Localized Tachyons and the g_cl conjecture

We consider C/Z_N and C^2/Z_N orbifolds of heterotic string theories and Z_N orbifolds of AdS_3. We study theories with N=2 worldsheet superconformal invariance and construct RG flows. Following Harvey, Kutasov, Martinec and Moore, we compute g_cl and show that it decreases monotonically along RG flows- as conjectured by them. For the heterotic string theories, the gauge degrees of freedom do not contribute to the computation of g_cl.Comment: Corrections and clarifications made, 19 page

Twistfield Perturbations of Vertex Operators in the Z_2-Orbifold Model

We apply Kadanoff's theory of marginal deformations of conformal field theories to twistfield deformations of Z_2 orbifold models in K3 moduli space. These deformations lead away from the Z_2 orbifold sub-moduli-space and hence help to explore conformal field theories which have not yet been understood. In particular, we calculate the deformation of the conformal dimensions of vertex operators for p^2<1 in second order perturbation theory.Comment: Latex2e, 19 pages, 1 figur

Seven parton amplitudes from recursion relations

We present the first calculation of two-quark and five-gluon tree amplitudes using on-shell recursion relations. These amplitudes are needed for tree level 5-jet cross-section and an essential ingredient for next-to-leading order 4-jet and next-to-next-to-leading order 3-jet production at hadronic colliders. Very compact expressions for all possible helicity configurations are provided, allowing for direct implementation in Monte-Carlo codes.Comment: 11 page

Color-dressed recursive relations for multi-parton amplitudes

Remarkable progress inspired by twistors has lead to very simple analytic expressions and to new recursive relations for multi-parton color-ordered amplitudes. We show how such relations can be extended to include color and present the corresponding color-dressed formulation for the Berends-Giele, BCF and a new kind of CSW recursive relations. A detailed comparison of the numerical efficiency of the different approaches to the calculation of multi-parton cross sections is performed.Comment: 31 pages, 4 figures, 6 table

The orbifold transform and its applications

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the theory of permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions

Efficient analytic computation of higher-order QCD amplitudes

URL: http://www-spht.cea.fr/articles/t95/026/ Le calcul analytique efficace des amplitudes aux ordres supérieurs en QCDWe review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. Particularly useful are the constraints imposed by perturbative unitarity, collinear singularities and a supersymmetry-inspired organization of helicity amplitudes. Certain sequences of one-loop helicity amplitudes with an arbitrary number of external gluons have been obtained using these constraints

Gauge Coupling Unification from Unified Theories in Higher Dimensions

Higher dimensional grand unified theories, with gauge symmetry breaking by orbifold compactification, possess SU(5) breaking at fixed points, and do not automatically lead to tree-level gauge coupling unification. A new framework is introduced that guarantees precise unification -- even the leading loop threshold corrections are predicted, although they are model dependent. Precise agreement with the experimental result, \alpha_s^{exp} = 0.117 \pm 0.002, occurs only for a unique theory, and gives \alpha_s^{KK} = 0.118 \pm 0.004 \pm 0.003. Remarkably, this unique theory is also the simplest, with SU(5) gauge interactions and two Higgs hypermultiplets propagating in a single extra dimension. This result is more successful and precise than that obtained from conventional supersymmetric grand unification, \alpha_s^{SGUT} = 0.130 \pm 0.004 \pm \Delta_{SGUT}. There is a simultaneous solution to the three outstanding problems of 4D supersymmetric grand unified theories: a large mass splitting between Higgs doublets and their color triplet partners is forced, proton decay via dimension five operators is automatically forbidden, and the absence of fermion mass relations amongst light quarks and leptons is guaranteed, while preserving the successful m_b/m_\tau relation. The theory necessarily has a strongly coupled top quark located on a fixed point and part of the lightest generation propagating in the bulk. The string and compactification scales are determined to be around 10^{17} GeV and 10^{15} GeV, respectively.Comment: 29 pages, LaTe

Constructing the Tree-Level Yang-Mills S-Matrix Using Complex Factorization

A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants --- these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins >2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ~1/z^2.Comment: 35 pages, 6 figure

A Space-Time Orbifold: A Toy Model for a Cosmological Singularity

We explore bosonic strings and Type II superstrings in the simplest time dependent backgrounds, namely orbifolds of Minkowski space by time reversal and some spatial reflections. We show that there are no negative norm physical excitations. However, the contributions of negative norm virtual states to quantum loops do not cancel, showing that a ghost-free gauge cannot be chosen. The spectrum includes a twisted sector, with strings confined to a ``conical'' singularity which is localized in time. Since these localized strings are not visible to asymptotic observers, interesting issues arise regarding unitarity of the S-matrix for scattering of propagating states. The partition function of our model is modular invariant, and for the superstring, the zero momentum dilaton tadpole vanishes. Many of the issues we study will be generic to time-dependent cosmological backgrounds with singularities localized in time, and we derive some general lessons about quantizing strings on such spaces.Comment: 21 pages, 2 figure

Chiral rings and GSO projection in Orbifolds

The GSO projection in the twisted sector of orbifold background is sometimes subtle and incompatible descriptions are found in literatures. Here, from the equivalence of partition functions in NSR and GS formalisms, we give a simple rule of GSO projection for the chiral rings of string theory in \C^r/\Z_n, $r=1,2,3$. Necessary constructions of chiral rings are given by explicit mode analysis.Comment: 24 page