657952
Coleman-De Luccia Tunneling and The Gibbons-Hawking Temperature
We study Coleman–de Luccia tunneling in some detail. We show that, for a single scalar field potential with a true and a false vacuum, there are four types of tunneling, depending on the properties of the potential. A general tunneling process involves a combination of thermal (Gibbons–Hawking temperature) fluctuation part way up the barrier followed by quantum tunneling. The thin-wall approximation is a special limit of the case (of only quantum tunneling) where inside the nucleation bubble is the true vacuum while the outside reaches the false vacuum. Hawking–Moss tunneling is the (only thermal fluctuation) limit of the case where the inside of the bubble does not reach the true vacuum at the moment of its creation, and the outside is cut off by the de Sitter horizon before it reaches the false vacuum. A typical tunneling process is a combination of thermal and quantum tunnelings. We estimate the tunneling rate for this case and find that the corrections to the Hawking–Moss formula can be large. In all cases, we see that the Euclidean action of the bounce decreases rapidly as the vacuum energy density increases, signaling that the tunneling is not exponentially suppressed. This phenomenon may be interpreted as a finite temperature effect due to the Gibbons–Hawking temperature of the de Sitter space. As an application, we discuss the implication of this tunneling property to the cosmic landscape.
118631762
Multivariate residues and maximal unitarity
A bstractWe extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated at three loops in gauge theories with any number of fermions and scalars in the adjoint representation. Deca-cuts realized by replacement of real slice integration contours by higher-dimensional tori encircling the global poles are used to factorize the planar triple box onto a product of trees. We apply computational algebraic geometry and multivariate complex analysis to derive unique projectors for all master integral coefficients and obtain compact analytic formulae in terms of tree-level data.
119230697
Elliptic functions and maximal unitarity
Modern perturbative scattering amplitudes in gauge theories such as QCD are calculated from general principles of analyticity and unitarity without inspecting Feynman diagrams. By virtue of analyticity, amplitudes are reconstructed from their singularity structure, while unitarity ensures that residues factorize onto simpler objects. Starting from complex internal momenta and three-point amplitudes whose form is entirely xed by eld theory arguments, all trees are generated recursively
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.
15207037
Global structure of curves from generalized unitarity cut of three-loop diagrams
A bstractThis paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus of the algebraic curve. We use the Riemann-Hurwitz formula to compute the geometric genus of algebraic curves with the help of techniques involving convex hull polytopes and numerical algebraic geometry. Some interesting properties of genus for arbitrary loop orders are also explored where computing the genus serves as an initial step for integral or integrand reduction of three-loop amplitudes via an algebraic geometric approach.
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.
18567161
Finite-dimensional representations of quantum affine algebras
We give a practical method for the construction of finite-dimensional representations of Uq(G), where G is a non-twisted affine Kac-Moody algebra with no derivation and zero central charge. It is well known that the finite-dimensional representations of a quantum group Uq(G) at generic q are simply deformations of the corresponding irreps of the classical Lie algebra G. This is, however, no longer true when one goes over to an affine Kac-Moody algebra G and its q-deformation Uq(G). In most cases it is necessary to take the direct sum of several irreducible Uq(G)-modules to form an irreducible Uq(G)-module which then becomes reducible at q=1. We illustrate our technique by working out explicit examples for G=C2 and G=G2. These finite-dimensional modules may, for example, determine the multiplet structure of quantum solitons in affine Toda theory.
14743625
A self-gravitating Dirac–Born–Infeld global monopole
We generalize the field theory of the global monopole to the Dirac–Born–Infeld (DBI) field and investigate the gravitational property of a DBI global monopole in four-dimensional spherically symmetric spacetime. The coupled equations for the metric and the DBI scalar field are solved asymptotically and numerically. It is found that, just as for a canonical global monopole, the gravitational effect of the DBI global monopole is equivalent to that of a deficit solid angle in the metric plus a negative mass at the origin. However, compared with a canonical global monopole, for the same false vacuum and symmetry-breaking scale, a DBI global monopole has a relatively smaller core and a larger absolute value of effective mass. Thus, it can yield a larger deflect angle when the light is passing by. Especially, when the scale of the warp factor is small enough, the effective mass of a DBI global monopole does not depend apparently on the value of the false vacuum, which is qualitatively different from that of a canonical global monopole.
119002340
gl(2|2) current superalgebra and non-unitary conformal field theory
Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2|2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy–momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented.
19788205
CP-violating phenomenology of flavor conserving two Higgs doublet models
We analyze the constraints on CP-violating, flavor conserving two Higgs doublet models implied by measurements of Higgs boson properties at the Large Hadron Collider (LHC) and by the nonobservation of permanent electric dipole moments (EDMs) of molecules, atoms, and neutrons. We find that the LHC and EDM constraints are largely complementary, with the LHC studies constraining the mixing between the neutral CP-even states and the EDMs probing the effect of mixing between the CP-even and CP-odd scalars. Presently, the most stringent constraints are implied by the nonobservation of the ThO molecule EDM signal. Future improvements in the sensitivity of neutron and diamagnetic atom EDM searches could yield competitive or even more severe constraints. We analyze the quantitative impact of hadronic and nuclear theory uncertainties on the interpretation of the latter systems and conclude that these uncertainties cloud the impact of projected improvements in the corresponding experimental sensitivities.
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.