9682866
Integrable sigma-models and Drinfeld–Sokolov hierarchies
Abstract Local commuting charges in sigma-models with classical Lie groups as target manifolds are shown to be related to the conserved quantities appearing in the Drinfeld–Sokolov (generalized mKdV) hierarchies. Conversely, the Drinfeld–Sokolov construction can be used to deduce the existence of commuting charges in these and in wider classes of sigma-models, including those whose target manifolds are exceptional groups or symmetric spaces. This establishes a direct link between commuting quantities in integrable sigma-models and in affine Toda field theories.
16517190
Exact scattering in the SU(n) supersymmetric principal chiral model
Abstract The complete spectrum of states in the supersymmetric principal chiral model based on SU(n) is conjectured, and an exact factorizable S-matrix is proposed to describe scattering amongst these states. The SU(n)L × SU(n)R symmetry of the Lagrangian is manifest in the S-matrix construction. The supersymmetries, on the other hand, are incorporated in the guise of spin - 1 2 charges acting on a set of RSOS kinks associated with su(n) at level n. To test the proposed S-matrix, calculations of the change in the ground-state energy in the presence of a coupling to a background charge are carried out. The results derived from the Lagrangian using perturbation theory and from the S-matrix using the TBA are found to be in complete agreement for a variety of background charges which pick out, in turn, the highest weight states in each of the fundamental representations of SU(n). In particular, these methods rule out the possibility of additional CDD factors in the S-matrix. Comparison of the expressions found for the free-energy also yields an exact result for the mass gap in these models: m Λ MS = ( n π ) sin ( π n ) .
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 .
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.
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.
122945882
On Dirac's methods for constrained systems and gauge-fixing conditions with explicit time dependence
Abstract It is shown that Dirac's methods for constrained hamiltonian systems require careful application if gauge-fixing conditions with explicit time dependence are used. It is non-trivial, in general, to find both an appropriate set of variables for the physical phase space and a hamiltonian furnishing the correct time evolution of these quantities. This problem is solved for a certain class of gauge-fixing conditions. As well as offering the possibility of new applications the solution provides a more systematic understanding of some well-known cases, among which are the light-cone and temporal gauges for relativistic particles and strings.
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.
118637173
Minimal conformal technicolor and precision electroweak tests
We study the minimal model of conformal technicolor, an SU(2) gauge theory near a strongly coupled conformal fixed point, with conformal symmetry softly broken by technifermion mass terms. Conformal symmetry breaking triggers chiral symmetry breaking in the pattern SU(4) → Sp(4), which gives rise to a pseudo-Nambu-Goldstone boson that can act as a composite Higgs boson. The top quark is elementary, and the top and electroweak gauge loop contributions to the Higgs mass are cut off entirely by Higgs compositeness. In particular, the model requires no top partners and no “little Higgs” mechanism. A nontrivial vacuum alignment results from the interplay of the top loop and technifermion mass terms. The composite Higgs mass is completely determined by the top loop, in the sense that mh/mt is independent of the vacuum alignment and is computable by a strong-coupling calculation. There is an additional composite pseudoscalar A with mass larger than mh and suppressed direct production at LHC. We discuss the electroweak fit in this model in detail. Corrections to $ Z \to \bar{b}b $ and the T parameter from the top sector are suppressed by the enhanced Sp(4) custodial symmetry. Even assuming that the strong contribution to the S parameter is positive and usuppressed, a good electroweak fit can be obtained for v/f ≲ 0.25, where v and f are the electroweak and chiral symmetry breaking scales respectively. This requires fine tuning at the 10% level.
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.
121693849
Searching For Resonances inside Top-like Events
In extended Higgs sectors, heavy Higgs bosons can decay via cascades to a light Higgs boson plus W and Z bosons. We study signals of such sectors at the Tevatron and LHC that result from resonant production of a heavy H{sup 0} followed by the decay H{sup 0} {yields} H{sup {+-}}W{sup {+-}} with H{sup +} {yields} W{sup +}h{sup 0} {yields} W{sup +} b{bar b} or H{sup +} {yields} t{bar b} {yields} W{sup +} b{bar b}. The final states have the same particle content as that of t{bar t} production, but with a resonant structure that can be used to distinguish signal events from background events. We propose analysis techniques and estimate the experimental sensitivity of the Tevatron and LHC experiments to these signals.
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.