Superstring Research Articles

Null SuperP-Branes Quantum Theory in 4-Dimensional Space-Time

A twistor-like harmonic formulation of the theory of extended supersymmetrical null objects is suggested. A new harmonic form of the action for null super string and null supermembrane with N-extended global SUSY in 4-dimensional space-time is built. A way for a covariant quantization of null super p-branes is suggested. This way unifies the harmonic approach and the BRST-BFV quantization method modified by the idea of the conversion of the second class constraints into the effective first class ones. The absence of anomalies and the quantum selfconsistency of null super p-branes, including null super membranes (p = 2), null superstrings (p = 1) and massless superparticle (p = 0) in 4-dimensional space-time are proved. For the completeness the BRST-BFV quantization of null p-brane is discussed too. The BRST-BFV quantization method is described in details using the simple example of massless particle theory. The description of a massless particle with arbitrary spin using the Lorentz-harmonic variables is suggested.

Algebraic?geometric quantization of interacting strings and superstrings

The method of algebraic-geometric quantization is used to find an explicit expression for the measure on the (super)moduli space for all possible interaction diagrams of open and closed (super)strings.

Model-building for fractional superstrings

We investigate heterotic string-type model-building for the recently proposed fractional superstring theories. We concentrate on the cases with critical space-time dimensions four and six, and find that a correspondence can be drawn between the new fractional superstring models and a special subset of the traditional heterotic string models. This allows us to generate the partition functions of the new models, and demonstrate that their number is indeed relatively limited. It also appears that these strings have uniquely natural compactifications to lower dimensions. In particular, the D c = 6 fractional superstring has a natural interpretation in four-dimensional space-time.

Fermionic strings on the compactified moduli space

On the compactified moduli space we consider theN=2,N=4 local supersymmetric string theories. It would be proven that theN=2,N=4 fermionic string theories might not develop any tachyon pole, which might imply theg-loop partition functions forN=2,N=4 fermionic string would be finite.

Number of generations and higher-dimensional monopoles

The authors give a method for the computation of the number of generations in the context of both heterotic superstring and Kaluza-Klein supergravity theories.

Supersymmetry breaking and dynamical determination of superstring parameters

The characteristics of the effective potentials coming from phenomenologically promising compactified superstring theories are examined, paying special attention to the supersymmetry breaking issue. We briefly review the status and some of the recent work on the subject and present a mechanism for generating the large gauge hierarchy by gaugino condensation effect in the case that the hidden sector possesses more than one condensate. Explicit examples based on orbifold compactification in which this is realized are also given. Minimization of the effective potential not only determines the gauge hierarchy but also fixes other important parameters of the theory, in particular the gauge coupling constant at the unification point and the expectation values of the moduli which give the size and shape of the compactified space. These get reasonable values which may, in turn, lead to a determination of the family mass hierarchy.

Negative energy in string theory

It is shown that superstring (and heterotic string) theory has negative energy solutions that asymptotically resemble toroidal compactifications with constant gauge fields. The toroidal compactifications are not supersymmetric but are tachyon free. This implies that the corresponding flat, zero energy toroidal compactifications are unstable. Instantons are presented that describe semiclassical tunnelling from these flat vacua to nonflat zero energy solutions.

N = 2 superconformal algebras and Jordan triple systems

We give a construction of N = 2 superconformal algebras over hermitian Jordan triple systems (JTS). The N = 2 superconformal algebras obtained by this method correspond to realizations over hermitian symmetric spaces, which can be compact or non- compact. Over the hermitian JTS's one can construct a large class of N = 2 superconformal algebras with central charge c = 9, which characterize the “internal sector” of the four-dimensional superstring or heterotic string theories with N = 1 space-time supersymmetry.

Hierarchical supersymmetry breaking and dynamical determination of compactification parameters by non-perturbative effects

The characteristics of the effective potentials coming from phenomenologically promising compactified superstring theories are examined, paying special attention to the supersymmetry breaking issue. We find a mechanism for generating the large gauge hierarchy by gaugino condensation effect in the case that the hidden sector possesses more than one condensate. We construct an explicit example based on orbifold compactification in which this is realized. Minimization of the effective potential not only determines the gauge hierarchy but also fixes other important parameters of the theory, in particular the gauge coupling constant at the unification point and the expectation values of the moduli which give the size and shape of the compactified space. These get reasonable values which may, in turn, lead to a determination of the family mass hierarchy.

Non-critical superstrings

We construct “space-time” supersymmetric non-critical string theories. They interpolate between the non-critical c ̂ <1 theories and the critical superstring, thus penetrating the c ̂ =1 barrier. If the matter is unitary, the theories are free of tachyons and the world-sheet is stable. We discuss some of the properties of these theories.

Towards covariantly quantized D = 10 type-II Green-Schwarz σ-models

The complete gauge algebra of all symmetries which occur in D = 10 Green-Schwarz formulations of closed superstring theories are investigated in the presence of nontrivial backgrounds. Explicit expressions for nonclosure functions required for the Batalin-Vilkovisky quantization technique are obtained. This technique is then employed to covariantly quantize the σ-model describing type II-A Green-Schwarz superstrings propagating in N = 2, D = 10 curved superspace, using a gauge-fixing fermion analogous to the one proposed recently for the quantization of the free D = 10 heterotic string. The ultraviolet properties of the one-loop d = 2 effective action are examined in some detail. In particular, we show that the violation of space-time Lorentz invariance found earlier using a Lorentz noncovariant quantization ansatz disappears in this manifestly covariant formulation.

Superinvolutions on super-Riemann surfaces and the supergeometry of type-I superstrings

The supergeometry appropriate to the perturbation theory of type-I superstrings is described, to arbitrary loop order, by means of a superinvolution on a closed super-Riemann surface. It is known that the superfields of relevant local U(1) weights restricted to be even under the superinvolution reproduce the required type-I superstring boundary conditions. Such fields can be unambiguously integrated on the world sheet. More interestingly, the ambiguity in the supermoduli integral of the string measure is shown to be removable by vacuum shifts. The constraints imposed by the superinvolution on the super-period matrix (for both even and odd spin structures) are derived and it is also shown that the gauge-fixing superdeterminant factors into two equal components.

Constraints on grand unified superstring theories

We evaluate some constraints on the construction of grand unified superstring theories (GUSTs) using higher level Kac-Moody algebras on the world-sheet. In the most general formulation of the heterotic string in four dimensions, an analysis of the basic GUST model-building constraints, including a realistic hidden gauge group, reveals that there are no E 6 models and any SO(10) models can only exist at level-5. Also, any such SU(5) models can exist only for levels 4⩽ k⩽19. These SO(10) and SU(5) models risk having many large, massless, phenomenogically troublesome representations. We also show that with a suitable hidden sector gauge group, it is possible to avoid free light fractionally charged particles, which are endemic to string derived models. We list all such groups and their representations for the flipped SU(5)×U(1) model. We conclude that a sufficiently binding hidden sector gauge group becomes a basic model-building constraint.

The relation between Kahler potentials and superpotentials in string theory

A relationship between the Kahler potential and the superpotential is shown to exist in any N=1 spacetime supersymmetric string theory possessing target space symmetries of a specific type. The relationship is explicitly constructed for the untwisted moduli and matter scalar sectors of the (2,2) symmetric Z3 orbifold, and is used to calculate the complete superpotential in terms of the Kahler potential. The authors demonstrate, within the context of conformal field theory, the existence and consistency of the required target space symmetries.

Phenomenological and cosmological consequences of gauge singlets in superstring theories

Superstring theories contain a large number of massless singlet fields. In this paper we examine their phenomenological and cosmological implications. In particular from the general constraints on their couplings we argue that many of them couple very weakly to matter fields. We further examine their impact on the big bang nucleosynthesis and derive a constraint on the number of gauge singlet fields that can be tolerated. We also consider the effects of decaying singlets on the overall mass density of the universe, entropy production and light element abundances.

Path-integral approach to anomalies at finite temperature

The non-Abelian chiral anomaly for a fermion interacting with an external vector field in any even dimension and the conformal anomaly, in the limit of flat space–time, for a self-interacting scalar field are shown to be independent of temperature using a simple path-integral approach that employs dimensional regularization. The chiral anomaly is used as an example to show that the methods used to study the dimensionally regularized anomaly at finite temperature are readily transferable to the case of ζ-function regularization. The conformal anomaly in (super) string theory at finite temperature is briefly discussed in the light of known results. Some subtleties concerning the use of infrared cutoffs in a dimensionally regularized approach to the computation of the one-loop effective action at finite temperature are considered in an appendix.

Covariant two-loop fermion emission amplitude in closed superstring theories

We calculate the two-fermion-two-boson scattering amplitude at two loops in the NSR formalism of the heterotic and type II superstring theories by using the hyperelliptic representation of the genus 2 Riemann surface and the covariant fermion emission vertex. This computation entails the use of a modular invariant combination of a Θ-function and prime forms which we prove.

Spontaneous gauge symmetry breaking in conformal theories of a four-dimensional superstring

We formulate a mechanism of spontaneous gauge symmetry breaking with continuous parameters, in the superconformal theory approach to four-dimensional superstring theories. As an example, we inspect the 1 9-model with the breaking of the gauge group SO(26). Supersymmetry is unbroken, maintaining the zero cosmological constant, and realistic gauge groups such as E 8⊗ SU(3) ⊗ SU(2) ⊗ U(1) 11 are obtained after the gauge breaking for the 1 × 16 3-model with three generations.

The (low-energy) physics of the superstring

Superstring theories offer the prospect of a finite unified theory of the four fundamental interactions. However, their implications for low-energy physics are difficult to determine because there must be several stages of symmetry breaking leading from the underlying multidimensional supersymmetric string theory, relevant at the scale of string structure (not more thanO(10-32cm)), to the four-dimensional non-supersymmetric effective field theory relevant for physics at scales probed in the laboratory (not less thanO(10-15cm)). I discuss these stages of compactification, supersymmetry breaking and gauge-symmetry breaking and show how the resulting low-energy theory may closely approximate the observed structure. The implications for the multiplet structure, the masses and the couplings of the observed particle states are considered.

Cosmic strings from superstrings

In the low-energy theory of four-dimensional superstrings the spontaneous breakdown of a pseudo-anomalous U(1) can trigger (but not necessarily) the formation of global and/or local cosmic strings. When cosmic strings are formed, supersymmetry is broken inside the string cores with a positive cosmological constant and an exponential growth of the cosmic scale factor. Strings are conformally stretched with the inflationary expansion, never enter the physics horizon and can have no observable (e.g. optical) effects. Off-string regions are in a (radiation-dominated) FRW universe. Most of our observable universe would still be inflating today unless a late (conventional) period of inflation transforms an off-string region into our present universe. The required amount of inflation coincides with the one needed to solve the usual flatness and horizon problems of the standard cosmological model. We consider, as an example, the chaotic inflation associated with the low-energy breaking (∼1 TeV) of supersymmetry.