119263398
Multi-loop Integrand Reduction with Computational Algebraic Geometry
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Grobner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the MACAULAY2 computer algebra system and the Mathematica package BASISDET.
18535552
Massive nonplanar two-loop maximal unitarity
A bstractWe explore maximal unitarity for nonplanar two-loop integrals with up to four massive external legs. In this framework, the amplitude is reduced to a basis of master integrals whose coefficients are extracted from maximal cuts. The hepta-cut of the nonplanar double box defines a nodal algebraic curve associated with a multiply pinched genus-3 Riemann surface. All possible configurations of external masses are covered by two distinct topological pictures in which the curve decomposes into either six or eight Riemann spheres. The procedure relies on consistency equations based on vanishing of integrals of total derivatives and Levi-Civita contractions. Our analysis indicates that these constraints are governed by the global structure of the maximal cut. Lastly, we present an algorithm for computing generalized cuts of massive integrals with higher powers of propagators based on the Bezoutian matrix method.
118592385
The complete KLT-map between gravity and gauge theories
A bstractWe present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.
119221055
An integrand reconstruction method for three-loop amplitudes
A bstractWe consider the maximal cut of a three-loop four point function with massless kinematics. By applying Gröbner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.
118419441
Multi-loop integrand reduction techniques
We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.
54593568
On genera of curves from high-loop generalized unitarity cuts
A bstractGeneralized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases, i.e., a 4-dimensional L-loop diagram with (4L−1) cuts. The topology of a complex curve is classified by its genus. Hence in this paper, we use computational algebraic geometry to calculate the genera of curves from two and three-loop unitarity cuts. The global structure of degenerate on-shell equations under some specific kinematic configurations is also sketched. The genus information can also be used to judge if a unitary cut solution could be rationally parameterized.
121746713
The effective mass and screening mass of the rho meson for the vector dominance model and the vector coupling model at finite temperature and density
In the framework of thermo-field dynamics, the temperature and/or density dependences of the effective mass and the screening mass of the rho -meson for the vector dominance model and the nucleon-nucleon- rho -meson (NN rho ) vector coupling model have been calculated. We have found that for the vector dominance model, the effective mass and the screening mass of the rho -meson increase with temperature, and for the NN rho vector coupling model, they remain almost unchanged with temperature, but increase with density.
53124689
Coleman-de Luccia instanton in dRGT massive gravity
We study the Coleman-de Luccia (CDL) instanton characterizing the tunneling from a false vacuum to the true vacuum in a semi-classical way in dRGT (deRham-Gabadadze-Tolley) massive gravity theory, and evaluate the dependence of the tunneling rate on the model parameters. It is found that provided with the same physical Hubble parameters for the true vacuum HT and the false vacuum HF as in General Relativity (GR), the thin-wall approximation method implies the same tunneling rate as GR. However, deviations of tunneling rate from GR arise when one goes beyond the thin-wall approximation and they change monotonically until the Hawking-Moss (HM) case. Moreover, under the thin-wall approximation, the HM process may dominate over the CDL one if the value for the graviton mass is larger than the inverse of the radius of the bubble.
120673458
GENERALIZED SINE–GORDON THEORY AND PERTURBED SL(2)k WZNW MODEL
We present and study a new integrable model which is an interacting system of (β, γ) fields and a boson and describes the SL(2)k WZNW model perturbed by an analog of the (1, 3) operator. The theory (which we refer to as generalized sine–Gordon theory) turns out to possess an underlying BRST symmetry. The linear system for the new model is defined in terms of Kac–Moody algebra and classical r-matrix is found. We also work out the general classical solution to this model.
15601411
Quasi-Hopf superalgebras and elliptic quantum supergroups
We introduce the quasi-Hopf superalgebras which are Z(2)-graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is, the face type B-q,B-lambda(G) and the vertex type A(q,p)[sl(((n\) over cap\n)] (and A(q,p)[gl ((n\) over cap n)], where G is any Kac-Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for U-q[sl ((n\) over cap n) in a nonstandard system of simple roots, all of which are fermionic. (C) 1999 American Institute of Physics. [S0022-2488(99)00210-8].
55981517
Hawking-Moss instanton in nonlinear massive gravity
As a first step toward understanding a lanscape of vacua in a theory of non-linear massive gravity, we consider a landscape of a single scalar field and study tunneling between a pair of adjacent vacua. We study the Hawking-Moss (HM) instanton that sits at a local maximum of the potential, and evaluate the dependence of the tunneling rate on the parameters of the theory. It is found that provided with the same physical HM Hubble parameter HHM, depending on the values of parameters ?3 and ?4 in the action (2.2), the corresponding tunneling rate can be either enhanced or suppressed when compared to the one in the context of General Relativity (GR). Furthermore, we find the constraint on the ratio of the physical Hubble parameter to the fiducial one, which constrains the form of potential. This result is in sharp contrast to GR where there is no bound on the minimum value of the potential.