We construct a class of analytic solutions of WZW-type open superstring field theory describing marginal deformations of a reference D-brane background. The deformations we consider are generated by on-shell vertex operators with vanishing operator products. The superstring solution exhibits an intriguing duality with the corresponding marginal solution of the {\it bosonic} string. In particular, the superstring problem is ``dual'' to the problem of re-expressing the bosonic marginal solution in pure gauge form. This represents the first nonsingular analytic solution of open superstring field theory.
Bosonic model inspired by D=11 superstring action is investigated. An appropriate set of variables is find, in which the light-cone quantization turns out to be possible. It is shown that anomaly terms in the algebra of the light-cone Poincare generators are absent for the case D=27.
The superfield formulation of type II Green-Schwarz superstring with n= (1,0) worldsheet supersymmetry is constructed. It is shown that the inclusion of the second spinor coordinate in the target superspase leads to the possibility of the reparametrization invariant description of the superstring in the absence of any field from the two dimensional supergravity multiplet. The twistor-like action of Chern-Simons type for bosonic string in D=3,4,6,10 is obtained from the component form of the superstring action.
We derive the actions for type II Green-Schwarz strings up to second order in the fermions, for general bosonic backgrounds. We base our work on the so-called normal coordinate expansion. The resulting actions are $κ$-symmetric and, for the case of surviving background supersymmetries, supersymmetric. We first obtain the type IIa superstring action from the 11D supermembrane by double dimensional reduction. Then, by means of a generalization of T-duality we derive the type IIb superstring action. The resulting actions are surprisingly simple and elegant.
We construct analytic solutions of open superstring field theory for any exactly marginal deformation in any boundary superconformal field theory when properly renormalized operator products of the marginal operator are given. Our construction is an extension of the general framework for marginal deformations developed in arXiv:0707.4472 for open bosonic string field theory, and the solutions are based on integrated vertex operators which are closely related to finite deformations in boundary superconformal field theory.
We find solutions of supersymmetric string field theory that correspond to the photon marginal deformation in the boundary conformal field theory. We revisit the bosonic string marginal deformation and generate a real solution for it. We find a map between the solutions of bosonic and supersymmetric string field theories and suggest a universal solution to superstring field theory.
We construct an analytic solution for tachyon condensation around identity-based marginal solutions in Berkovits' WZW-like open superstring field theory. Using this, which is a kind of wedge-based solution, the gauge invariant overlaps for the identity-based marginal solutions can be calculated analytically. This is a straightforward extension of a method in bosonic string field theory, which has been elaborated by the authors, to superstring. We also comment on a gauge equivalence relation between the tachyon vacuum solution and its marginally deformed one. From this viewpoint, we can find th…
It is in general very subtle to integrate over the odd moduli of super Riemann surfaces in perturbative superstring computations. We study how these subtleties go away in favorable cases, including the embedding of N=0 string to N=1 string by Berkovits and Vafa, and the relation of the graviphoton amplitude and the topological string amplitude by Antoniadis, Gava, Narain and Taylor and Bershadsky, Cecotti, Ooguri and Vafa. The Poincaré dual of the moduli space of Riemann surfaces in the moduli space of super Riemann surfaces plays an important role.
It has long been known that in principle, the genus g vacuum amplitude for bosonic strings or superstrings in 26 or 10 dimensions can be entirely determined from conditions of holomorphy. Moreover, this has been done in practice for bosonic strings of low genus. Here we describe in a unified way how to determine the bosonic string and superstring vacuum amplitude in genus 1 and 2 via holomorphy. The main novelty is the superstring analysis in genus 2, where we use holomorphy to get a new understanding of some of the results that previously have been obtained by more explicit calculations.
We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular.
We construct a class of classical solutions in the Berkovits' open superstring field theory. The resulting solutions correspond to marginal boundary deformations in conformal field theory. The vacuum energy vanishes exactly for the solutions. Investigating the theory expanded around one of the solutions, we find that it reflects the effect of background Wilson lines. The solution has a well-defined Fock space expression and it is invariant under space-time supersymmetry transformation.
We construct tachyon vacuum and half-brane solutions, using an extension of KBc algebra, in the theory around a type of identity-based marginal solutions in modified cubic superstring field theory. With explicit computations, we find that their vacuum energies are the same as those of corresponding solutions around the original theory. It implies that the vacuum energy for the identity-based marginal solution vanishes although straightforward computation of it is subtle. We also evaluate the gauge invariant overlaps for those nontrivial solutions. The values for them are deformed according to …
We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We fi…
A string in four dimensions is constructed by supplementing it with forty four Majorana fermions. The later are represented by eleven vectors in the bosonic representation $SO(D-1,1)$. The central charge is 26. The fermions are grouped in such a way that the resulting action is world sheet supersymmetric. The energy momentum and current generators satisfy the super-Virasoro algebra. GSO projections are necessary for proving modular invariance. Space-time supersymmetry algebra is deduced and is substantiated for specific modes of zero mass. The symmetry group of the model can descend to the low…
We reconsider light-cone superstring field theory on the maximally supersymmetric pp-wave background. We find that the results for the fermionic Neumann matrices given so far in the literature are incomplete and verify our expressions by relating them to the bosonic Neumann matrices and proving several non-trivial consistency conditions among them, as for example the generalization of a flat space factorization theorem for the bosonic Neumann matrices. We also study the bosonic and fermionic constituents of the prefactor and point out a subtlety in the relation between continuum and oscillator…
We have covariantized the Lagrangians of the U(1)_V * U(1)_A models, which have U(1)_V * U(1)_A gauge symmetry in two dimensions, and studied their symmetric structures. The special property of the U(1)_V * U(1)_A models is the fact that all these models have an extra time coordinate in the target space-time. The U(1)_V * U(1)_A models coupled to two-dimensional gravity are string models in 26+2 dimensional target space-time for bosonic string and in 10+2 dimensional target space-time for superstring. Both string models have two time coordinates. In order to construct the covariant Lagrangians…
It is shown that an alternative supersymmetric version of the Liouville equation extracted from D=3 Green-Schwarz superstring equations naturally arises as a super-Toda model obtained from a properly constrained supersymmetric WZNW theory based on the $sl(2, R)$ algebra. Hamiltonian reduction is performed by imposing a nonlinear superfield constraint which turns out to be a mixture of a first- and second-class constraint on supercurrent components. Supersymmetry of the model is realized nonlinearly and is spontaneously broken. The set of independent current fields which survive the Hamiltonian…
The partition function of the discretized superstring in a target superspace of three (Euclidean) bosonic dimensions, is shown, for a fixed triangulation of the random world sheet, to be derived from the partition function of a discretized bosonic string with an external field present in the action in the form of a specific constant matrix, using first order forms of the actions. This latter partition function appears more amenable to an exact analytical treatment.
The potential of the closed bosonic bulk tachyon is investigated using $\mathcal{N}~=~1$ closed superstring field theory formulated around Berkovits' and Vafas embedding of the bosonic string into the superstring. From this point of view the bosonic minimum gets destabilized by new deformations of the underlying CFT. Another critical point of the potential is identified by solving the equation of motions and the properties of this new solution are discussed.
We construct analytic solutions of open superstring field theory in the Berkovits formulation using boundary condition changing operators under some regularity conditions, extending the previous construction in the bosonic string. We also consider the gauge-invariant observables corresponding to closed string one-point functions on the disk. We analytically calculate the gauge-invariant observables for the solutions both in the bosonic string and in the superstring and find the expected change of boundary conditions of the disk.
We discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. T-duality along four directions in Poincare parametrization of AdS5 maps the bosonic part of the superstring action into itself. On bosonic level, this duality may be understood as a symmetry of the first-order (phase space) system of equations for the coset components of the current. The associated Lax connection is invariant modulo the action of an so(2,4)-automorphism. We then show that this symmetry extends to the full superstring, provided one supplements the transfor…
Using the factorization approach of Gepner and Qiu, I systematically rederive the closed fractional superstring partition functions for K= 4, 8, and 16. For these theories the relationship between the massless graviton and gravi- tino sector and the purely massive sectors is explored. Properties of the massive sectors are investigated. A twist current in these models is found responsible for the occurrence of N=1 space-time supersymmetry. I show this twist current transforms bosonic (fermionic) projection states into fermionic (bosonic) non-projection states and vice-versa.
A bosonic string in twenty six dimensions is effectively reduced to four dimensions by eleven Majorana fermions which are vectors in the bosonic represetation SO(d-1,1). By dividing the fermions in two groups, actions can be written down which are world sheet supersymmetric, 2-d local and local 4-d supersymmetric. The novel string is anomally free, free of ghosts and the partition function is modular invariant.
We first derive all world-sheet action functionals for NSR superstring models with (1,1) supersymmetry and any number of abelian gauge fields, for gauge transformations of the standard form. Then we prove for these models that the BRST cohomology groups $H^g(s)$, $g<4$ (with the antifields taken into account) are isomorphic to those of the corresponding bosonic string models, whose cohomology is fully known. This implies that the nontrivial global symmetries, Noether currents, background charges, consistent deformations and candidate gauge anomalies of an NSR (1,1) superstring model are in one…
Some time ago the bosonic and fermionic 4-field terms of the non-abelian low energy effective action of the open superstring were obtained, to all order in $α'$. This was done at tree level by directly generalizing the abelian case, treated some time before, and considering the known expressions of all massless superstring 4-point amplitudes (at tree level). In the present work we obtain the bosonic 5-field terms of this effective action, to all order in $α'$. This is done by considering the simplified expression of the superstring 5-point amplitude for massless bosons, obtained some time ago.
We use level truncated superstring field theory to obtain the effective potential for the Wilson line marginal deformation parameter which corresponds to the constant vacuum expectation value of the U(1) gauge field on the D-brane in a particular direction. We present results for both the BPS and the non-BPS D-brane. In the case of non-BPS D-brane the effective potential has branches corresponding to the extrema of the tachyon potential. In the branch with vanishing tachyon vev (M-branch), the effective potential becomes flatter as the level of the approximation is increased. The branch which …
Working within the framework of both the $A_\infty$ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter. For a specific class of backgrounds, we find that this condition localizes on the boundary of the worldsheet moduli space, thus providing a very simple computational prescription for recovering algebraic constraints (generalized ADHM equations) which need to be satisfied by the moduli. Applying our results to the $\mathrm{D(-1)/D3}$ system, we confi…
We present an exact solution of superstring theory that interpolates in time between an initial type 0 phase and a final phase whose physics is exactly that of the bosonic string. The initial theory is deformed by closed-string tachyon condensation along a lightlike direction. In the limit of large tachyon vev, the worldsheet conformal field theory precisely realizes the Berkovits-Vafa embedding of bosonic string theory into superstring theory. Our solution therefore connects the bosonic string dynamically with the superstring, settling a longstanding question about the relationship between th…
A discussion of the number of degrees of freedom, and their dynamical properties, in higher-derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of auxiliary fields. As a by-product we present a consistent non-linear coupling of a spin-2 tensor to gravitation. It is shown that non-vanishing $(C_{μναβ})^{2}$ terms arise in $N=1$, $D=4$ superstring Lagrangians due to one-loop radiative corrections with light field internal lines.
We calculate emission rates of various bosonic/fermionic soft massless states of open/closed superstring from an ensemble of a highly excited open/closed superstring in the flat background. The resulting spectrum shows thermal distributions at the Hagedorn temperature. We find greybody factors for each process and observe their relation to the ones from blackholes.
The Coulomb gas representation of expectation values in SU(2) conformal field theory developed by Dotsenko is extended to the SL(2,R) WZW model and applied to bosonic string theory on AdS3 and to Type II superstrings on AdS3 x N. The spectral flow symmetry is included in the free field realization of vertex operators creating superstring states of both Ramond and Neveu-Schwarz sectors. Conjugate representations for these operators are constructed and a background charge prescription is designed to compute correlation functions. Two and three point functions of bosonic and fermionic string stat…
We analyze the free ambitwistor string field theory action for the bosonic string, heterotic string and both GSO sectors of the Type II string. The spectrum contains non-unitary states and provides an interesting consistency test for one-loop ambitwistor string computations.
Starting from the Nambu-Goto bosonic string, a four dimensional superstring model is constructed using the equivalence of one boson to two Majorana-Weyl fermions. The conditions of anomaly cancellation in a 'heterotic' string theory lead to the correct result and is found to be consistent with the requirements of the standard model.
The string equivalent of a massless particle ($m=0$) is the tensionless string ($T=0$). The study of such strings is of interest when trying to understand the high energy limit of ordinary strings. I discuss the classical $T\to 0$ limit of the bosonic string, the spinning string and the superstring. A common feature is the appearence of a space-time (super-)conformal symmetry replacing the world-sheet Weyl invariance. The question of whether this symmetry may survive quantization is addressed. A lightcone analysis of the quantized bosonic tensionless string leads to severe constraints on the p…
We consider fixing the bosonic light-cone gauge for string in AdS in the phase space framework, i.e. by choosing $x^+ = τ$, and by choosing $σ$ so that $P^+$ is distributed uniformly (its density is independent of $σ$). We discuss classical bosonic string in AdS space and superstring in AdS_5 x S^5. In the latter case the starting point is the action found in hep-th/0007036 where the kappa-symmetry is fixed by a fermionic light cone gauge. We derive the light cone Hamiltonian in the AdS_5 x S^5 case and in the case of superstring in AdS_3 x S^3. We also obtain a realization of the generators o…
In this work, the DDF-like approach to the pure spinor cohomology is extended to the next ghost number level, the so called antifields. In a direct (supersymmetric) parallel to the bosonic string, some properties of the ghost number two cohomology are derived with the enlargement of the DDF algebra. Also, the DDF conjugates of the b ghost zero mode emerge naturally from the extended algebra and the physical state condition is discussed. Unlike the bosonic string case, the cohomology analysis of the pure spinor b ghost is restricted to BRST-closed states.
A careful gauge fixing of the conformal killing group (CKG) on genus zero surfaces in bosonic string theory gives non-vanishing two point amplitudes that match the corresponding field theory expressions arXiv:1906.06051, arXiv:1909.03672 . An important ingredient for gauge fixing two point amplitudes in arXiv:1909.03672 was the mostly BRST (mBRST) exact operator. The utility of this operator in gauge fixing CKG perhaps is not just limited to two point amplitudes - we can insert a mBRST exact operator to fix a conformal killing vector (CKV) instead of fixing the position of a vertex operator in…
The 26 dimensional bosonic string, first suggested by Nambu and Goto, is reduced to a four dimensional superstring by using two species of 6 and 5 Majorana fermions as proposed by Deo. These two species of fermions differ in their 'neutrino-like' phase, and are vectors in the bosonic representation SO(d-1,1).Using Polchinski's equivalence between operators and states, we can write the Virasoro generators for 4 dimensional string theory. The theory is shown to give the same results as given by other superstrings and also reveals the well known aspects of four dimensional string theory.The boson…
The evolution of a closed NSR string is considered in the background of constant graviton and antisymmetric fields. The $σ$-model action is written in a manifestly supersymmetric form in terms of superfields. The first order formalism adopted for the closed bosonic string is generalised to implement duality transformations and the constant dual backgrounds are obtained for the dual theory. We recover the $G \rightarrow G^{-1}$ duality for the case when antisymmetric tensor field is set to zero. Next, the case when the backgrounds depend on one superfield, is also analysed. This scenario is sim…
The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic ${α'}^N$ order terms, it is necessary to know the open string (tree level) $(N+2)$-point amplitude of massless bosons, at least expanded at that order in $α'$. In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that…
We construct a class of nilpotent operators using the BRST current and ghost fields in superstring theory. The operator can be realized in cubic superstring field theory as a kinetic operator in the background of an identity-based solution. For a particular type of the deformed BRST operators, we find a homotopy operator and discuss its relationship to the cohomology in a similar way to the bosonic case, which has been elaborated by the authors.
The OPE between the composite $b$ ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The vanishing of the double pole singularity is Lorentz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.
The Pohlmeyer reduced equations for strings moving only in the AdS subspace of AdS_5 x S^5 have been used recently in the study of classical Euclidean minimal surfaces for Wilson loops and some semiclassical three-point correlation functions. We find an action that leads to these reduced superstring equations. For example, for a bosonic string in AdS_n such an action contains a Liouville scalar part plus a K/K gauged WZW model for the group K=SO(n-2) coupled to another term depending on two additional fields transforming as vectors under K. Solving for the latter fields gives a non-abelian Tod…
In this paper, based on the notion of plane wave string/gauge theory duality, we explore the pp wave limit associated with the bosonic sector of $ η$ deformed superstrings propagating in $ (AdS_5 \times S^{5})_η $. Our analysis reveals that in the presence of NS-NS and RR fluxes, the pp wave limit associated to full ABF background satisfies type IIB equations in its standard form. However, the beta functions as well as the string Hamiltonian start receiving non trivial curvature corrections as one starts probing beyond pp wave limit which thereby takes solutions away from the standard type IIB…
We examine the possibility of constructing analytical solutions describing marginal deformations in the open superstring field theory that is based on the non-minimal pure-spinor formalism. It is found out that some methods used for constructing solutions of bosonic and RNS string field theories do not seem to generalize to the pure-spinor case, while other methods do lead to reliable analytical solutions.
We discover new hard string scattering amplitudes (HSSA) with polarizations orthogonal to the scattering plane in the NS sector of 10D open superstring theory. The corresponding HSSA in the bosonic string theory are of subleading order in energy. In addition, all HSSA are found to be proportional to each other and the ratios among these HSSA are calculated to justify Gross conjecture in 1988 on high energy symmetry of string theory. Moreover, together with these new HSSA, the total number of HSSA calculated in the first massive level of NS sector are found to agree with those of hard polarized…
We discuss solutions of the heterotic string theory which are analogous to bosonic and superstring backgrounds related to coset conformal field theories. A class of exact `left-right symmetric' solutions is obtained by supplementing the metric, antisymmetric tensor and dilaton of the superstring solutions by the gauge field background equal to the generalised Lorentz connection with torsion. As in the superstring case, these backgrounds are $\a'$-independent, i.e. have a `semiclassical' form. The corresponding heterotic string sigma model is obtained from the combination of the (1,0) supersymm…
We reformulate the matrix models of minimal superstrings as loop gas models on random surfaces. In the continuum limit, this leads to the identification of minimal superstrings with certain bosonic string theories, to all orders in the genus expansion. RR vertex operators arise as operators in a Z_2 twisted sector of the matter CFT. We show how the loop gas model implements the sum over spin structures expected from the continuum RNS formulation. Open string boundary conditions are also more transparent in this language.
In this short note we give an example of the exact solution of the open bosonic string field theory defined on the background of $N$ coincided D0-branes. This solution leads to the change of the original background to the background where D0-branes are localised in general positions.
It is shown that the bosonic angular degrees of freedom in the one dimensional Marinari-Parisi superstring can be integrated out exactly in the Hamiltonian formulation without having to perform the Dabholkar truncation. The resulting Hamiltonian is that of a supersymmetric Calogero system plus a four fermions interaction. This extra interaction vanishes for all physical states with fermion number zero or one where supersymmetry is manifest. We confirm that supersymmetry is nonperturbativly broken by instanton effects.
We consider bosonic open string field theory in marginally deformed backgrounds, which is obtained by expanding the string field around the identity-based solutions associated with marginal deformations. We find a new set of string fields which satisfies the KBc algebra, but the nilpotent kinetic operator is that of the theory expanded around the identity-based marginal solution. By use of these string fields, we construct the tachyon vaccum solution in marginally deformed backgrounds. The vacuum energy density is equivalent to that of the tachyon vacuum without marginal deformations. The gaug…
In the framework of WZW-like open superstring field theory (SSFT) including the Ramond (R) sector whose action was constructed by Kunitomo and Okawa, we truncate the string fields in both the Neveu-Schwarz (NS) and R sectors up to the lowest massless level and obtain the ten-dimensional super Yang-Mills (SYM) action with bosonic extra term by explicit calculation of the SSFT action. Furthermore, we compute a contribution from the massive part up to the lowest order and find that the bosonic extra term is canceled and instead a fermionic extra term appears, which can be interpreted as a string …
I review the covariant quantization of the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. The BRST analysis yields massless bosonic and fermionic vertex operators in various ghost and picture number sectors, as well as picture-changers and their inverses, depending on the field basis chosen for bosonization. Two distinct GSO projections exist, one (untwisted) retaining merely the known bosonic scalar and its spectral-flow partner, the other (twisted) yielding two fermions and one boson, on the massless level. The absence of interactions in the latter case rules …
A discussion of the number of degrees of freedom, and their dynamical properties, in higher derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of auxiliary fields. As a by-product we present a consistent non-linear coupling of a spin-2 tensor to gravitation. It is shown that non-vanishing $(C_{μναβ})^{2}$ terms arise in $N=1$, $D=4$ superstring Lagrangians due to one-loop radiative corrections with light field internal lines. We discuss the general form of quadratic $(1,1)$ supergravity in two dimension…
The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint $\partial x^m (γ_mλ)_α=0$ where $λ^α$ is a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro constraint $\partial x^m \partial x_m =0$, and the Green-Schwarz fermionic spacetime spinor variables $θ^α$ arise as Faddeev-Popov ghosts for this constraint. In this paper, the purely bosonic classical action is simplified by replacing the classical d=10 pure spinor $λ^α$ with a d=10 projective pure spinor. The pure spinor an…
We test exact marginality of the deformation describing the blow-up of a zero-size D(-1) brane bound to a background of D3-branes by analyzing the equations of motion of superstring field theory to third order in the size. In the process we review the derivation of the instanton profile from string theory, extending it to include $α'$- corrections.
