Compact QED tree-level amplitudes from dressed BCFW recursion relations

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N²MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial.     

Diagrammatic proof of the BCFW recursion relation for gluon amplitudes in QCD

We present a proof of the Britto–Cachazo–Feng–Witten tree-level recursion relation for gluon amplitudes in QCD, based on a direct equivalence between BCFW decompositions and Feynman diagrams. We demonstrate that this equivalence can be made explicit when working in a convenient gauge. We exhibit that gauge invariance and the particular structure of Yang–Mills vertices guarantee the validity of the BCFW construction.     

Pomerons and BCFW recursion relations for strings on D-branes

We derive pomeron vertex operators for bosonic strings and superstrings in the presence of D-branes. We demonstrate how they can be used in order to compute the Regge behavior of string amplitudes on D-branes and the amplitude of ultrarelativistic D-brane scattering. After a lightning review of the BCFW method, we proceed in a classification of the various BCFW shifts possible in a field/string theory in the presence of defects/D-branes. The BCFW shifts present several novel features, such as the possibility of performing single particle momentum shifts, due to the breaking of momentum conservation in the directions normal to the defect. Using the pomeron vertices we show that superstring amplitudes on the disc involving both open and closed strings should obey BCFW recursion relations. As a particular example, we analyze explicitly the case of 1→1$1\to 1$ scattering of level one closed string states off a D-brane. Finally, we investigate whether the eikonal Regge regime conjecture holds in the presence of D-branes.     

Scattering amplitudes with open loops

We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and Ossola-Papadopoulos-Pittau reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As demonstrated with nontrivial applications, the open-loop approach will permit us to obtain precise predictions for a very wide range of collider processes.     

Chiral Schwinger model with massive fermions

We study the chiral Schwinger model with massive fermions. By bosonizing it within the path integral framework, we find an equivalent bosonic lagrangian with an interaction term of the sine-Gordon type. The consistency of the theory is discussed.     

Compact multigluonic scattering amplitudes with heavy scalars and fermions

Combining the Berends-Giele and on-shell recursion relations we obtain an extremely compact expression for the scattering amplitude of a complex massive scalar-antiscalar pair and an arbitrary number of positive helicity gluons. This is one of the basic building blocks for constructing other helicity configurations from recursion relations. We also show explicitly that the scattering amplitude of massive fermions to gluons, all with positive helicity, is proportional to the scalar one, confirming in this way the recently advocated SUSY-like Ward identities relating both amplitudes.     

Scattering of fermions by gravitons

The interaction between gravitons and fermions is investigated in the teleparallel gravity. The scattering of fermions and gravitons in the weak field approximation is analyzed. The transition amplitudes of M\(\varnothing \)ller, Compton and new gravitational scattering are calculated.     

Extended projection method for massive fermions

Tensor reduction is of considerable importance in calculations of multi-loop amplitudes,and the projection method is one of the most popular approaches for tensor reduction.However,the projection method can be problematic when applied to amplitudes with massive fermions,due to the inconsistency between helicity and chirality.We propose an extended projection method for reducing the loop amplitude which contains a fermion chain with two massive spinors.The extension is achieved by decomposing one of the massive spinors into two massless spinors,the"null spinor"and the"reference spinor".The extended projection method can be effectively applied in all processes,including the production of massive fermions.We present the tensor reduction for a virtual Z boson decaying into a top-quark pair as a demonstration of our approach.     

Scattering amplitudes from multivariate polynomial division

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.     

The holographic fermions dual to massive gravity

We investigate the properties of the spectral function of the fermionic operator in the field theory which is dual to a 4-dimensional massive gravity. We first study the Fermi surface and the dispersion relation in the dual boundary theory. We find that as the massive parameters is decreased, the Fermi momentum becomes lower and the low energy excitation near Fermi surface behaves more like non-Fermi liquid. Then, we introduce a dipole coupling in the bulk theory and explore the emergence of a gap in the fermionic spectral function. It is found that larger critical dipole coupling is needed to open the gap than that in Einstein gravity. Accordingly, in the field theory dual to massive gravity, it requires stronger negative dipole coupling to generate the marginal Fermi liquid.     

Path integral bosonization of massive two-dimensional fermions

The bosonization of the Pauli-Villars regularized functional integral for massive fermions is discussed. Thereby the role of the mass dependence in the functional jacobian for finite chiral rotations of the fermionic integration variables is clarified.     

Scattering amplitudes in open superstring theory

This review is concerned with scattering amplitudes in open superstring theories. In particular, we introduce two different formalisms to compute tree level amplitudes – the Ramond Neveu Schwarz‐ (RNS‐) and the Pure Spinor (PS‐) formalism. The RNS approach proves to be flexible in describing compactifications from ten to four flat spacetime dimensions. We solve the technical problems due to the underlying interacting conformal field theory on the worldsheet. This is exploited to extract phenomenologically relevant scattering amplitudes of gluons and quarks as well as production‐ and decay rates of massive vibration modes which have already been identified as virtual exchange particles at the massless level. In case of a TeV string scale, string specific signatures in parton collisions might be observed at the LHC experiment in the near future and constitute the first experimental evidence for string theory. These statements apply to a wide class of string vacua and therefore bypass the so‐called landscape problem of string theory. The PS formalism allows for a manifestly supersymmetric treatment of scattering amplitudes in ten spacetime dimensions with sixteen supercharges. We introduce a family of superfields which arises in tree amplitudes of massless open string states and can be naturally identified with diagrams made of cubic vertices. We firstly achieve a compact superspace representation of multiparticle field theory amplitudes and moreover express the complete n point superstring amplitude as a minimal linear combination of partial field theory amplitudes and hypergeometric functions. The latter carry the stringy effects and are analyzed from different perspectives.     

On the computation of one-loop amplitudes with external fermions in 4D heterotic superstrings

We present the technical tools needed to compute any one-loop amplitude involving external spacetime fermions in a four-dimensional heterotic string model à la Kawai-Lewellen-Tye. As an example, we compute the one-loop three-point amplitude with one “photon” and two external massive fermions (“electrons”). As a check of our computation, we verify that the one-loop contribution to the Anomalous Magnetic Moment vanishes if the model has spacetime supersymmetry, as required by the supersymmetric sum rules.