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.
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 ) .
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.
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.
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.
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.
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.
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.
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.
119096508
A swarm of Bs
A bstractNew physics signals containing five or more b-tagged jets, but without T or leptons, could realistically be sitting within the current 8 TeV LHC data set without receiving meaningful constraints from any of the existing LHC searches at either ATLAS or CMS. This work provides several examples of simple, motivated models that yield final states containing many b-jets. To study the potential for uncovering new physics in these high b-jet multiplicity channels, this paper focuses on a natural supersymmetry scenario where each of the pair-produced stops decays to an on-shell chargino, which subsequently decays via an MFV-motivated, R-parity violating coupling. This gives rise to an eight-jet final state containing six b-quarks. Although no public measurements exist, estimates indicate that the standard model backgrounds in high b-jet multiplicity channels should be very small. To circumvent the background uncertainty, an asymmetric method is presented that utilizes two different techniques to conservatively exclude or to discover new physics in high b-jet multiplicity final states.