Reparametrization Invariance of Path Integrals

We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the failure of earlier authors to establish reparametrization invariance which led them to introduce, superfluously, a compensating potential depending on the connection of the coordinate system. We show that problems with invariance are absent by defining path integrals as the epsilon-> 0 -limit of 1+ epsilon -dimensional functional integrals.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re289/preprint.htm

Spectrum of k-string tensions in SU(N) gauge theories

We compute, for the four-dimensional SU(4) and SU(6) gauge theories formulated on a lattice, the string tensions sigma_k related to sources with Z_N charge k, using Monte Carlo simulations. Our results are compatible with sigma_k \propto sin (k pi/N), and show sizeable deviations from Casimir scaling.Comment: Lattice2001(confinement

Folded Supersymmetry and the LEP Paradox

We present a new class of models that stabilize the weak scale against radiative corrections up to scales of order 5 TeV without large corrections to precision electroweak observables. In these `folded supersymmetric' theories the one loop quadratic divergences of the Standard Model Higgs field are cancelled by opposite spin partners, but the gauge quantum numbers of these new particles are in general different from those of the conventional superpartners. This class of models is built around the correspondence that exists in the large N limit between the correlation functions of supersymmetric theories and those of their non-supersymmetric orbifold daughters. By identifying the mechanism which underlies the cancellation of one loop quadratic divergences in these theories, we are able to construct simple extensions of the Standard Model which are radiatively stable at one loop. Ultraviolet completions of these theories can be obtained by imposing suitable boundary conditions on an appropriate supersymmetric higher dimensional theory compactified down to four dimensions. We construct a specific model based on these ideas which stabilizes the weak scale up to about 20 TeV and where the states which cancel the top loop are scalars not charged under Standard Model color. Its collider signatures are distinct from conventional supersymmetric theories and include characteristic events with hard leptons and missing energy.Comment: 18 pages, 5 figures, references correcte

Supersymmetric Quantum Chromodynamics: How Confined Non-Abelian Monopoles Emerge from Quark Condensation

We consider N =1 supersymmetric QCD with the gauge group U(N) and N_f=N quark flavors. To get rid of flat directions we add a meson superfield. The theory has no adjoint fields and, therefore, no 't Hooft-Polyakov monopoles in the quasiclassical limit. We observe a non-Abelian Meissner effect: condensation of color charges (squarks) gives rise to confined monopoles. The very fact of their existence in N =1 supersymmetric QCD without adjoint scalars was not known previously. Our analysis is analytic and is based on the fact that the N =1 theory under consideration can be obtained starting from N =2 SQCD in which the 't Hooft-Polyakov monopoles do exist, through a certain limiting procedure allowing us to track the status of these monopoles at various stages. Monopoles are confined by BPS non-Abelian strings (flux tubes). Dynamics of string orientational zero modes are described by supersymmetric CP(N-1) sigma model on the string world sheet. If a dual of N =1 SQCD with the gauge group U(N) and N_f=N quark flavors could be identified, in this dual theory our demonstration would be equivalent to the proof of the non-Abelian dual Meissner effect.Comment: 33 pages, 3 figures. V2 reference and a brief comment added; typos corrected. V3 two comments added; final version accepted for publication to PR

Duality cascades and duality walls

We recast the phenomenon of duality cascades in terms of the Cartan matrix associated to the quiver gauge theories appearing in the cascade. In this language, Seiberg dualities for the different gauge factors correspond to Weyl reflections. We argue that the UV behavior of different duality cascades depends markedly on whether the Cartan matrix is affine ADE or not. In particular, we find examples of duality cascades that can't be continued after a finite energy scale, reaching a "duality wall", in terminology due to M. Strassler. For these duality cascades, we suggest the existence of a UV completion in terms of a little string theory.Comment: harvmac, 24 pages, 4 figures. v2: references added. v3: reference adde

Anarchy and Hierarchy

We advocate a new approach to study models of fermion masses and mixings, namely anarchy proposed in hep-ph/9911341. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the Delta m^2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measure-dependent. U_{e3} has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin delta is preferred to be maximal. We present a simple SU(5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.Comment: 26 page

The LHC Phenomenology of Vectorlike Confinement

We investigate in detail the LHC phenomenology of "vectorlike confinement", where the Standard Model is augmented by a new confining gauge interaction and new light fermions that carry vectorlike charges under both the Standard Model and the new gauge group. If the new interaction confines at the TeV scale, this framework gives rise to a wide range of exotic collider signatures such as the production of a vector resonance that decays to a pair of collider-stable charged massive particles (a "di-CHAMP" resonance), to a pair of collider-stable massive colored particles (a "di-R-hadron resonance), to multiple photons, $W$s and $Z$s via two intermediate scalars, and/or to multi-jet final states. To study these signals at the LHC, we set up two benchmark models: one for the di-CHAMP and multi-photon signals, and the other for the di-R-hadron and multijet signals. For the di-CHAMP/multi-photon model, Standard Model backgrounds are negligible, and we show that a full reconstruction of the spectrum is possible, providing powerful evidence for vectorlike confinement. For the di-R-hadron/multijet model, we point out that in addition to the di-R-hadron signal, the rate of the production of four R-hadrons can also be sizable at the LHC. This, together with the multi-jet signals studied in earlier work, makes it possible to single out vectorlike confinement as the underlying dynamics.Comment: 32 pages, 28 figures. Several typos fixed, one paragraph added elaborating choice of benchmarks. Version accepted by JHEP

Long-Lived Neutralino NLSPs

We investigate the collider signatures of heavy, long-lived, neutral particles that decay to charged particles plus missing energy. Specifically, we focus on the case of a neutralino NLSP decaying to Z and gravitino within the context of General Gauge Mediation. We show that a combination of searches using the inner detector and the muon spectrometer yields a wide range of potential early LHC discoveries for NLSP lifetimes ranging from 10^(-1)-10^5 mm. We further show that events from Z(l+l-) can be used for detailed kinematic reconstruction, leading to accurate determinations of the neutralino mass and lifetime. In particular, we examine the prospects for detailed event study at ATLAS using the ECAL (making use of its timing and pointing capabilities) together with the TRT, or using the muon spectrometer alone. Finally, we also demonstrate that there is a region in parameter space where the Tevatron could potentially discover new physics in the delayed Z(l+l-)+MET channel. While our discussion centers on gauge mediation, many of the results apply to any scenario with a long-lived neutral particle decaying to charged particles.Comment: 31 pages, 12 figure

Induced N=2 composite supersymmetry in 2+1 dimensions

Starting from N=1 scalar supermultiplets in 2+1 dimensions, we build explicitly the composite superpartners which define a N=2 superalgebra induced by the initial N=1 supersymmetry. The occurrence of this extension is linked to the topologically conserved current out of which the composite superpartners are constructed.Comment: 11 pages LATEX, no figure

A Composite Little Higgs Model

We describe a natural UV complete theory with a composite little Higgs. Below a TeV we have the minimal Standard Model with a light Higgs, and an extra neutral scalar. At the TeV scale there are additional scalars, gauge bosons, and vector-like charge 2/3 quarks, whose couplings to the Higgs greatly reduce the UV sensitivity of the Higgs potential. Stabilization of the Higgs mass squared parameter, without finetuning, occurs due to a softly broken shift symmetry--the Higgs is a pseudo Nambu-Goldstone boson. Above the 10 TeV scale the theory has new strongly coupled interactions. A perturbatively renormalizable UV completion, with softly broken supersymmetry at 10 TeV is explicitly worked out. Our theory contains new particles which are odd under an exact "dark matter parity", (-1)^{(2S+3B+L)}. We argue that such a parity is likely to be a feature of many theories of new TeV scale physics. The lightest parity odd particle, or "LPOP", is most likely a neutral fermion, and may make a good dark matter candidate, with similar experimental signatures to the neutralino of the MSSM. We give a general effective field theory analysis of the calculation of corrections to precision electroweak observables.Comment: 28 page