Disk Amplitudes Research Articles

$ \mathcal{N} = 2 $ instanton effective action in Ω-background and D3/D(−1)-brane system in R-R background

We study the relation between the ADHM construction of instantons in the Ω-background and the fractional D3/D(−1)-branes at the orbifold singularity of $ \mathbb{C} \times {{{{\mathbb{C}^2}}} \left/ {{{\mathbb{Z}_2}}} \right.} $ in Ramond-Ramond (R-R) 3-form field strength background. We calculate disk amplitudes of open strings connecting the D3/D(−1)-branes in certain R-R background to obtain the D(−1)-brane effective action deformed by the R-R background. We show that the deformed D(−1)-brane effective action agrees with the instanton effective action in the Ω-background.

The supergravity fields for a D-brane with a travelling wave from string amplitudes

We calculate the supergravity fields sourced by a D-brane with a null travelling wave from disk amplitudes in type IIB string theory compactified on T4×S1. The amplitudes reproduce all the non-trivial features of the previously known two-charge supergravity solutions in the D-brane/momentum duality frame, providing a direct link between the microscopic bound states and their macroscopic descriptions.

On-shell recursion in string theory

We prove that all open string theory disc amplitudes in a flat background obey Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relations, up to a possible reality condition on a kinematic invariant. Arguments that the same holds for tree level closed string amplitudes are given as well. Non-adjacent BCFW-shifts are related to adjacent shifts through monodromy relations for which we provide a novel CFT based derivation. All possible recursion relations are related by old-fashioned string duality. The field theory limit of the analysis for amplitudes involving gluons is explicitly shown to be smooth for both the bosonic string as well as the superstring. In addition to a proof a less rigorous but more powerful argument based on the underlying CFT is presented which suggests that the technique may extend to a much more general setting in string theory. This is illustrated by a discussion of the open string in a constant B-field background and the closed string on the level of the sphere.

Higher derivative brane couplings from T-duality

The Wess-Zumino coupling on D-branes in string theory is known to receive higher derivative corrections which couple the Ramond-Ramond potential to terms involving the square of the spacetime curvature tensor. Consistency with T-duality implies that the branes should also have four-derivative couplings that involve the NS-NS B-field. We use T-duality to predict some of these couplings. We then confirm these results with string worldsheet computations by evaluating disc amplitudes with insertions of one R-R and two NS-NS vertex operators.

Fractional-superstring amplitudes, multi-cut matrix models and non-critical M theory

Multi-cut two-matrix models are studied in the Z k symmetry breaking k-cut ( p ˆ , q ˆ ) critical points which should correspond to ( p ˆ , q ˆ ) minimal k-fractional superstring theory. FZZT-brane or macroscopic loop amplitudes are obtained in all of these critical points and found to have two kinds of solutions in general. Each of these solutions is expressed by hyperbolic cosine or sine functions with proper phase shifts. The algebraic geometries and ZZ-brane disk amplitudes (instanton actions) of these solutions are also studied. In particular, our results suggest that minimal ∞-fractional superstring theory can be viewed as a mother theory which includes all the minimal k-fractional superstring theories ( k = 1 , 2 , … ) as its perturbative vacua in the weak-coupling string Landscape. Our results also indicate that, in the strong coupling regime of this fractional superstring theory, there is a three-dimensional theory which would be understood as the non-critical version of M theory in the sense proposed by P. Hořava and C.A. Keeler.

The LHC String Hunter's Companion (II): Five-particle amplitudes and universal properties

We extend the study of scattering amplitudes presented in “The LHC String Hunter's Companion” [1] to the case of five-point processes that may reveal the signals of low mass strings at the LHC and are potentially useful for detailed investigations of fundamental Regge excitations. In particular, we compute the full-fledged string disk amplitudes describing all 2 → 3 parton scattering subprocesses leading to the production of three hadronic jets. We cast our results in a form suitable for the implementation of stringy partonic cross sections in the LHC data analysis. We discuss the universal, model-independent features of multi-parton processes and point out the existence of even stronger universality relating N-gluon amplitudes to the amplitudes involving N − 2 gluons and one quark–antiquark pair. We construct a particularly simple basis of two functions describing all universal five-point amplitudes. We also discuss model-dependent amplitudes involving four fermions and one gauge boson that may be relevant for studying jets associated to Drell–Yan pairs and other processes depending on the spectrum of Kaluza–Klein particles, thus on the geometry of compact dimensions.

Vertex operators of type IIB matrix model via calculation of disk amplitudes

We investigate the vertex operators of the supergravity multiplet in IIB (IKKT) matrix model by calculating the disk amplitudes, exploiting the technique of conformal field theory. The vertex operators of IIB matrix model are given as the coupling of a closed string and the open strings which are introduced by the existence of D(−1)-branes. We consider the most generic couplings which involve both the bosonic and fermionic open strings. Our results are consistent with the previous results based on supersymmetry. We thus confirm the structure of the IIB matrix model vertex operators from the first principle.

MHV, CSW and BCFW: field theory structures in string theory amplitudes

Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of alpha'-corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the alpha'^3-correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.

Flux interactions on D-branes and instantons

We provide a direct world-sheet derivation of the couplings of NS-NS and R-R fluxes to various types of D-branes (including instantonic ones) by evaluating disk amplitudes among two open string vertex operators at a generic brane intersection and one closed string vertex representing the background fluxes. This world-sheet approach is in full agreement with the derivation of the flux couplings in the brane effective actions based on supergravity methods, but it is applicable also to more general brane configurations involving fields with twisted boundary conditions. As an application, we consider an orbifold compactification of Type IIB string theory with fractional D-branes preserving N=1 supersymmetry and study the flux-induced fermionic mass terms both on space-filling branes and on instantonic ones. Our results show the existence of a relation between the soft supersymmetry breaking and the lifting of some instanton fermionic zero-modes, which may lead to new types of non-perturbative couplings in brane-world models.

Constraining the D3-brane effective action

We consider higher derivative corrections of the type D^{2k} R^2 in the effective action of the D3-brane with trivial normal bundle. Based on the perturbative disc and annulus amplitudes, and constraints of supersymmetry and duality, we argue that these interactions are protected, at least for small values of k. Their coefficient functions receive only a finite number of perturbative contributions, and non-perturbative contributions from D-instantons. We propose expressions for these modular forms for low values of k.

D-brane States and Disk Amplitudes in OSp Invariant Closed String Field Theory

D-brane States and Disk Amplitudes in OSp Invariant Closed String Field Theory

D-brane states and disk amplitudes inOSpinvariant closed string field theory

We construct solitonic states in the OSp invariant string field theory, which are BRST invariant in the leading order of regularization parameter $\epsilon$. We calculate the disk amplitudes using these solitonic states and show that they describe D-branes and ghost D-branes.

Deformation of super Yang-Mills theories in R-R 3-form background

We study deformation of = 2 and = 4 super Yang-Mills theories, which are obtained as the low-energy effective theories on the (fractional) D3-branes in the presence of constant Ramond-Ramond 3-form background. We calculate the Lagrangian at the second order in the deformation parameter from open string disk amplitudes. In = 4 case we find that all supersymmetries are broken for generic deformation parameter but part of supersymmetries are unbroken for special case. We also find that classical vacua admit fuzzy sphere configuration. In = 2 case we determine the deformed supersymmetries. We rewrite the deformed Lagrangians in terms of = 1 superspace, where the deformation is interpreted as that of coupling constants.

Deformation of Script N = 4 super Yang–Mills theory in graviphoton background

We study deformation of N=4 super Yang-Mills theory from type IIB superstrings with D3-branes in the constant R-R background. We compute disk amplitudes with one graviphoton vertex operator and investigate the zero-slope limit of the amplitudes. We obtain the effective action deformed by the graviphoton background, which contains the one defined in non(anti)commutative N=1 superspace as special case. The bosonic part of the Lagrangian gives the Chern-Simons term coupled with the R-R potential. We study the vacuum configuration of the deformed Lagrangian and find the fuzzy sphere configuration for scalar fields.

A string field theoretical description of (p,q) minimal superstrings

A string field theory of (p,q) minimal superstrings is constructed with the free-fermion realization of 2-component KP (2cKP) hierarchy, starting from 2-cut ansatz of two-matrix models. Differential operators of 2cKP hierarchy are identified with operators in super Liouville theory, and we obtain algebraic curves for the disk amplitudes of \eta=-1 FZZT-branes and the partition functions of neutral/charged \eta=-1 ZZ branes, which correctly reproduce those of type 0B (p,q) minimal superstrings in conformal backgrounds. In the course of study, some subtle points are clarified, including a difference of (p,q) even/odd models and quantization of flux, and we show that the Virasoro constraints naturally incorporate quantized fluxes without ambiguity. We also argue within this string field framework that type 0A minimal superstrings can be obtained by orbifolding the type 0B strings with a Z_2 symmetry existing when special backgrounds are taken.

Multigluon scattering in open superstring theory

We discuss the amplitudes describing $N$-gluon scattering in type I superstring theory, on a disk world sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit (${\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\rightarrow}0$) is particularly simple. We obtain the full-fledged MHV disk amplitudes for $N=4$, 5, and $N=6$ gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals---generalized Euler integrals---which for $N\ensuremath{\ge}6$ correspond to multiple hypergeometric series (generalized Kamp\'e de F\'eriet functions). Their ${\ensuremath{\alpha}}^{\ensuremath{'}}$ expansions lead to Euler-Zagier sums. For arbitrary $N$, we show that the leading string corrections to the Yang-Mills amplitude, of order $\mathcal{O}({\ensuremath{\alpha}}^{\ensuremath{'}2})$, originate from the well-known ${\ensuremath{\alpha}}^{\ensuremath{'}2}\text{ }\mathrm{Tr}{F}^{4}$ effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary $N$. We argue that such a procedure can be extended to all orders in ${\ensuremath{\alpha}}^{\ensuremath{'}}$. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multijet production at the Large Hadron Collider (LHC).

Non(anti)commutative Script N = 2 supersymmetric gauge theory from superstrings in graviphoton background

We study open string amplitudes with the D3-branes in type IIB superstring theory compactified on C^2/Z_2. We introduce constant graviphoton background along the branes and calculate disk amplitudes using the NSR formalism. We take the zero slope limit and investigate the effective Lagrangian on the D3-branes deformed by the graviphoton background. We find that the deformed Lagrangian agrees with that of N=2 supersymmetric U(N) gauge theory defined in non(anti)commutative N=1 superspace by choosing appropriate graviphoton background. It is also shown that abelian gauge theory defined in N=2 harmonic superspace with specific non-singlet deformation is consistent with the deformed theory.

Notes on the algebraic curves in (p,q) minimal string theory

Loop amplitudes in (p,q) minimal string theory are studied in terms of the continuum string field theory based on the free fermion realization of the KP hierarchy. We derive the Schwinger-Dyson equations for FZZT disk amplitudes directly from the W_{1+\infty} constraints in the string field formulation and give explicitly the algebraic curves of disk amplitudes for general backgrounds. We further give annulus amplitudes of FZZT-FZZT, FZZT-ZZ and ZZ-ZZ branes, generalizing our previous D-instanton calculus from the minimal unitary series (p,p+1) to general (p,q) series. We also give a detailed explanation on the equivalence between the Douglas equation and the string field theory based on the KP hierarchy under the W_{1+\infty} constraints.

Superstring disk amplitudes in a rolling tachyon background

We study the tree level scattering or emission of $n$ closed superstrings from a decaying non-BPS brane in Type II superstring theory. We attempt to calculate generic $n$-point superstring disk amplitudes in the rolling tachyon background. We show that these can be written as infinite power series of Toeplitz determinants, related to expectation values of a periodic function in Circular Unitary Ensembles. Further analytical progress is possible in the special case of bulk-boundary disk amplitudes. These are interpreted as probability amplitudes for emission of a closed string with initial conditions perturbed by the addition of an open string vertex operator. This calculation has been performed previously in bosonic string theory, here we extend the analysis for superstrings. We obtain a result for the average energy of closed superstrings produced in the perturbed background.

Collisions of cosmic F- and D-strings

Recent work suggests that fundamental and Dirichlet strings, and their (p,q) bound states, may be observed as cosmic strings. The evolution of cosmic string networks, and therefore their observational signals, depends on what happens when two strings collide. We study this in string perturbation theory for collisions between all possible pairs of strings; different cases involve sphere, disk, and annulus amplitudes. The result also depends on the details of compactification; the dependence on ratios of scales is only logarithmic, but this is still numerically important. We study a range of models and parameters, and find that in most cases these strings can be distinguished from cosmic strings that arise as gauge theory solitons.