It is shown that the generating function of $\mathscr{N}=2$ topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. This background, which corresponds to an exact CFT, realises in string theory the six-dimensional $\varOmega$-background of Nekrasov, in the case of opposite deformation parameters $ε_1=-ε_2$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary $\mathscr{N}=2$ and $\mathscr{N}=2^*$ theories.
The recently introduced anomaly-free twistor string in 4 dimensions is further explored. The spectrum based on the physical states and its Minkowski interpretation are examined. Scattering amplitudes with vertex operators involving gravitons and fermions are computed and are compared with Einstein-Yang-Mills amplitudes. Tree and one-loop scattering amplitudes are shown to have proper unitary factorization properties. Finally a string field theory is proposed.
In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory…
We continue our study of the Kawai-Lewellen-Tye (KLT) factorization of winding string amplitudes. In a toroidal compactification, amplitudes for winding closed string states factorize into products of amplitudes for open strings ending on an array of D-branes localized in the compactified directions; the specific D-brane configuration is determined by the closed string data. In this paper, we study a zero Regge slope limit of the KLT relations between winding string amplitudes. Such a limit of string theory requires a critically tuned Kalb-Ramond field in a compact direction, and leads to a se…
We overview symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the infinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scattering…
We compute the normalization of the D-instanton amplitudes in type 0B string theory in two dimensions and find perfect agreement with the dual matrix model result.
We evaluate four-gauge-particle tree level scattering amplitudes using the Polyakov string path integral in the proper-time gauge, where the string path integral can be cast into the Feynman-Schwinger proper-time representation. We compare the resultant scattering amplitudes, which include $\ap$-corrections, with the conventional ones that may be obtained by substituting local vertex operators for the external string states. In the zero-slope limit, both amplitudes are reduced to the four-gauge-particle scattering amplitude of non-Abelian Yang-Mills gauge theory. However, when the string corre…
Plahte identities are monodromy relations between open string scattering amplitudes at tree level derived from the Koba-Nielsen formula. We represent these identities by polygons in the complex plane. These diagrams make manifest the appearance of sign changes and singularities in the analytic continuation of amplitudes. They provide a geometric expression of the KLT relations between closed and open string amplitudes. We also connect the diagrams to the BCFW on-shell recursion relations and generalise them to complex momenta resulting in a relation between the complex phases of partial amplit…
In this paper, we study the open topological string amplitudes on Calabi-Yau threefolds by the extended holomorphic anomaly equation. The disk two-point function determined by the domainwall tension, together with the Yukawa couplings, solves the amplitudes with high genus and boundaries recursively. The BPS invariants encoded in the amplitudes are extracted by mirror symmetry.
We explore and exploit the relation between non-planar correlators in ${\cal N}=4$ super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS$_5\times S^5$ in the low-energy expansion, dual to an ${\cal N}=4$ super-Yang-Mills correlator in the 't Hooft limit at order $1/c^2$ in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduc…
We present an integration-by-parts reduction of any massless tree-level string correlator to an equivalence class of logarithmic functions, which can be used to define a field-theory amplitude via a Cachazo-He-Yuan (CHY) formula. The string amplitude is then shown to be the double copy of the field-theory one and a special disk/sphere integral. The construction is generic as it applies to any correlator that is a rational function of correct SL(2) weight. By applying the reduction to open bosonic/heterotic strings, we get a closed-form CHY integrand for the $(DF)^2+\text{YM}+ϕ^3$ theory.
We point out some common qualitative features of the Coon amplitude$\unicode{x2014}$a family of deformations of the Veneziano amplitude with logarithmic Regge trajectories$\unicode{x2014}$and the open string scattering amplitude for strings ending on a D-brane in AdS. Both reduce to the Veneziano amplitude at relatively low energies. Both systems have an accumulation point in their spectrum, with an infinite number of states below a certain energy. The approach to this point is very similar. Both have the same high-energy fixed-angle behavior. Nevertheless, we find some differences in the spec…
Abstract: We show that boundary string field theory realizes the minimal model of open string field theory. More precisely, we observe that the expansion of the (co)homological vector field, $Q$ of boundary string field theory in the cohomology of its linear part reproduces the S-matrices of perturbative string theory. In mathematical terms, boundary string field theory realizes the minimal model map of the cohomological perturbation lemma.
In this text we review various relations between building blocks of closed and open string amplitudes at tree-level and genus one. We explain that KLT relations between tree-level closed and open string amplitudes follow from the holomorphic factorisation of conformal correlation functions on conformal blocks. We give a simple hands-on evaluation of the $α'$-expansion of tree-level closed string amplitudes displaying the special single-valued nature of the coefficients. We show that the same techniques can be used also at genus-one, where we give a new proof of the single-valued nature of the …
We present a series of new gauge invariant quantities in Witten's open string field theory. They are defined for a given set of open string states which satisfy the physical state condition around a classical solution. For known classical solutions, we show that these gauge invariant quantities compute on shell tree-level scattering amplitudes around the correspondent D-brane configuration.
