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.
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.
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.
17352266
A Geometrical approach to time dependent gauge fixing
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is nontrivial to restrict the system in such a way that one can find a Hamiltonian time-evolution equation involving the Dirac bracket. Using a geometrical formulation, we derive an explicit condition which is both necessary and sufficient for this to be possible, and we give a formula defining the resulting Hamiltonian function. Some previous results are recovered as special cases.
119096562
Trialities and Exceptional Lie Algebras: DECONSTRUCTING the Magic Square
A construction of the magic square, and hence of exceptional Lie algebras, is carried out using trialities rather than division algebras. By way of preparation, a comprehensive discussion of trialities is given, incorporating a number of novel results and proofs. Many of the techniques are closely related to, or derived from, ideas which are commonplace in theoretical physics. The importance of symmetric spaces in the magic square construction is clarified, allowing the Jacobi property to be verified for each algebra in a uniform and transparent way, with no detailed calculations required. A variation on the construction, corresponding to other symmetric spaces, is also given.
118254263
From PCM to KDV and Back
This is a summary of progress made [1]–[4] in understanding the occurrence and properties of local, conserved, commuting charges in non-linear sigma-models, including principal chiral models (PCMs) and WZW models.
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.
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.
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.