Related papers: Evaluating one-loop string amplitudes

We relate one-loop scattering amplitudes of massless open- and closed-string states at the level of their low-energy expansion. The modular graph functions resulting from integration over closed-string punctures are observed to follow from…

The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…

We study the behavior of the effective potential between revolving D$p$-branes at all ranges of the distance $r$, interpolating $r \gg l_s$ and $r \ll l_s$ ($l_s$ is the string length). Since the one-loop open string amplitude cannot be…

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method…

Exact Superstring solutions are constructed moving in 4-D space-time with positive curvature and non-trivial dilaton and antisymmetric tensor fields. The full spectrum of string excitations is derived as a function of moduli fields $T^{i}$…

We show that the single trace heterotic N-point tree-level gauge amplitude A_HET can be obtained from the corresponding type I amplitude A_I by the single-valued (sv) projection: A_HET=sv(A_I). This projection maps multiple zeta values to…

We present the complete four-loop four-point amplitude in N=4 super-Yang-Mills theory, for a general gauge group and general D-dimensional covariant kinematics, and including all non-planar contributions. We use the method of maximal cuts…

We study scalar one-loop amplitudes in massive $\phi^3$-theory within causal loop-tree duality. We derive a recurrence relation for the integrand of the amplitude. The integrand is by construction free of spurious singularities on…

We discuss algebraic/numeric methods to compute one-loop corrections for multiparticle/jet production cross sections. By using efficient reduction algorithms a compact expression for the ggg\gamma\gamma -> 0 amplitude is obtained. Further a…

We analyze the fixed-angle high-energy ($\alpha' \to \infty$) structure of $n$-point tree-level string amplitudes from complementary perspectives: locally via saddle-point expansions, algebraically via difference equations and their…

This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop…

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism.

Recent progress in the computation of one-loop gluon amplitudes is reviewed. These methods were originally derived from superstring theory and are significantly more efficient than conventional Feynman rules. With these methods, explicit…

We compute the imaginary parts of genus-one string scattering amplitudes. Following Witten's $i\varepsilon$ prescription for the integration contour on the moduli space of worldsheets, we give a general algorithm for computing unitarity…

The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…

Using the recent results in the pure spinor formulation, we lay out a ground-work towards the full momentum space amplitudes of open superstrings at three-loop. After briefly reviewing the one-loop amplitude, we directly work out the…

The overall coefficient of the two-loop 4-particle amplitude in superstring theory is determined by making use of the factorization and unitarity. To accomplish this we computed in detail all the relevant tree and one-loop amplitudes…

We express one-loop closed string amplitudes as weighted sums over squares of open string one-loop subamplitudes. These findings generalize - subject to final complex structure modulus integration - the celebrated tree-level relationships…

The open string with one-dimensional target space is formulated in terms of an SOS, or loop gas, model on a random surface. We solve an integral equation for the loop amplitude with Dirichlet and Neumann boundary conditions imposed on…

We show that, in analyzing differential equations obeyed by one-loop gauge theory amplitudes, one must take into account a certain holomorphic anomaly. When this is done, the results are consistent with the simplest twistor-space picture of…