15287410
Dynkin diagrams and integrable models based on Lie superalgebras
Abstract An analysis is given of the structure of a general two-dimensional Toda field theory involving bosons and fetmions which is defined in terms of a set of simple roots for a Lie superalgebra. It is shown that a simple root system for a superalgebra has two natural bosonic root systems associated with it which can be found very simply using Dynkin diagrams; the construction is closely related to the question of how to recover the signs of the entries of a Cartan matrix for a superalgebra from its Dynkin diagram. The significance for Toda theories is that the bosonic root systems correspond to the purely bosonic sector of the integrable model, knowledge of which can determine the bosonic part of the extended conformal symmetry in the theory, or its classical mass spectrum, as appropriate. These results are applied to some special kinds of models and their implications are investigated for features such as supersymmetry, positive kinetic energy and generalized reality conditions for the Toda fields. As a result, some new families of integrable theories with positive kinetic energy are constructed, some containing a mixture of massless and massive degrees of freedom, others being purely massive and supersymmetric, involving a number of coupled sine/ sinh-Gordon theories.
121797186
Complex Toda theories and twisted reality conditions
The Toda equations (based on a finite-dimensional or affine Lie algebra of superalgebra) are discussed as integrable non-linear differential equations for a set of complex scalar fields. We show that such complex Toda fields can either be restricted to take real values the standard way or else they can be subjected to a “twisted” reality condition associated to any Z2 symmetry of the Cartan matrix of Dynkin diagram of the underlying algebra. Different reality conditions give rise to different lagrangian field theories. In the conformal case, however, these theories have the same central charge, while in the affine case they have the same mass spectrum. The construction of N = 2 superconformal theories based on the superalgebras A(n, n−1) is clarified, and a new class of conformal field theories with positive kinetic energy based on the superalgebras C(n) is presented. The ideas developed are also relevant to understanding soliton solutions in affine Toda theories with imaginary coupling constant.
18118661
Integrable theories that are asymptotically CFT
Abstract A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories — in fact SU(2) WZW models at level k . In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed “asymptotically CFI”. These theories have previously been conjectured to be quantum integrable; this is confirmed by postulating a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-function and allows for an evaluation of the mass gap (the ratio of the physical mass to the Λ-parameter) to leading order in 1 k .
119053557
Geometry and Dynamics with Time-Dependent Constraints
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.
123140877
Supersymmetric Toda field theories
We analyse a class of integrable two-dimensional field theories with N =1 and N = 2 supersymmetry via the Lax, or zero-curvature, construction based on a Lie superalgebra. Some of the theories exhibit extended superconformal symmetries, generalizing the bosonic W-algebras. We also investigate the possible integrable deformations of these models and find that in some cases supersymmetry is broken and in other cases it is preserved.
18871816
Integrable N=2 supersymmetric field theories
Abstract A classification is given of Toda-like theories with N = 2 supersymmetry which are integrable by virtue of some underlying Lie superalgebra. In addition to the N = 2 superconformal theories based on sl( m , m −1), which generalize the Liouville model, a family of massive N = 2 theories based on the algebras sl( m , m ) (1) is found, providing natural generalizations of the sine-Gordon theory. A third family of models based on sl( m , m ) which have global supersymmetry, a version of conformal invariance, but no superconformal invariance is also briefly discussed. Unlike their N = 0 and N = 1 cousins, the N = 2 massive theories apparently cannot be directly thought of as integrable deformations of the corresponding N = 2 superconformal theories. It is shown that these massive theories admit supersymmetric soliton solutions and a form for their exact S -matrices is conjectured.
119179723
Flavor in minimal conformal technicolor
We construct a complete, realistic, and natural UV completion of minimal conformal technicolor that explains the origin of quark and lepton masses and mixing angles. As in “bosonic technicolor,” we embed conformal technicolor in a supersymmetric theory, with supersymmetry broken at a high scale. The exchange of heavy scalar doublets generates higher-dimension interactions between technifermions and quarks and leptons that give rise to quark and lepton masses at the TeV scale. Obtaining a sufficiently large top quark mass requires strong dynamics at the supersymmetry breaking scale in both the top and technicolor sectors. This is natural if the theory above the supersymmetry breaking also has strong conformal dynamics. We present two models in which the strong top dynamics is realized in different ways. In both models, constraints from flavor-changing effects can be easily satisfied. The effective theory below the supersymmetry breaking scale is minimal conformal technicolor with an additional light technicolor gaugino. We argue that this light gaugino is a general consequence of conformal technicolor embedded into a supersymmetric theory. If the gaugino has mass below the TeV scale it will give rise to an additional pseudo Nambu-Goldstone boson that is observable at the LHC.
118632441
Possibility of early Higgs boson discovery in nonminimal Higgs sectors
Particle physics models with more than one Higgs boson occur in many frameworks for physics beyond the standard model, including supersymmetry, technicolor, composite Higgs, and ''little Higgs'' models. If the Higgs sector contains couplings stronger than electroweak gauge couplings, there will be heavy Higgs particles that decay to lighter Higgs particles plus heavy particles such as W, Z, and t. This motivates searches for final states involving multiple W, Z, t, and bb pairs. A two Higgs doublet model with custodial symmetry is a useful simplified model to describe many of these signals. The model can be parameterized by the physical Higgs masses and the mixing angles {alpha} and {beta}, so discovery or exclusion in this parameter space has a straightforward physical interpretation. We illustrate this with a detailed analysis of the process gg{yields}A followed by A{yields}hZ and h{yields}WW. For m{sub A}{approx_equal}330 GeV, m{sub h}{approx_equal}200 GeV we can get a 4.5{sigma} signal with 1 fb{sup -1} of integrated luminosity at the Large Hadron Collider.
119264520
LHC coverage of RPV MSSM with light stops
A bstractWe examine the sensitivity of recent LHC searches to signatures of supersymmetry with R-parity violation (RPV). Motivated by naturalness of the Higgs potential, which would favor light third-generation squarks, and the stringent LHC bounds on spectra in which the gluino or first and second generation squarks are light, we focus on scenarios dominated by the pair production of light stops. We consider the various possible direct and cascade decays of the stop that involve the trilinear RPV operators. We find that in many cases, the existing searches exclude stops in the natural mass range and beyond. However, typically there is little or no sensitivity to cases dominated by UDD operators or LQD operators involving taus. We propose several ideas for searches which could address the existing gaps in experimental coverage of these signals.
26484819
Strong electroweak symmetry breaking and spin-0 resonances.
We argue that theories of the strong electroweak symmetry breaking sector necessarily contain new spin 0 states at the TeV scale in the tt and tb/bt channels, even if the third generation quarks are not composite at the TeV scale. These states couple sufficiently strongly to third generation quarks to have significant production at LHC via gg --> phi(0) or gb --> tphi(-). The existence of narrow resonances in QCD suggests that the strong electroweak breaking sector contains narrow resonances that decay to tt or tb/bt, with potentially significant branching fractions to 3 or more longitudinal W and Z bosons. These may give new "smoking gun" signals of strong electroweak symmetry breaking.
119238429
Sensitivity of an Upgraded LHC to R-Parity Violating Signatures of the MSSM
We present a sensitivity study for the pair-production of supersymmetric particles which decay through R-parity violating channels. As the scope of possible RPV signatures is very broad, the reach of several selected signatures spanning a representative variety of possible final states is considered. Preference in representation is given to spectra motivated by naturalness, i.e. light higgsinos, stops and gluinos. The sensitivity studies are presented for proton-proton collisions at 14 TeV with an integrated luminosity of 300 and 3000 fb^-1, as well as at 33 TeV with an integrated luminosity of 3000 fb^-1.