We perform a detailed study of the type IIA superstring in AdS(4) x CP(3). After introducing suitable bosonic light-cone and fermionic kappa worldsheet gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone Hamiltonian up to quartic order in fields.
As a first application of our derivation we calculate energy shifts for string configurations in a closed fermionic subsector and successfully match these with a set of light-cone Bethe equations. We then turn to investigate the mismatch between the degrees of freedom of scattering states and oscillatory string modes. Since only light string modes appear as fundamental Bethe roots in the scattering theory, the physical role of the remaining $4_F+4_B$ massive oscillators is rather unclear. By continuing a line of research initiated by Zarembo, we shed light on this question by calculating quantum corrections for the propagators of the bosonic massive fields. We show that, once loop corrections are incorporated, the massive coordinates dissolve in a continuum state of two light particles.
In this paper we consider the worldsheet of superstring as a noncommutative space. Some additional terms can be added to the superstring action, such that for ordinary worldsheet they are zero. Expansion of this extended action up to the first order of the noncommutativity parameter, leads to the new supersymmetric action for string. For the closed superstring, we obtain the boundary state that describes a brane. From the open string point of view, the new boundary conditions on the worldsheet bosons, generalize the noncommutativity of spacetime. Finally, we suggest some definitions for the no…
We construct the type IIA Green-Schwarz superstring action on a ten-dimensional IIA plane wave background with 24 supersymmetries keeping the full 32 fermionic coordinates. Starting from the symmetry superalgebra for the maximally supersymmetric eleven dimensional plane wave background, we obtain the eleven dimensional superfields. The Kaluza-Klein reduction leads to the ten dimensional superfields for the IIA plane wave background, from which the type IIA superstring action is constructed. We show that the superstring action reduces correctly to the previously known light-cone gauge fixed act…
In this paper some properties of the superstring with noncommutative worldsheet are studied. We study the noncommutativity of the spacetime, generalization of the Poincaré symmetry of the superstring, the changes of the metric, antisymmetric tensor and dilaton.
Large N topological string dualities have led to a class of proposed open/closed dualities for superstrings. In the topological string context, the worldsheet derivation of these dualities has already been given. In this paper we take the first step in deriving the full ten-dimensional superstring dualities by showing how the dualities arise on the superstring worldsheet at the level of F terms. As part of this derivation, we show for F-term computations that the hybrid formalism for the superstring is equivalent to a $\hat c=5$ topological string in ten-dimensional spacetime. Using the $\hat …
We study the superstring theory with an Abelian worldsheet gauge field. The components of the gauge field appear as a space and a time coordinates. We call them as "fictitious coordinates". The worldsheet supersymmetry and the Poincaré symmetry of this model will be analyzed. The $T$-duality and quantization of the two fictitious coordinates also will be obtained.
We propose a new formulation of the $D=3$ type II superstring which is manifestly invariant under both target-space $N=2$ supersymmetry and worldsheet $N=(1,1)$ super reparametrizations. This gives rise to a set of twistor (commuting spinor) variables, which provide a solution to the two Virasoro constraints. The worldsheet supergravity fields are shown to play the rôle of auxiliary fields.
The compactification of type IIA superstring on n-dimensional Calabi-Yau manifolds is discussed. In particular, a conjecture is given for type IIA extremal p-dimensional black brane attractors corresponding to Ads_{p+2}\times S^{8-2n-p} horizon geometries.
In this brief note, we show that the residual symmetries that arise in the analysis of the tensionless superstrings in the equivalent of the conformal gauge is (a trivial extension of) the recently discovered 3d Super Bondi-Metzner-Sachs algebra, discussed in the context of asymptotic symmetries of 3d Supergravity in flat-spacetimes. This helps us uncover a limiting approach to the construction of the tensionless superstring from the point of view of the worldsheet, analogous to the one we had adopted earlier for the closed tensionless bosonic string.
We consider the AdS_4 x CP^3 IIA superstring sigma-model in the background of the "spinning string" classical solution, which possesses two Noether spins. In the limit when one of the spins is infinite there are massless excitations, which govern the infrared worldsheet properties of the model. We obtain a sigma-model of CP^3 with fermions, which describes the dynamics of these massless modes.
In this work we propose a systematic way to compute the logarithmic divergences of composite operators in the pure spinor description of the $AdS_5\times S^5$ superstring. The computations of these divergences can be summarized in terms of a dilatation operator acting on the local operators. We check our results with some important composite operators of the formalism.
The twistor--like formulation of the type IIA superstring $σ$--model in D=10 is obtained by performing a dimensional reduction of the recently proposed twistor--like action of the supermembrane in D=11. The superstring action is invariant under local, worldsheet $(n,n)$ supersymmetry where $3\leq n \leq 8$ and is classical equivalent to the standard Green--Schwarz action (at least for $n=8)$
By defining the heterotic Green-Schwarz superstring action on an N=(2,0) super-worldsheet, rather than on an ordinary worldsheet, many problems with the interacting Green-Schwarz superstring formalism can be solved. In the light-cone approach, superconformally transforming the light-cone super-worldsheet onto an N=(2,0) super-Riemann surface allows the elimination of the non-trivial interaction-point operators that complicate the evaluation of scattering amplitudes. In the Polyakov approach, the ten-dimensional heterotic Green-Schwarz covariant action defined on an N=(2,0) super-worldsheet can…
We determine the off-shell symmetry algebra and representations of Type IIB superstring theory on $AdS_3\times S^3 \times T^4$ with mixed R-R and NS-NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R-R theory.
We show that the M-theory/IIA and IIA/IIB superstring dualities together with the diffeomorphism invariance of the underlying theories require the presence of certain p-brane bound states in IIA and IIB superstring theories preserving 1/2 of the spacetime supersymmetry. We then confirm the existence of IIA and IIB supergravity solutions having the appropriate p-brane bound states interpretation.
We compute one-loop corrections to the energy of a IIA giant magnon solution in the $AdS_4 \times CP^3$ background by using the standard quantum field theory (QFT) techniques. The string action is expanded around the solution to the quadratic order in the fluctuation fields. The resulting action has 2D coordinate dependent-coefficients, a feature that complicates the analysis. The solution contains a worldsheet velocity parameter $v$, and is expanded in terms of the parameter. A perturbative analysis is carried out by treating the $v$-dependent parts as vertices. The energy is computed by firs…
Two of the important unresolved issues concerning fractional superstrings have been the appearance of new massive sectors whose spacetime statistics properties are unclear, and the appearance of new types of ``internal projections'' which alter or deform the worldsheet conformal field theory in a highly non-trivial manner. In this paper we provide a systematic analysis of these two connected issues, and explicitly map out the effective post-projection worldsheet theories for each of the fractional-superstring sectors. In this way we determine their central charges, highest weights, fusion rule…
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 ${\hat D}$-dimensional target space worldsheet action and compactify the theory on a d-dimensional torus, $T^d$. 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 …
This paper considers the Free Differential Algebra and rheonomic parametrization of type IIA Supergravity, extended to include the BRS differential and the ghosts. We consider not only the ghosts lambda's of supersymmetry but also the ghosts corresponding to gauge and Lorentz transformations. In this way we can derive not only the BRS transformations of fields and ghosts but also the standard pure spinor constraints on lambda's. Moreover the formalism allows to derive the action for the pure spinor formulation of type IIA superstrings in a general background, recovering the action first obtain…
We study the low-lying excitations of Type IIA superstring theory in a plane wave background with 24 supersymmetries. In the light-cone gauge, the superstring action has ${\cal N}=(4,4)$ supersymmetry and is exactly solvable, since it is quadratic in superstring coordinates. We obtain explicitly the spectrum of the Type IIA supergravity fluctuation modes in the plane wave background and give its correspondence with the spectrum of string states from the zero-mode sector of the light-cone superstring Hamiltonian.
The physical states of D=5 holomorphic Chern-Simons theory correspond to on-shell D=10 open superstring states in the cohomology of $q_+$, where $q_+$ is one of the 16 spacetime supersymmetry generators. Scattering amplitudes of these states can be computed either using the usual Ramond-Neveu-Schwarz (RNS) superstring prescription with N=1 worldsheet supersymmetry, or using a topological $\hat c$=5 string theory with twisted N=2 worldsheet supersymmetry. It will be argued that the relation between D=5 holomophic Chern-Simons and the RNS superstring is identical to the relation between the the …
In light of the present LHC Run II at $\sqrt{s}=13$ $TeV$, string y standard-like model is studied. Concretely, a singlet $S $ scalar-extended SM given in terms four stacks of intersecting D6-branes in a type IIA superstring compactification producing a large gauge symmetry is examined. The involved scales are dealt with. According to the dark matter relic density, the mass of the scalar dark matter beyond the SM $m_{S}\lesssim 10^{3}GeV$ and the corresponding Higgs portal couplings $λ_{SH}\lesssim 10^{-8}$ are approached.
$\mathcal{G}$-structures, where $\mathcal{G}$ is a Lie group, are a uniform characterisation of many differential geometric structures of interest in supersymmetric compactifications of string theories. Calabi-Yau $n$-folds are instances of torsion-free $SU(n)$-structures, while more general structures with non-zero torsion are required for heterotic flux compactifications. Exceptional geometries in dimensions $7$ and $8$ with $\mathcal{G}=G_2$ and $Spin(7)$ also feature prominently in this thesis. We discuss multiple connections between such geometries and the worldsheet theory describing str…
We propose a new formulation of the heterotic $D=10$ Green-Schwarz superstring whose worldsheet is a superspace with two even and eight odd coordinates. The action is manifestly invariant under both target-space supersymmetry and a worldsheet reparametrisation supergroup. It contains only a finite set of auxiliary fields. The key ingredient are the commuting spinor (twistor) variables, which naturally arise as worldsheet superpartners of the target space Grassmann coordinates. These spinors parametrise the sphere $S^8$ regarded as a coset space of the $D=10$ Lorentz group. The sphere is associ…
We calculate the entropy of 4-charge extremal black holes in Type IIA supersting theory by using Sen's entropy function method. Using the low energy effective actions in both $10D$ and 4D, we find precise agreements with the Bekenstein-Hawking entropy of the black hole. We also calculate the higher order corrections to the entropy and find that they depend on the exact form of the higher order corrections to the effective action.
We compute the massive-sector worldsheet S-matrix for superstring theories in AdS(n) x S(n) x T(10-2n) (with n=2,3,5) in the near BMN expansion up to one-loop order in inverse string tension. We show that, after taking into account the wave function renormalization, the one-loop S-matrix is UV finite. In an appropriate regularization scheme the S-matrix is consistent with the underlying symmetries of the superstring theory, i.e. for the n=3,5 cases it coincides with the one implied by the light-cone gauge symmetries with the dressing phases determined from the crossing equations. For the n=2,3…
A quantizable worldsheet action is constructed for the superstring in a supersymmetric plane wave background with Ramond-Ramond flux. The action is manifestly invariant under all isometries of the background and is an exact worldsheet conformal field theory.
In the previous paper, the authors pointed out correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background from the viewpoint of symmetries and spectrum. In this paper we further investigate the correspondence from dynamical aspects by comparing scattering amplitudes in the matrix model and those in the type IIA theory. In the latter, cocycle factors are introduced to vertex operators in order to reproduce correct transformation laws and target-space statistics. By a perturbative treatment of the Ramond-R…
This is the second installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this second part, we study worldsheet functions defined on a genus-one surface built from the coefficient functions of the Kronecker--Einsenstein series. We construct two classes of worldsheet functions whose properties lead to several simplifying features within our description of one-loop correlators with the pure-spinor formalism. The first class is described by functions with prescribed mon…
We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the correspond…
Fractional superstrings are non-trivial generalizations of ordinary superstrings and heterotic strings, and have critical spacetime dimensions which are less than ten by virtue of a worldsheet fractional supersymmetry relating worldsheet bosons to worldsheet parafermions. In this paper, I provide a short non-technical survey of the fundamental issues involved in these recently-proposed theories. After introducing the basic ideas which underlie these new string theories, I review their early successes and outline some related outstanding questions. ( Talk given at the Internal Workshop on Strin…
Motivated by the M-theory compactification physics, we study a type IIA superstring quiver model with an open string axion field associated with the U(1)_{PQ} Peccei-Quinn global symmetry using D6-brane physics. This realization extends the symmetry of the SM-Like and contributes to the mediation of the electroweak symmetry breaking. The associated axion energy scales are approached in terms of D2 and D6-branes in type IIA compactifications on Calabi-Yau threeforlds. Using the fermion mass scales as well as string theory results, the allowed axion window is discussed in terms of intersecting D…
Witten proposed that the low energy physics of strongly coupled D=10 type-IIA superstring may be described by D=11 supergravity. To explore the stringy aspects of the underlying theory we examine the stringy massive states. We propose a systematic formula for identifying non-perturbative states in D=10 type-IIA superstring theory, such that, together with the elementary excited string states, they form D=11 supersymmetric multiplets multiplets in SO(10) representations. This provides hints for the construction of a weakly coupled D=11 theory that is dual to the strongly coupled D=10 type IIA s…
A brane picture in Type IIA superstring for the Yang Monopole is reconsidered. It makes use of D2 and D4-branes wrapped on cycles in the K3 surface. When the model was first presented some problems concerning the charges of the monopoles arised. In this paper, they are shown to be cured by the model itself. Surprisingly, the incompatibility between the multi-charge configuration and the spherical symmetry of the Yang Monopole is seen in the brane description as the emergence of the enhancon shell and the fuzzy geometry. This consistency is deep and surprising, and is the point that triggered t…
We study the annulus amplitudes in the (2,4) minimal superstring theory using the continuum worldsheet approach. Our results reproduce the semiclassical behavior of the wavefunctions of FZZT-branes recently studied in hep-th/0412315 using the dual matrix model. We also study the multi-point functions of neutral FZZT-branes and find the agreement between their semiclassical limit and the worldsheet annulus calculation.
In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected …
A covariant action for closed D=11 superstring with local $κ$-symmetry and global supersymmetry transformations obeying the algebra $\{Q_α,Q_β\}=CΓ^{μν}P_μn_ν$ is suggested. Physical sector variables of the model and their dynamics exactly coincide with those of the D=10 type IIA Green-Schwarz superstring. It is shown that action of the D=10 type IIA Green-Schwarz superstring can be considered as a partially gauge fixed version of the D=11 superstring action.
We lift the bosonic AdS_4 x CP^3 solution of type IIA supergravity preserving 24 supersymmetries to a D=10 superspace which has 32 Grassmann-odd directions. The type IIA superspace is obtained from D=11 via dimensional reduction of the coset superspace OSp(8|4)/SO(7) x SO(1,3) by realizing the latter as a Hopf fibration over the former. This construction generalizes to superspace the Hopf fibration of S^7 as a U(1) bundle over CP^3, and is suitable for writing the explicit form of Green-Schwarz-type actions encoding the dynamics of the type IIA string and branes in the AdS_4 x CP^3 superbackgr…
Fractional superstrings experience new types of ``internal projections'' which alter or deform their underlying worldsheet conformal field theories. In this talk I summarize some recent results concerning both the worldsheet theory which remains after the internal projections have acted, and the spacetime statistics properties of its various sectors.
We present a geometric formulation of type-IIA and -IIB superstring theories in which the Wess-Zumino term is second order in the supersymmetric currents. The currents are constructed using supergroup manifolds corresponding to superalgebras: the IIA superalgebra derived from M-algebra and the IIB superalgebra obtained by a T-duality transformation of the IIA superalgebra. We find that a slight modification of the IIB superalgebra is needed to describe D-string theories, in which the U(1) gauge field on the worldsheet is explicitly constructed in terms of D-string charges. A unification of the…
We consider orientifolds of Calabi-Yau 3-folds in the context of Type IIA and Type IIB superstrings. We show how mirror symmetry can be used to sum up worldsheet instanton contributions to the superpotential for Type IIA superstrings. The relevant worldsheets have the topology of the disc and ${\bf RP^2}$.
As was observed by Grigoriev and Tseytlin, the Pohlmeyer-reduced AdS_2 x S^2 superstring theory possesses N=(2,2) worldsheet supersymmetry. We show, at the classical level, that the AdS_3 x S^3 and AdS_5 x S^5 superstring theories in the Pohlmeyer-reduced form reveal hidden N=(4,4) and N=(8,8) worldsheet supersymmetries. Our consideration is based on the modified mass-deformed gauged WZW action for the superstring equations. We present the explicit form of the supersymmetry transformations for both the off-shell action and the superstring equations. The characteristic feature of these transfor…
In this short review (to appear as a contribution to an edited volume) we discuss perturbative and non-perturbative approaches to the quantization of the Green-Schwarz string in AdS backgrounds with RR-fluxes, where the guiding thread is the use of genuine field theory methods, the search for a good regularization scheme associated to them and the generality of the analysis carried out. We touch upon various computational setups, both analytical and numerical, and on the role of their outcomes in understanding the detailed structure of the AdS/CFT correspondence.
The pure spinor formalism for the superstring can be formulated as a twisted N=2 worldsheet theory with fermionic generators $j_{BRST}$ and composite $b$ ghost. After untwisting the formalism to an N=1 worldsheet theory with fermionic stress tensor $j_{BRST}+b$, the worldsheet variables combine into N=1 worldsheet superfields $X^m$ and $Θ^α$ together with a superfield constraint relating $DX^m$ and $DΘ^α$. The constraint implies that the worldsheet superpartner of $θ^α$ is a bosonic twistor variable, and different solutions of the constraint give rise to the pure spinor or extended RNS formali…
In this note we study worldsheet two- and four-point functions at the one-loop level for the type IIA superstring in AdS(3) x S(3) x M(4) . We first address the regularization ambiguity that appears in the dispersion relation derived from integrability. We demonstrate that only the regulator treating all fields equally respects worldsheet supersymmetry. This is done in an implicit regularization scheme where all divergent terms are collected into master tadpole-type integrals. We then investigate one-loop two-body scattering on the string worldsheet and verify that a recent proposal for the dr…
We study N=1 four dimensional gauge theories as the world volume theory of D4-branes between NS 5-branes. We find constructions for a number of known field theory dualities involving $SU(N_c)\times SU(N_c')$ groups, coupled by matter fields F in the $(N_c, \bar N_c)$ representation, in terms of branes of type IIA string theory. The dual gauge group follows from simply reversing the ordering of the NS 5-branes and the D6-branes while conserving magnetic charge on the world volume of the branes. We interpret many field theory phenomena such as deformation of the superpotential $W = \Tr (F\tilde …
It was earlier shown that an SO(9,1) $θ^\a$ spinor variable can be constructed from RNS matter and ghost fields. $θ^\a$ has a bosonic worldsheet super-partner $λ^\a$ which plays the role of a twistor variable, satisfying $λΓ^μλ= \partial x^μ+iθΓ^μ\partialθ$. For Type IIA superstrings, the left-moving $[θ_L^\a,λ_L^\a]$ and right-moving $[θ_{R\a},λ_{R\a}]$ can be combined into 32-component SO(10,1) spinors $[θ^A,λ^A]$. This suggests that $λ^A Γ^{11}_{AB}λ^B= 2λ_L^\a λ_{R\a}$ can be interpreted as momentum in the eleventh direction. Evidence for this interpretation comes from the zero-momentum ve…
We consider superstring theories on pp-wave backgrounds which result in an integrable ${\cal N}=(2,2)$ supersymmetric Landau-Ginzburg theory on the worldsheet. We obtain exact eigenvalues of the light-cone gauge superstring hamiltonian in the massive and interacting world-sheet theory with superpotential $Z^3-Z$. We find the modes of the supergravity part of the string spectrum, and their space-time interpretation. Because the system is effectively at strong coupling on the worldsheet, these modes are not in one-to-one correspondence with the usual type IIB supergravity modes in the $p_{-} \to…
It is developed the phase-space formulation for the Type IIA superstring on the AdS_4 x CP^3 background in the kappa-symmetry light-cone gauge for which the light-like directions are taken from the D=3 Minkowski boundary of AdS_4. After fixing bosonic light-cone gauge the superstring Hamiltonian is expressed as a function of the transverse physical variables and in the quadratic approximation corresponds to the light-cone gauge-fixed IIA superstring in flat space.
We calculate the symmetry currents for the type IIB superstring on a maximally supersymmetric plane wave background using the N=(2,2) superconformally covariant U(4) formulation developed by Berkovits, Maldacena and Maoz. An explicit realization of the U(4) generators together with 16 fermionic generators is obtained in terms of the N=(2,2) worldsheet fields. Because the action is no longer quadratic, we use a light-cone version to display the currents in terms of the covariant worldsheet variables.
We analyze the interaction between the massless RR states with a dilaton in a type IIB superstring. By constructing vertex operators for massless and massive RR states and computing their correlation functions with a dilaton we find the Ramond-Ramond part of the superstring low-energy effective action. The RR terms appearing in the action do not contain the standard dilatonic factor (string coupling constant). The geometrical interpretation of this fact is presented. Namely we argue that the spin operators in the RR vertices effectively decrease the Euler character of the worldsheet by 1 unit.…
We analyze the vector multiplet prepotential of d=4, N=2 type IIA compactifications. We find that the worldsheet instanton corrections have a natural interpretation as one-loop corrections in five dimensions, with the extra dimension being compactified on a circle of radius $g_{s}\ell_{s}$. We argue that the relation between spacetime and worldsheet instantons is natural from this point of view. We also discuss the map between the type IIA worldsheet instantons and the spacetime instantons in the heterotic dual.
We point out that different choices of Gliozzi-Scherk-Olive (GSO) projections in superstring theory can be conveniently understood by the inclusion of fermionic invertible phases, or equivalently topological superconductors, on the worldsheet. This allows us to find that the unoriented Type $\rm 0$ string theory with $Ω^2=(-1)^{\sf f}$ admits different GSO projections parameterized by $n$ mod 8, depending on the number of Kitaev chains on the worldsheet. The presence of $n$ boundary Majorana fermions then leads to the classification of D-branes by $KO^n(X)\oplus KO^{-n}(X)$ in these theories, …
The topological part of the M-theory partition function was shown by Witten to be encoded in the index of an E8 bundle in eleven dimensions. This partition function is, however, not automatically anomaly-free. We observe here that the vanishing W_7=0 of the Diaconescu-Moore-Witten anomaly in IIA and compactified M-theory partition function is equivalent to orientability of spacetime with respect to (complex-oriented) elliptic cohomology. Motivated by this, we define an elliptic cohomology correction to the IIA partition function, and propose its relationship to interaction between 2-branes and…
In superstring theory spin structures are present on both the 2-dimensional worldsheet and 10-dimensional spacetime. We present a new proposal for the B-field in superstring theory and demonstrate its interaction with worldsheet spin structures. Our formulation generalizes to orientifolds, where various twistings appear. A special case of the orientifold worldsheet B-field amplitude is a KO-theoretic construction of the Z/8Z-valued Kervaire invariant on pin-minus surfaces.
