Superconformal Ghost Research Articles

Complete action for open superstring field theory: Table 1.

We construct a complete action for open superstring field theory that includes the Neveu-Schwarz sector and the Ramond sector. For the Neveu-Schwarz sector, we use the string field in the large Hilbert space of the superconformal ghost sector, and the action in the Neveu-Schwarz sector is the same as the Wess-Zumino-Witten-like action of the Berkovits formulation. For the Ramond sector, it is known that the BRST cohomology on an appropriate subspace of the small Hilbert space reproduces the correct spectrum, and we use the string field projected to this subspace. We show that the action is invariant under gauge transformations that are consistent with the projection for the string field in the Ramond sector.

New analytic solutions in string field theory: Towards a collective higher spin vacuum

We construct analytic solutions in cubic open superstring field theory at higher superconformal ghost numbers.The solutions are the pure ghost ones and are given by combinations of Bell polynomials of bosonized superconformal ghost fields multiplied by exponents of the bosonized ghosts. Based on the structure of the solutions, we conjecture them to describe the ghost part of collective vacuum for higher spin modes in open string theory.

From the Berkovits formulation to the Witten formulation in open superstring field theory

The Berkovits formulation of open superstring field theory is based on the large Hilbert space of the superconformal ghost sector. We discuss its relation to the Witten formulation based on the small Hilbert space. We introduce a one-parameter family of conditions for partial gauge fixing of the Berkovits formulation such that the cubic interaction of the theory under the partial gauge fixing reduces to that of the Witten formulation in a singular limit. The local picture-changing operator at the open-string midpoint in the Witten formulation is regularized in our approach, and the divergence in on-shell four-point amplitudes coming from collision of picture-changing operators is resolved. The quartic interaction inherited from the Berkovits formulation plays a role of adjusting different behaviors of the picture-changing operators in the $s$ channel and in the $t$ channel of Feynman diagrams with two cubic vertices, and correct amplitudes in the world-sheet theory are reproduced. While gauge invariance at the second order in the coupling constant is obscured in the Witten formulation by collision of picture-changing operators, it is well defined in our approach and is recovered by including the quartic interaction inherited from the Berkovits formulation.

Open superstring field theory I: gauge fixing, ghost structure, and propagator

The WZW form of open superstring field theory has linearized gauge invariances associated with the BRST operator Q and the zero mode eta_0 of the picture minus-one fermionic superconformal ghost. We discuss gauge fixing of the free theory in a simple class of gauges using the Faddeev-Popov method. We find that the world-sheet ghost number of ghost and antighost string fields ranges over all integers, except one, and at any fixed ghost number, only a finite number of picture numbers appear. We calculate the propagators in a variety of gauges and determine the field-antifield content and the free master action in the Batalin-Vilkovisky formalism. Unlike the case of bosonic string field theory, the resulting master action is not simply related to the original gauge-invariant action by relaxing the constraint on the ghost and picture numbers.

NEW BRST CHARGES IN RNS SUPERSTRING THEORY AND DEFORMED PURE SPINORS

We show that new BRST charges in RNS superstring theory with nonstandard ghost numbers, constructed in our recent work, can be mapped to deformed pure spinor (PS) superstring theories, with the nilpotent pure spinor BRST charge QPS = ∮λαdα still retaining its form but with singular operator products between commuting spinor variables λα. Despite the OPE singularities, the pure spinor condition λγmλ = 0 is still fulfilled in a weak sense, explained in the paper. The operator product singularities correspond to introducing interactions between the pure spinors. We conjecture that the leading singularity orders of the OPE between two interacting pure spinors is related to the ghost number of the corresponding BRST operator in RNS formalism. Namely, it is conjectured that the BRST operators of minimal superconformal ghost pictures n > 0 can be mapped to nilpotent BRST operators in the deformed pure spinor formalism with the OPE of two commuting spinors having a leading singularity order λ(z)λ(w) ~ O(z-w)-2(n2+6n+1). The conjecture is checked explicitly for the first nontrivial case n = 1.

Fractional supersymmetric Liouville theory and the multi-cut matrix models

We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that ( p , q ) minimal fractional superstring theories appear in the Z k -symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.

Boundary State of Superstring in Open String Channel

We derive boundary state of superstring in the open string channel. It describes the superconformal field theory of open string emission and absorption by D-brane. We define the boundary state by conformal mappings from upper half plane with operators inserted at two points corresponding to the corners of semi-infinite strip. We obtain explicit oscillator forms analytically for the fermion and superconformal ghost sectors. For the fermion sector we compare this with numerical result obtained by using naive boundary condition.

NEW SUPERSTRING ISOMETRIES AND HIDDEN DIMENSIONS

We study the hierarchy of hidden space–time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space–time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies Hn ~ H-n-2(n≥0) and associate these generators with a chain of hidden space–time dimensions, with each ghost cohomology Hn ~ H-n-2 "contributing" an extra dimension. Namely, we show that each ghost cohomology Hn ~ H-n-2 of noncritical superstring theory in d-dimensions contains d+n+1 α-symmetry generators and the generators from Hk ~ H-k-2, 1≤k ≤n, combined together, extend the space–time isometry group from the naive SO (d, 2) to SO (d+n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space–time dimension.

GHOST COHOMOLOGIES AND HIDDEN SPACE–TIME SYMMETRIES

We observe and study new nonlinear global space–time symmetries of the full ghost + matter action of RNS superstring theory. We show that these surprising new symmetries are generated by the special worldsheet currents (physical vertex operators) of RNS superstring theory, violating the equivalence of superconformal ghost pictures. We review the questions of BRST-invariance and nontriviality of picture-dependent vertex operators and show their relation to hidden space–time symmetries and hidden space–time dimensions. In particular, we relate the space–time transformations, induced by picture-dependent currents, to the symmetries observed in the 2T physics approach.

THREE GENERATIONS OF SUSY STANDARD MODEL OF NAMBU–GOTO STRING

A four-dimensional superstring have been constructed starting from a 26-dimensional bosonic string. Fermions are introduced by noting the Mandelstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the superstring is invariant under SO (6) ⊗ SO (5) in the worldsheet. It has four bosonic coordinates and 44 Majorana fermions of SO (3, 1). Here the superstring action is shown to be invariant under conformal and superconformal transformations with the usual conformal and superconformal ghosts of the ten-dimensional superstrings. The massless spectrum obtained by quantizing the action, contain vector mesons which are generators of the SO (6) ⊗ SO (5). Using Wilson loops, this product group is proven to descend to Z3 ⊗ SU (3) ⊗ SU (2) ⊗ U (1) without breaking supersymmetry. Thus there are just three generations of quarks and leptons.

Ghosts in the matter forms

In this paper we study the matter form of the conformal and super-conformal ghosts action. That is, the ghost fields will be expressed in terms of some scalar and spinor fields. Thus, we obtain a two-dimensional covariant action in the matter form, $i.e.$ $S_g$. The Poincar\'e-like symmetries and various supersymmetries of this covariant action are analyzed. The signatures 10+2 and 11+3 for the total target space of the superstring theory also will be discussed.

WORLD SHEET LOGARITHMIC CFT IN AdS STRINGS, GHOST-MATTER MIXING AND M THEORY

We discuss several closely related concepts in the NSR formulation of superstring theory. We demonstrated that recently proposed NSR model for superstrings on AdS 5× S5 is described by the world sheet logarithmic conformal field theory (LCFT). The origin of LCFT on a world sheet is closely connected to the matter-ghost mixing in the structure of a brane-like vortex operators. We suggest a dynamical origin of M theory as a string theory with an extra dimension given by bosonized superconformal ghosts.

On the moduli space of c=0 topological conformal field theories

We studied the marginal deformation of the c=0 topological conformal field theories (TCFT). We showed that topological SL(2) Wess-Zumino-Witten (WZW) models, topological superconformal ghost systems, TCFT constructed from the N=2 superconformal system and two dimensional topological gravity belong to the same one parameter family (moduli space) of the c=0 TCFTs. We conjectured that the N=2 TCFT constructed from the Wolf space realization of N=4 superconformal algebra belongs to another family.

Bosonized superconformal ghosts and operator construction of g-loop amplitudes

Using the operator approach with bosonized representation of the superconformal ghosts β and γ, the g-loop operator is constructed out of vertices and propagators together with a projector. This projector is introduced to restrict the degrees of freedom of the bosonized representation to those of the original βγ system, by specifying the picture of each loop and projecting out redundant zero-modes. Using the g-loop operator, we derive the general correlation functions which can also include spin operators. It is shown that the correlation functions are independent of the picture chosen by the projector. The role of the zero-modes of the fermion fields η and ξ in relation with the Riemann-Roch theorem is clarified. The Feynman-like rules of the superstring are also discussed.

Superconformal ghost correlations on Riemann surfaces

We give a short summary of chiral bosonization on Riemann surfaces, with emphasis on commuting fermions, so-called (β, γ) systems. Employing Fay's trisecant identity a new, fermionic representation for superconformal ghost correlations is found. Especially useful for multi-loop superstring calculations, it completes an earlier proof that the cosmological constant vanishes up to eight loops.

EXCEPTIONAL GROUPS IN STRING THEORY

We review the occurrence of exceptional groups in string theory: their dual role as gauge symmetry and as a symmetry unifying space-time, superconformal ghost and internal degrees of freedom. In both cases the relation to the extended world-sheet supersymmetries is discussed in detail. This is used to construct the supermultiplet structure of the massless sectors of all supergravity theories possible in string theory, in even space-time dimensions between four and ten.

Chiral bosonization of superconformal ghosts on the Riemann surface and path-integral measure

The bosonization of the bosonic ghosts β and γ using a pair of scalar fields φ and χ is formulated for the case of the Riemann surface with higher genus. The measure of the path integral over φχ fields is defined with a projector which specifies the picture of each loop and removes the zero-modes. Nevertheless, the resulting correlation functions are independent of the chosen pictures. The correspondence between the anomalous ghost number conservation laws and the Riemann-Roch theorem becomes also manifest.

BRST cohomology and generalized bosonization of superconformal ghosts

We introduce a family of possible bosonizations of the superconformal ghost. We divide this into two classes on the basis of the value of one of the parameters specifying the bosonization prescription. The BRST cohomology in the large algebra is trivial for one class and non-trivial for other class of bosonization. We demonstrate that the properties of the picture changing operator X( z) regulate the cohomology of Q BRST in the large algebra.

Multiloop modular invariance of d = 10 type II superstring theory

Using the picture-changing prescription for supermoduli and the bosonization formula for the superconformal ghost determinant, it is shown explicitly that the higher loop amplitudes of the type II superstrung theory in ten-dimensional flat background are modular invariant.

Superconformal ghost correlators and picture changing

We compute the correlation functions for the system of superconformal ghosts β, γ (λ = 3 2 ) , including the corresponding spin fields, on arbitrary Riemann surfaces. Using fermionization, defined as a change of variables in the functional integration, we derive and generalize previous results obtained by bosonization. As an application we study the picture changing mechanism in the Ramond sector of the superstring.