Fermionic String Theory Research Articles

Fermionic string theories with deformed dispersion relations

Fermionic string theories with deformed dispersion relations

Massive superstring scatterings in the Regge regime

We calculate four classes of high-energy massive string scattering amplitudes of fermionic string theory at arbitrary mass levels in the Regge regime (RR). We show that all four leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. Based on the summation algorithm of a set of extended signed Stirling number identities, we show that all four ratios calculated previously by the method of decoupling of zero-norm states among scattering amplitudes in the Gross regime can be extracted from this Kummer function in the RR. Finally, we conjecture and give evidence that the existence of these four Gross regime ratios in the RR persists to subleading orders in the Regge expansion of all high-energy fermionic string scattering amplitudes.

Unitary and Complex Matrix Models as 1-d Type 0 Strings

We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter coupled to super-Liouville theory. We examine in detail the $\hat c=0$ or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on $(2, 4k)$ super-minimal models.

FERMIONIC SUBSPACES OF THE BOSONIC STRING

A universal symmetric truncation of the bosonic string Hilbert space yields all known closed fermionic string theories in ten dimensions, their D-branes and their open descendants. We highlight the crucial role played by group theory and two-dimensional conformal field theory in the construction and emphasize the predictive power of the truncation. Such circumstantial evidence points towards the existence of a mechanism which generates space-time fermions out of bosons dynamically within the framework of bosonic string theory.

Numerical study of nonlinear equations with an infinite number of derivatives

We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation is of much interest in mathematical physics and applications, in particular in cosmology. Differential equations with an infinite number of derivatives can be written as nonlinear integral equations. We perform a numerical investigation of the solutions of these equations. It is established that these equations have two different regimes of solutions: interpolating and periodic. The critical value of the parameter q separating these regimes is found to be q 2 cr ≈ 1.37. The convergence of the iterative procedure for these equations is proven.

Fermionic subspaces of the bosonic string

A universal symmetric truncation of the bosonic string Hilbert space yields all known closed fermionic string theories in ten dimensions, their D-branes and their open descendants. We highlight the crucial role played by group theory and two-dimensional conformal field theory in the construction and emphasize the predictive power of the truncation. Such circumstantial evidence points towards the existence of a mechanism which generates spacetime fermions out of bosons dynamically within the framework of bosonic string theory.

Noncommutative solitons in open N = 2 string theory

Coincident D2-branes in open N=2 fermionic string theory with a B-field background yield an integrable modified U(n) sigma model on noncommutative R^{2,1}. This model provides a showcase for an established method (the `dressing approach') to generate solutions for integrable field equations, even in the noncommutative case. We demonstrate the technique by constructing moving U(1) and U(2) solitons and by computing their energies. It is outlined how to derive multi-soliton configurations with arbitrary relative motion; they correspond to D0-branes moving inside the D2-branes.

The no-ghost theorem for AdS 3 and the stringy exclusion principle

A complete proof of the no-ghost theorem for bosonic and fermionic string theories on AdS 3, or the group manifold of SU(1, 1), is given. It is then shown that the restriction on the spin (in terms of the level) that is necessary to obtain a ghost-free spectrum corresponds to the stringy exclusion principle of Maldacena and Strominger.

Torsion-Free Sheaves and Moduli of Generalized Spin Curves

This article treats compactifications of the space of generalized spin curves. Generalized spin curves, or r-spin curves, are pairs (X,L) with X a smooth curve and L a line bundle whose rth tensor power is isomorphic to the canonical bundle of X. These are a natural generalization of 2-spin curves (algebraic curves with a theta-characteristic), which have been of interest recently, in part because of their applications to fermionic string theory. Three different compactifications over Z[1/r], all using torsion-free sheaves, are constructed. All three yield algebraic stacks, one of which is shown to have Gorenstein singularities that can be described explicitly, and one of which is smooth. All three compactifications generalize constructions of Deligne and Cornalba done for the case when r=2.

Noninvertible N=1 superanalog of complex structure

We consider an alternative tangent space reduction in N=1 superspace, which leads to some odd N=1 superanalog of complex structure (the even one is widely used in two-dimensional superconformal theories and in the fermionic string theory calculations via super Riemann surfaces). New N=1 superconformal-like transformations are similar to the antiholomorphic ones of the complex function theory. They are dual to the ordinary superconformal transformations subject to the Berezinian addition formula presented, noninvertible, highly degenerated and twist parity of the tangent space in the standard basis, and they also lead to some “mixed cocycle condition.” A new parametrization for the superconformal group is presented which allows us to extend it to a semigroup and to unify the description of old and new transformations.

On the equivalence of fermionic string to bosonic string in two dimensions

Two-dimensional fermionic string theory is shown to have a structure of topological model, which is isomorphic to a tensor product of two topological ghost systems independent of each other. One of them is identified with c = 1 bosonic string theory while the other has trivial physical contents. This fact enables us to regard two-dimensional fermionic string theory as an embedding of c = 1 bosonic string theory in the moduli space of fermionic string theories. Upon this embedding, the discrete states of c = 1 string theory are mapped to those of fermionic string theory, which is considered to be the origin of the similarity between the physical spectra of these two theories. We also discuss a novel BRST operator associated with this topological structure.

How many N = 4 strings exist?

Possible ways of constructing new extended fermionic strings with non-linear N=4 world-sheet supersymmetry are considered. N=4 string theory constraints are required to form a quasi-superconformal algebra, and have conformal dimensions . The most general non-linear N=4 quasi-superconformal algebra is , whose linearization is the so-called `large' N=4 superconformal algebra. The algebra has affine Lie component, and . We construct a quantum BRST charge for this algebra, and show that it is nilpotent only if . This restricts the previously proposed continuous -family of critical N=4 strings to only one theory based on the algebra which is isomorphic to the SO(4)-based Bershadsky--Knizhnik quasi-superconformal algebra. We propose the (non-covariant) Hamiltonian action for the new N=4 string theory. Our results imply the existence of two different critical N=4 fermionic string theories: the `old' one based on the `small' linear N=4 superconformal algebra and having the total ghost central charge , and the new one with the non-linearly realized N=4 supersymmetry, based on the SO(4) quasi-superconformal algebra and having . Both critical N=4 string theories have negative `critical dimensions' and do not admit unitary matter representations.

Massive inter-particle symmetry and Ward identity in fermionic string theory

We show that there exist enlarged stringy (α′→∞) symmetries for (evenG-parity) massive modes in the 10D fermionic string theory. These symmetries are derived from on-shell Ward identities corresponding to the decoupling of massive gauge states in the spectrum. In the generalized massive supersymmetric σ-model formalism, some symmetry transformations relate particles with different spins in the first order weak field approximation.

TOPOLOGICAL STRUCTURE IN $\hat c =1$ FERMIONIC STRING THEORY

[Formula: see text] fermionic string theory, which is considered as a fermionic string theory in two dimensions, is shown to decompose into two mutually independent parts, one of which can be viewed as a topological model and the other is irrelevant for the theory. The physical contents of the theory is largely governed by this topological structure, and the discrete physical spectrum of [Formula: see text] string theory is naturally explained as the physical spectrum of the topological model. This topological structure turns out to be related with a novel hidden N = 2 superconformal algebra (SCA) in the enveloping algebra of the N = 3 SCA in fermionic string theories.

N = 2 super-Weyl symmetry, super-Liouville theory and super-Riemannian surfaces

The finite form of the N=2 super-Weyl transformations in the chiral and twisted-chiral irreducible formulations of the two-dimensional N=2 superfield supergravity are found in N=2 superspace. The super-Weyl anomaly of the N=2 extended fermionic string theory is computed in terms of the N=2 superfields, by using a short-time expansion of the N=2 chiral heat kernel. The super-Weyl invariant N=2 superconformal structure is introduced, and a new definition of the N=2 super-Riemannian surfaces is proposed.

Spacetime supersymmetry of extended fermionic strings in 2+2 dimensions

The N=2 fermionic string theory is revisited in the light of its recently proposed equivalence to the non-compact N=4 fermionic string model. The issues of spacetime Lorentz covariance and supersymmetry for the BRST quantized N=2 strings living in uncompactified 2+2 dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the spacetime symmetries of the extended fermionic strings and their interactions. The considerations support Siegel's (1992) ideas about the presence of SO(2,2) Lorentz symmetry as well as at least two self-dual spacetime supersymmetries in the theory of N=2(4) fermionic strings, though the authors do not have a compelling reason to argue for the necessity of maximal spacetime supersymmetry. The worldsheet arguments for the absence of all massive string modes in the physical spectrum and the vanishing of all string-loop amplitudes in the Polyakov (1981) approach, are given on the basis of the general consistency of the theory.

World-sheet supersymmetry without contact terms

Green and Seiberg showed that, in simple treatments of fermionic string theory, it is necessary to introduce contact interactions when vertex operators collide. Otherwise, certain superconformal Ward identities would be violated. In this note, we show how these contact terms arise naturally when proper account is taken of the superconformal geometry involved when punctures collide. More precisely, we show that there is no contact term at all! Rather, corrections arise to the “naive” formula when the boundary of moduli space is described correctly.

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.

Stability of the homology of the moduli spaces of Riemann surfaces with spin structure

Recently, due largely to its importance in fermionic string theory, there has been much interest in the moduli spaces ~/gl-e] of Riemann surfaces of genus g with spin structure of Arf invariant e e Z/2Z. Algebraic geometers have long studied these spaces in their alternate guise as moduli spaces of pairs (algebraic curve, square root of the canonical bundle). For topologists these spaces are rational classifying spaces for spin mapping class groups. However, despite the fact that ~r162 is a finite cover of the ordinary moduli space J/4g, little is known about the topology of these spaces. In this paper we begin a study of the homology of ~'g[e] by proving that its homology groups are independent of g and e when g is adequately large (Theorem3.1). In a second paper [H4] we will compute nl(v//g[e]) and H2(./r thereby calculating the Picard group of Jlg[e]. Putting this all together we know approximately the same amount about the homology of Jt'g[e] as we do about that of d/g itself. The techniques used here are an extension of those of [H 2] which are in turn strongly related to those of [C; Q; V; W] and others. We begin by constructing several simplicial complexes from configurations of simple closed curves and properly imbedded arcs in a surface of genus g. The homology of the spin moduli space is identified with that of the spin mapping class group G, which acts on these complexes in a natural way. The Borel construction is then applied to obtain a spectral sequence which describes the homology of G in terms the homology of the stabilizers of the cells of these complexes. These turn out to be spin mapping class groups (in an extended sense) of smaller genus and the result is established inductively. The complexes are exactly the same as those of [H 2]; however, the spectral sequence arguments are more difficult because there are more orbits of cells under the action of G. Furthermore, in Sect. 4 we apply an entirely different and much simpler version of the argument of [H 2] to obtain stability in the case of a closed surface.

GAUGE MODELS OF FERMIONIC DISCRETE "STRINGS"

A new class of constrained hamiltonian systems with a finite number of bosonic and fermionic degrees of freedom is proposed. Coordinates of these systems are divided into two groups of independent variables analogous to the left and right movers of the standard closed fermionic string theory. Hamiltonians are obtained by gauging some subgroups of the linear supercanonical transformations for the left and right variables. It is argued that some of the new models can be regarded as discrete analogs of the standard fermionic string theory. The extension of the models obtained by adding ghost variables is also constructed as a prerequisite to quantizing them.