: (II). The interacting heterotic string

The theory of interacting heterotic strings is presented. Vertex operators are derived in both the bosonic and fermionic formulations of the theory and are shown to be consistent with gauge invariance, Lorentz invariance, and supersymmetry. Three- and four-point amplitudes for the scattering of massless string states are calculated and used to derive the low-energy field theory limit of the heterotic string. Divergences in string theories are discussed and it is shown that one-loop heterotic string amplitudes are finite and modular invariant only for gauge group E₈×E₈ or spin (32)/Z₂.     

Spontaneous dynamical breaking of gauge symmetry in dual models

The consequences of gauge invariance are re-examined in dual models with unit intercept when the dimension of space-time has the maximum value compatible with the absence of ghosts. In that case, reggeon-reggeon bound states of zero mass are formed already at second order of perturbation theory. Gauge invariance no longer guarantees that the initially massless SU(3) singlet vector meson remains massless, and the mixing between the reggeon and pomeron sectors of the model yields a massive unitary singlet vector meson already at order g². A Lagrangian model which exhibits similar features to the dual situation is discussed.     

Nonrotating cosmic strings interacting with gravitational waves in Einstein-Maxwell-dilaton gravity

We present methods for the construction of exact diagonal cylindrically symmetric solutions in a four dimensional low energy limit of string theory, the Einstein-Maxwell-dilaton gravity. The methods allow us to generate exact string backgrounds from known solutions to the equations of Einstein or Einstein gravity coupled to a massless scalar field. We also give and analyze explicit examples of such solutions. It is shown that they are free of curvature singularities,(quasi)regular on the axis of symmetry, asymptotically flat and describe nonrotating cosmic strings interacting with gravitational, dilaton and electromagnetic waves.     

Massive self-duality solution associated with invariant one-forms

A massive self-duality solution associated with invariant 1-forms is presented. At the zero mass limit the massive self-dual theory of the SO(3) gauge group on 4 dimensions cannot be reduced to that of massless self-duality.In such a case the self-dual connection turns to the flat connection and one cannot obtain a massless theory in such an approach.     

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.     

Massless QCD and chiral symmetry breaking

It is well known that chiral symmetry is spontaneously broken in QCD. To relate this fact to non-perturbative features of the theory, like instantons, we start with a massless lagrangian and perform a non-linear chiral colored singlet transformation on the quark fields which yields (by means of Fujikawa's method) essentially two terms in the lagrangian. First a quark mass term induced by instantons and secondly a coupling between pseudoscalar mesons and the axial anomaly. Ward-Takahashi identities can be derived. To clarify the presence of this induced mass term we calculate its first perturbative part up to the two-loop level.     

Renormalization of the Mass Gap

We have explicitly shown that QCD is the color gauge invariant theory at non-zero mass gap as well. It has been defined as the value of the regularized full gluon self-energy at some finite point. The mass gap is mainly generated by the nonlinear interaction of massless gluon modes. All this allows one to establish the structure of the full gluon propagator in the explicit presence of the mass gap. In this case, the two independent general types of formal solutions for the full gluon propagator as a function of the regularized mass gap have been found. The nonlinear iteration solution at which the gluons remain massless is explicitly present. The existence of the solution with an effective gluon mass is also demonstrated.     

On the relation between the Abelian Higgs model and the spontaneously broken massless scalar electrodynamics

An analysis is made of the connection between the “massless” field theories, in the presence of the Coleman-Weinberg phenomenon and the corresponding models with a “negative mass” term as origin of the spontaneous breakdown. For the very interesting case of an Abelian gauge theory, i.e. the Higgs model, we find the conditions for the parameters of the theory which make it equivalent to the spontaneously broken scalar massless electrodynamics. The properties of the effective potential in this limit are studied.     

Massive Nordström scalar (density) gravities from universal coupling

Both particle physics and the 1890s Seeliger–Neumann modification of Newtonian gravity suggest considering a “mass term” for gravity, yielding a finite range due to an exponentially decaying Yukawa potential. Unlike Nordström’s “massless” theory, massive scalar gravities are strictly Special Relativistic, being invariant under the Poincaré group but not the conformal group. Geometry is a poor guide to understanding massive scalar gravities: matter sees a conformally flat metric, but gravity also sees the rest of the flat metric, barely, in the mass term. Infinitely many theories exhibit this bimetric ‘geometry,’ all with the total stress–energy’s trace as source. All are new except the Freund–Nambu theory. The smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities. The ease of accommodating electrons, protons and other fermions using density-weighted Ogievetsky–Polubarinov spinors in scalar gravity is noted.     

All the fundamental massless fields in bosonic string theory

A systematic analysis of the massless fields in the mass spectra of bosonic strings is carried in arbitrary spacetime dimension D > 2. The emphasis is put on the derivations of their propagators, their polarization aspects and the underlying constraints involved. The treatment is given, in the presence of external sources, in the celebrated Coulomb gauge for the second rank tensors and vector fields, which ensures positivity – a result which is also established in the process. No constraints are imposed on the external sources so that their components may be varied independently generating complete expressions for the propagators. This latter condition is an important one in the generation of dynamical theories with constraints involving such modifications as Faddeev‐Popov factors.     

Dual-resonance models

Dual-resonance models are treated both as S-matrix theories and as systems of interacting strings. We show how Veneziano was able to construct a dual four-point amplitude with narrow resonances and rising Regge trajectories. The construction is generalized to the N-point amplitude in the manifestly dual manner suggested by Koba and Nielsen. We develop the operator formalism which exhibits the factorization property of the above amplitude. The related questions of ghost elimination and null states are discussed. Models with extra degrees of freedom and, in particular, the Neveu-Schwarz-Ramond model with spin, are treated. The latter model has a quark-line spectrum of mesons, but it possesses massless vector mesons and fermions. It is shown how the operator formalism is related to a quantized string. The theory of such a string is developed, with particular emphasis on the ghost-free “Coulomb-gauge” quantization. By constructing theories of interacting strings, we reproduce the dual-model S-matrix. A brief account is given of the theory of loops, in which one attempts to improve on the narrow-resonance model in a perturbative manner.     

EXACT SOLUTIONS OF CLASSICAL SCALAR FIELD EQUATIONS

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first-order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.     

Direct production of lightest Regge resonances

We discuss direct production of Regge excitations in the collisions of massless four-dimensional superstring states, focusing on the first excited level of open strings ending on D-branes extending into higher dimensions. We construct covariant vertex operators and identify “universal” Regge states with the internal parts either trivial or determined by the world-sheet SCFT describing superstrings propagating on an arbitrary Calabi–Yau manifold. We evaluate the amplitudes involving one such massive state and up to three massless ones and express them in the helicity basis. The most important phenomenological applications of our results are in the context of low-mass string (and large extra dimensions) scenarios in which excited string states are expected to be produced at the LHC as soon as the string mass threshold is reached in the center-of-mass energies of the colliding partons. In order to facilitate the use of partonic cross sections, we evaluate them and tabulate for all production processes: gluon fusion, quark absorbing a gluon, quark–antiquark annihilation and quark–quark scattering.     

Interacting Singletons

There is a chance that singleton fields, that in the context of strings and membranes have been regarded as topological gauge fields that can interact only at the boundary of anti-De Sitter space, at spatial infinity, may have a more physical manifestation as constituents of massless fields in spacetime. The composite character of massless fields is expressed by field-current identities that relate ordinary massless field operators to singleton currents and stress-energy tensors. Naive versions of such identities do not make sense, but when the singletons are described in terms of dipole structures, then such constructions are at least formally possible. The new proposal includes and generalizes an early composite version of QED, and includes quantum gravity, super gravity and models of QCD. Unitarity of such theories is conjectural.