Transplanckian collisions at future accelerators

Scattering at transplanckian energies offers model independent tests of TeV scale gravity. Black-hole production is one spectacular signal, though a full calculation of the cross section is not yet available. Another signal is given by gravitational elastic scattering, which is maybe less spectacular but which can be nicely computed in the forward region using the eikonal approximation. In this talk I discuss the distinctive signatures of eikonalized scattering at future accelerators.Comment: 11 pages, 2 figures; talk given at the XXXVIIth Rencontres de Moriond, Electroweak Interactions and Unified Theories, Les Arcs, March 9-16, 200

Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff

We classify condensed matter systems in terms of the spacetime symmetries they spontaneously break. In particular, we characterize condensed matter itself as any state in a Poincar\'e-invariant theory that spontaneously breaks Lorentz boosts while preserving at large distances some form of spatial translations, time-translations, and possibly spatial rotations. Surprisingly, the simplest, most minimal system achieving this symmetry breaking pattern---the "framid"---does not seem to be realized in Nature. Instead, Nature usually adopts a more cumbersome strategy: that of introducing internal translational symmetries---and possibly rotational ones---and of spontaneously breaking them along with their space-time counterparts, while preserving unbroken diagonal subgroups. This symmetry breaking pattern describes the infrared dynamics of ordinary solids, fluids, superfluids, and---if they exist---supersolids. A third, "extra-ordinary", possibility involves replacing these internal symmetries with other symmetries that do not commute with the Poincar\'e group, for instance the galileon symmetry, supersymmetry or gauge symmetries. Among these options, we pick the systems based on the galileon symmetry, the "galileids", for a more detailed study. Despite some similarity, all different patterns produce truly distinct physical systems with different observable properties. For instance, the low-energy $2\to 2$ scattering amplitudes for the Goldstone excitations in the cases of framids, solids and galileids scale respectively as $E^2$, $E^4$, and $E^6$. Similarly the energy momentum tensor in the ground state is "trivial" for framids ($\rho +p=0$), normal for solids ($\rho+p>0$) and even inhomogenous for galileids.Comment: 58 pages, 1 table, 1 free cut-and-paste project for rainy days in Appendi

Soft Supersymmetry Breaking in Deformed Moduli Spaces, Conformal Theories, and N = 2 Yang-Mills Theory

We give a self-contained discussion of recent progress in computing the non-perturbative effects of small non-holomorphic soft supersymmetry breaking, including a simple new derivation of these results based on an anomaly-free gauged U(1)_R background. We apply these results to N = 1 theories with deformed moduli spaces and conformal fixed points. In an SU(2) theory with a deformed moduli space, we completely determine the vacuum expectation values and induced soft masses. We then consider the most general soft breaking of supersymmetry in N = 2 SU(2) super-Yang-Mills theory. An N = 2 superfield spurion analysis is used to give an elementary derivation of the relation between the modulus and the prepotential in the effective theory. This analysis also allows us to determine the non-perturbative effects of all soft terms except a non-holomorphic scalar mass, away from the monopole points. We then use an N = 1 spurion analysis to determine the effects of the most general soft breaking, and also analyze the monopole points. We show that naive dimensional analysis works perfectly. Also, a soft mass for the scalar in this theory forces the theory into a free Coulomb phase.Comment: 37 pages, LaTeX2e, 4 eps figure

The Composite Twin Higgs scenario

Based on an explicit model, we propose and discuss the generic features of a possible implementation of the Twin Higgs program in the context of composite Higgs models. We find that the Twin Higgs quadratic divergence cancellation argument can be uplifted to a genuine protection of the Higgs potential, based on symmetries and selection rules, but only under certain conditions which are not fulfilled in some of the existing models. We also find that a viable scenario, not plagued by a massless Twin Photon, can be obtained by not gauging the Twin Hypercharge and taking this as the only source of Twin Symmetry breaking at a very high scale.Comment: 19 pages; v2: typos and notation corrected, results unchanged; v3: published versio

CP Violation Beyond the Standard Model

We review CP violation in various extensions of the electroweak sector of the Standard Model. A particular emphasis is put on supersymmetric models. We describe the two CP problems of supersymmetry, concerning $d_N$ and $\epsilon_K$. We critically review the various mechanisms that have been suggested to solve these problems: exact universality, approximate CP symmetry, alignment, approximate universality and heavy squarks. We explain how future measurements of CP violation will test these mechanisms. We describe extensions of the quark sector and their implications on CP asymmetries in neutral B decays, on the $K_L \to \pi \nu \bar\nu$ decay and on $\Delta\Gamma(B_s)$. We discuss CP violation in charged scalar exchange in models with natural flavor conservation and explain how transverse lepton polarization in meson decays can probe such models. CP violation in neutral scalar exchange arises in models of horizontal symmetries and may be manifest in heavy quark (b and t) physics. We describe the implications of Left-Right Symmetric models on $d_N$, $\epsilon_K$, $\epsilon'/\epsilon$ and CP asymmetries in B decays. Finally, we briefly discuss the potential of future measurements of CP violation to discover New Physics.Comment: 50 pages, harvmac, 1 figure. To appear in the Review Volume "Heavy Flavours II", eds. A.J. Buras and M. Lindner, Advanced Series on Directions in High Energy Physics, World Scientific Publishing Co., Singapor

Bounds in 4D Conformal Field Theories with Global Symmetry

We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function , where Phi is a primary scalar operator in a given representation R. These constraints take the form of 'vectorial sum rules' for conformal blocks of operators whose representations appear in R x R and R x Rbar. The coefficients in these sum rules are related to the Fierz transformation matrices for the R x R x Rbar x Rbar invariant tensors. We show that the number of equations is always equal to the number of symmetry channels to be constrained. We also analyze in detail two cases - the fundamental of SO(N) and the fundamental of SU(N). We derive the vectorial sum rules explicitly, and use them to study the dimension of the lowest singlet scalar in the Phi x Phi* OPE. We prove the existence of an upper bound on the dimension of this scalar. The bound depends on the conformal dimension of Phi and approaches 2 in the limit dim(Phi)-->1. For several small groups, we compute the behavior of the bound at dim(Phi)>1. We discuss implications of our bound for the Conformal Technicolor scenario of electroweak symmetry breaking.Comment: 30 page

Gaugid inflation

The spectrum of primordial gravitational waves is one of the most robust inflationary observables, often thought of as a direct probe of the energy scale of inflation. We present a simple model, where the dynamics controlling this observable is very different than in the standard paradigm of inflation. The model is based on a peculiar finite density phase---the magnetic gaugid---which stems from a highly non-linear effective theory of a triplet of abelian gauge fields. The gaugid extends the notion of homogeneous isotropic solid, in that its spectrum of fluctuations includes helicity-2 phonons. We show how, upon implementing the gaugid to drive inflation, the helicity-2 phonon mixes with the graviton, significantly affecting the size of the primordial tensor spectrum. The rest of the features of the theory, in particular the vector and scalar perturbations, closely resemble those of solid inflation.Comment: 35+8 page

Probing the Scattering of Equivalent Electroweak Bosons

We analyze the kinematic conditions under which the scattering of equivalent massive spin-1 vector bosons factorizes out of the complete process. In practice, we derive the conditions for the validity of the effective W approximation, proposed long ago but never established on a firm basis. We also present a parametric estimate of the corrections to the approximation and explicitly check its validity in two examples.Comment: 36 pages, 14 figures, references adde

Patterns of Strong Coupling for LHC Searches

Even though the Standard Model (SM) is weakly coupled at the Fermi scale, a new strong dynamics involving its degrees of freedom may conceivably lurk at slightly higher energies, in the multi TeV range. Approximate symmetries provide a structurally robust context where, within the low energy description, the dimensionless SM couplings are weak, while the new strong dynamics manifests itself exclusively through higher-derivative interactions. We present an exhaustive classification of such scenarios in the form of effective field theories, paying special attention to new classes of models where the strong dynamics involves, along with the Higgs boson, the SM gauge bosons and/or the fermions. The IR softness of the new dynamics suppresses its effects at LEP energies, but deviations are in principle detectable at the LHC, even at energies below the threshold for production of new states. Our construction provides the so far unique structurally robust context where to motivate several searches in Higgs physics, diboson production, or WW scattering, which were so far poorly justified. Perhaps surprisingly, the interplay between weak coupling, strong coupling and derivatives, which is controlled by symmetries, can override the naive expansion in operator dimension, providing instances where dimension-8 dominates dimension-6, well within the domain of validity of the low energy effective theory. This result reveals the limitations of an analysis that is both ambitiously general and restricted to dimension-6 operators.Comment: 37 pages, 1 figur