NSR String Research Articles

Geometrical framework for picture changing operators in the pure spinor formalism

It is well known in NSR string theory, that vertex operators can be constructed in various “pictures”. Recently this was discussed in the context of pure spinor formalism. NSR picture changing operators have an elegant super-geometrical interpretation. In this paper we provide a generalization of this super-geometrical construction, which is also applicable to the pure spinor formalism.

Dimensional transmutation by monopole condensation in QCD

We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation which is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence. With this we show that, just as the GSO-projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation. This establishes the monopole dominance in QCD. In doing so we point out critical defects in the calculation of the Savvidy-Nielsen-Olesen (SNO) effective action.

T-DUALITY OF NSR SUPERSTRING: THE WORLDSHEET PERSPECTIVE

We formulate target space duality symmetry of NSR superstring from the perspectives of worldsheet. The worldsheet action is presented in the superspace formalism in the presence of massless backgrounds. We start from a [Formula: see text]-dimensional target space worldsheet action and compactify the theory on a d-dimensional torus, Td. It is assumed that the backgrounds are independent of compact (super)coordinates. We adopt the formalism of our earlier work to introduce dual supercoordinates along compact directions and introduce the corresponding dual backgrounds. It is demonstrated that combined equations of motion of the two sets of coordinates can be expressed in a manifestly O(d, d) covariant form analogous to the equations of motions for closed bosonic string derived by us. Furthermore, we show that the vertex operators associated with excited massive levels of NSR string can be expressed in an O(d, d) invariant form generalizing earlier result for closed bosonic string.

Light-cone gauge NSR strings in noncritical dimensions

Light-cone gauge NSR string theory in noncritical dimensions should correspond to a string theory with a nonstandard longitudinal part. Supersymmetrizing the bosonic case [arXiv:0909.4675], we formulate a superconformal worldsheet theory for the longitudinal variables X^{\pm}, \psi^{\pm}. We show that with the transverse variables and the ghosts combined, it is possible to construct a nilpotent BRST charge.

NSR STRING IN AdS3 BACKGROUND: NONLOCAL CHARGES

We consider NSR superstring in AdS3⊗S3⊗R4 background. The action is expressed in terms of the variables on the group manifolds SL (2, R) and SU(2) as (1+1)-dimensional σ-models with Wess–Zumino terms, associated with AdS3 and S3 respectively. R4 is the flat Euclidean space. We show the existence of classical nonlocal conserved currents in the superspace formulation for the nonlinear σ-model with WZ term in the context of NSR string. We propose Ward identities utilizing existence of the nonlocal conserved currents.

CONFORMAL MODULI AND b-c PICTURES FOR NSR STRINGS

We explore the geometry of superconformal moduli of the NSR superstring theory in order to construct the consistent sigma-model for NSR strings, free of picture-changing complications. The sigma-model generating functional is constructed by the integration over the bosonic and fermionic moduli, corresponding to insertions of the vertex operators in scattering amplitudes. While the integration over the supermoduli leads to the standard picture-changing insertions, the integration over the bosonic moduli results in the appearance of picture-changing operators for the b-c fermionic ghosts with the ghost number -1. Important example of the b-c ghost pictures involves the vertex operators in integrated and unintegrated forms. We obtain the BRST-invariant expressions for the b-c picture-changing operators for open and closed strings and study some of their properties. We also show that the superconformal moduli spaces of the NSR theory contain the global singularities, leading to the phenomenon of ghost-matter mixing and the appearance of nonperturbative D-brane creation operators.

Neveu-Schwarz 5-brane and little string duality in thepp-wave limit

We study NSR strings in the Nappi-Witten background, which is the Penrose limit of a certain NS5-brane supergravity solution. We solve the theory in the light-cone gauge, obtaining the spectrum, which is space-time supersymmetric. In light of the LST/NS5-brane duality, this spectrum should be in correspondence with the states of little string theory in the appropriate limit. A semiclassical analysis verifies that the relationship between energy and angular momentum, after a field redefinition, matches the known result for a flat background.

The no-ghost theorem in curved backgrounds with a timelike u(1): NSR string

It is well known that the standard no-ghost theorem is valid as long as the background has the light-cone directions. We prove the no-ghost theorem for the NSR string when only the timelike direction is flat. This is done by the BRST quantization, using the technique of Frenkel, Garland and Zuckerman and our previous results for the bosonic string. The theorem actually applies as long as the timelike direction is written as a u(1) SCFT.

BRST quantization of string theory inAdS3

We study the BRST quantization of bosonic and NSR strings propagating in AdS(3) x N backgrounds. The no-ghost theorem is proved using the Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations of affine SL(2,R) appear on an equal footing. Possible generalizations to related curved backgrounds are discussed.

DBI ACTION FROM CLOSED STRINGS AND D-BRANE SECOND QUANTIZATION

Brane-like vertex operators play an important role in a world-sheet formulation of D-branes and M theory. In this paper we derive the DBI D-brane action from closed NSR string with brane-like states. We also show that these operators carry RR charges and define D-brane wave functions in a second quantized formalism.

New Superembeddings for Type II Superstrings

Possible ways of generalization of the superembedding approach for the supersurfaces with the number of Grassmann directions being less than the half of that for the target superspace are considered on example of Type II superstrings. Focus is on n=(1,1) superworldsheet embedded into D=10 Type II superspace that is of the interest for establishing a relation with the NSR string.

Covariant κ—symmetry gauge fixing and the classical relation between physical variables of the NSR string and the type II GS superstring

The main goal of this paper is the manifestly covariant derivation of the classical relation between the gauge-fixed Grassmann variables of the NSR string and the Type II GS superstring. To this end we analyze the superembedding equation for the Type II superstring to derive the relation between the original variables of the NSR string and the Type II GS superstring and, further, by means of Lorentz harmonic variables we fix κ—symmetry of the GS superstring in the manifestly Lorentz covariant way.

Sigma model approach to string theory effective actions with tachyons

Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within the sigma model approach. In particular, we demonstrate that the renormalized partition function Z(T,A) of the boundary sigma model gives the effective action for massless vectors which is consistent with the string S-matrix and beta function, resolving an old problem with this suggestion in the bosonic string case at the level of the leading F2(dF)2 derivative corrections to Born–Infeld action. We give a manifestly gauge invariant definition of Z(T,A) in non-Abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss the derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories. In the bosonic case the tachyon potential has the structure −T2e−T, but it vanishes in the NSR string case.

On covariant κ-symmetry fixing and the relation between the NSR string and the type II GS superstring

By considering the superembedding equation for the type II superstring we derive the classical relation between the NSR string and the type II GS superstring grassmannian variables. The connection between the actions of these two models is also established. Then introducing the proper twistor-like Lorentz harmonic variables we fix κ-symmetry of the GS formulation in the manifestly SO(1,9) Lorentz covariant manner and establish the relation between the gauge-fixed variables of the NSR and the type II GS models.

Asymptotic freedom and infrared behavior in the type 0 string approach to gauge theory

In a recent paper we considered the type 0 string theories, obtained from the ten-dimensional closed NSR string by a GSO projection which excludes space-time fermions, and studied the low-energy dynamics of N coincident D-branes. This led us to conjecture that the four-dimensional SU( N) gauge theory coupled to six adjoint massless scalars is dual to a background of type 0 theory carrying N units of R-R 5-form flux and involving a tachyon condensate. The tachyon background leads to a “soft breaking” of conformal invariance, and we derived the corresponding renormalization group equation. Minahan has subsequently found its asymptotic solution for weak coupling and showed that the coupling exhibits logarithmic flow, as expected from the asymptotic freedom of the dual gauge theory. We study this solution in more detail and identify the effect of the 2-loop beta function. We also demonstrate the existence of a fized point at infinite coupling. Just like the fixed point at zero coupling, it is characterized by the AdS 5 × S 5 Einstein frame metric. We argue that there is a RG trajectory extending all the way from the zero coupling fixed point in the UV to the infinite coupling fixed point in the IR.

D-branes and dual gauge theories in type 0 strings

We consider the type 0 theories, obtained from the closed NSR string by a diagonal GSO projection which excludes space-time fermions, and study the D-branes in these theories. The low-energy dynamics of N coincident D-branes is governed by a U( N) gauge theory coupled to adjoint scalar fields. It is tempting to look for the type 0 string duals of such bosonic gauge theories in the background of the R-R charged p-brane classical solutions. This results in a picture analogous to the one recently proposed by Polyakov (hep-th/9809057). One of the serious problems that needs to be resolved is the closed string tachyon mode which couples to the D-branes and appears to cause an instability. We study the tachyon terms in the type 0 effective action and argue that the background R-R flux provides a positive shift of the (mass) 2 of the tachyon. Thus, for sufficiently large flux, the tachyonic instability may be cured, removing the most basic obstacle to constructing the type 0 duals of non-supersymmetric gauge theories. We further find that the tachyon acquires an expectation value in the presence of the R-R flux. This effect is crucial for breaking the conformal invariance in the dual description of the 3 + 1-dimensional non-supersymmetric gauge theory.

N=2 structures in string theories

The BRST cohomology of any topological conformal field theory admits the structure of a Batalin–Vilkovisky algebra, and string theories are no exception. Loosely speaking, we say that two topological conformal field theories are cohomologically equivalent if their BRST cohomologies are isomorphic as Batalin–Vilkovisky algebras. In this paper we argue that any string theory (regardless of the matter background) is cohomologically equivalent to some twisted N=2 superconformal field theory. We discuss three string theories in detail: the bosonic string, the NSR string and the W3 string. In each case the way the cohomological equivalence is constructed can be understood as coupling the topological conformal field theory to topological gravity. These results lend further supporting evidence to the conjecture that any topological conformal field theory is cohomologically equivalent to some topologically twisted N=2 superconformal field theory. We end the paper with some speculative comments on Massey products in topological conformal field theories.

Path-Integral Quantization of the (2,2) String

A complete treatment of the (2,2) NSR string in flat (2 + 2)-dimensional space–time is given, from the formal path integral over N = 2 super Riemann surfaces to the computational recipe for amplitudes at any loop or gauge instanton number. We perform in detail the superconformal gauge fixing, discuss the spectral flow, and analyze the supermoduli space with emphasis on the gauge moduli. Background gauge field configurations in all instanton sectors are constructed. We develop chiral bosonization on punctured higher-genus surfaces in the presence of gauge moduli and instantons. The BRST cohomology is recapitulated, with a new space–time interpretation for picture-changing. We point out two ways of combining left- and right-movers, which lead to different three-point functions.

N = 2 worldsheet instantons yield cubic self-dual Yang-Mills

When the gauge instantons on the N=2 string worldsheet are properly included in the sum over topologies, the breaking of SO(2,2) Lorentz symmetry in R^{2,2} is parametrized by a spacetime twistor containing the string coupling and theta angle. The resulting (tree-level) effective action for the open string is not Yang's but Leznov's cubic action for self-dual Yang-Mills in a light-cone gauge. In the closed case, Plebanski's action for self-dual gravity gets modified analogously. In contrast to the N=1 NSR string, picture-changing is not locally invertible, but produces a semi-infinite tower of massless physical states with ever-increasing spin, perhaps related to harmonic superspace. A truncation yields the two-field action of Chalmers and Siegel.

Picture-changing operators and space-time supersymmetry

We explore the geometrical properties of fermionic vertex operators for a NSR superstring in order to establish the connection between world-sheet and target space supersymmetries. The mechanism of picture changing is obtained as a result of imposing certain constraints on a world-sheet gauge group of the NSR superstring theory. We find that picture-changing operators of different integer ghost numbers form a polynomial ring. By using properties of the picture-changing formalism, we establish a relation between the NSR and GS string theories. We show that, up to picture-changing transformations, the stress-energy tensor of the N = 1 NSR superstring theory can be obtained from the stress-energy tensor of the N = 1 GS superstring theory in a flat background by a simple field redefinition. The equations of motion of a GS superstring are shown to be fulfilled in the NSR operator formalism; they are also shown to be invariant under κ-symmetry, in terms of operator products in the NSR theory. This allows us to derive the space-time supersymmetry transformation laws for the NSR string theory. Then, we explore the properties of the κ-symmetry in the NSR formalism and find that it leads to some new relations between bosonic and fermionic correlation functions.