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.
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.
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 .
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.
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.
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.
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.
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.
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.