相关论文: Tropical Amplitudes
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the…
The tree-level amplitudes in $\beta$-deformed theory are studied from twistor string theory. We first show that a simple generalization of the proposal in hep-th/0410122 gives the correct results for all of the tree-level amplitudes to the…
The two-loop Feynman diagram contribution to the four-graviton amplitude of eleven-dimensional supergravity compactified on a two-torus, T^2, is analyzed in detail. The Schwinger parameter integrations are re-expressed as integration over…
We present all-multiplicity formulae, derived from first principles in the MHV sector and motivated by twistor string theory for general helicities, for the tree-level S-matrix of gluon scattering on self-dual radiative backgrounds. These…
A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized N=2 F-terms of the form F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms involve…
We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of $\mathbb{Z}_2$ symmetry and that the particle is $\mathbb{Z}_2$ odd. We consider two classes of amplitudes: the fully…
The analysis of the Lyman-alpha forest of absorption lines in quasar spectra has emerged as a potentially powerful technique to constrain the linear matter power spectrum. In most previous work, the amplitude of the ionizing background was…
Starting from the superstring amplitude describing interactions among D-branes with a constant world-volume field strength, we present a detailed analysis of how the open string degeneration limits reproduce the corresponding field theory…
We use tropical and nonarchimedean geometry to study the moduli space of genus $0$ stable maps to $\mathbb{P}^1$ relative to two points. This space is exhibited as a tropical compactification in a toric variety. Moreover, the fan of this…
We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper. Using dihedral coordinates on the moduli spaces of…
Four-dimensional conformal fishnet theory is an integrable scalar theory which arises as a double scaling limit of $\gamma$-deformed maximally supersymmetric Yang-Mills. We give a perturbative reformulation of $\gamma$-deformed…
Starting from tree and one-loop tachyon amplitudes of open string theory in the presence of a constant B-field, we explore two problems. First we show that in the noncommutative field theory limit the amplitudes reduce to tree and one-loop…
We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…
We analyze the one-loop effective gauge-field action in $Z_2$-orbifold compactifications of type-I theory. We show how, for non-abelian group factors, the threshold effects are ultraviolet finite though given entirely by a six-dimensional…
We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
We present the analytic form of the two-loop four-graviton scattering amplitudes in Einstein gravity. To remove ultraviolet divergences we include counterterms quadratic and cubic in the Riemann curvature tensor. The two-loop numerical…
We calculate on-shell scattering amplitudes involving fermions at the tree level in open superstring field theory. We confirm that four-point and five-point amplitudes in the world-sheet path integral with the standard prescription using…
Motivated by the standard form of string-theory amplitude, we calculate the field-theory amplitude to complete the higher-derivative terms in type II supergravity theories in their conventional form. We derive explicitly the $ O(\alpha'^3)…
Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique…