Unitary Gauge Research Articles

Integration without integration: New Killing spinor spacetimes

Non-conformally flat spacetimes admitting a non-null two-index Killing spinor are investigated by means of the Geroch-Held-Penrose formalism. Claims appearing in the literature that such spacetimes are all explicitly known are incorrect. This was shown in [5] for the family where, in the canonical frame, the spin coefficients ρ or μ, vanish. Here the general case with non-vanishing ρ, μ, π and τ is re-considered. It is shown that the construction in [4] hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations for the spin coefficients and the components of the Ricci spinor. All (conformal classes of) spacetimes, in which one of these conditions is violated, are obtained by invariant integration. The resulting classes are each other's Sachs transform and are characterised by one free function. They admit in general no Killing vectors, but still admit a conformal gauge (different from the trivial unitary gauge) in which a Killing tensor exists.

Calculation of Decay μ → eγ in Rξ Gauge in a Model of Electroweak-Scale Right-Handed Neutrinos

The lepton flavor violating process μ → eγ has been previously studied in a model of electroweak-scale right-handed neutrinos. In that work the decay amplitude was computed in unitarity gauge, augmented by some technical considerations that correct the leading term thus obtained. This complication arises because the mixing matrices appearing in the weak charged currents are not unitary in the model. In this paper, we recalculate the amplitude in Rξ gauge. The cancellation of the ξ dependence in the final result serves as a useful check to both the obtained amplitude and the technical points made in the previous work.

On higher derivatives in 3D gravity and higher-spin gauge theories

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their "self-dual" limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the "extended Chern-Simons" term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for "self-dual" spin 3.

Nonperturbative decay ofuddandQLdflat directions

The minimal supersymmetric standard model has several flat directions, which can naturally be excited during inflation. If they have a slow (perturbative) decay, they may affect the thermalization of the inflaton decay products. In the present paper, we consider the system of $udd$ and $QLd$ flat directions, which breaks the $U(1)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(3)$ symmetry completely. In the unitary gauge and assuming a general soft breaking mass configuration, we show that for a range of parameters, the background condensate of flat directions can undergo a fast nonperturbative decay, due to nonadiabatic evolution of the eigenstates. We find that both the background evolution and part of the decay can be described accurately by previously studied gauged toy models of flat direction decay.

Penguin and box diagrams in unitary gauge

We evaluate one-loop diagrams in the unitary gauge that contribute to flavor-changing neutral current (FCNC) transitions involving two and four fermions. Specifically, we deal with penguin and box diagrams arising within the standard model (SM) and in nonrenormalizable extensions thereof with anomalous couplings of the W boson to quarks. We show explicitly in the SM the subtle cancelation among divergences from individual unitary-gauge contributions to some of the physical FCNC amplitudes and derive expressions consistent with those obtained using R_xi gauges in the literature. Some of our results can be used more generally in certain models involving fermions and gauge bosons which have interactions similar in form to those we consider.

Electroweak and flavour structure of a warped extra dimension with custodial protection

We present the electroweak and flavour structure of a model with a warped extra dimension and the bulk gauge group SU(3) x SU(2)_L x SU(2)_R x P_LR x U(1)_X. The presence of SU(2)_R implies an unbroken custodial symmetry in the Higgs system allowing to eliminate large contributions to the T parameter, whereas the P_LR symmetry and the enlarged fermion representations provide a custodial symmetry for flavour diagonal and flavour changing couplings of the SM Z boson to left-handed down-type quarks. We diagonalise analytically the mass matrices of charged and neutral gauge bosons including the first KK modes. We present the mass matrices for quarks including heavy KK modes and discuss the neutral and charged currents involving light and heavy fields. We give the corresponding complete set of Feynman rules in the unitary gauge.

Z→bb¯and chiral currents in Higgsless models

In this paper we compute the flavor-dependent chiral-logarithmic corrections to the decay $Z\ensuremath{\rightarrow}b\overline{b}$ in the three-site Higgsless model. We compute these corrections diagrammatically in the gaugeless limit in which the electroweak couplings vanish. We also compute the chiral-logarithmic corrections to the decay $Z\ensuremath{\rightarrow}b\overline{b}$ using a renormalization group equation analysis in effective field theory, and show that the results agree. In the process of this computation, we compute the form of the chiral current in the gaugeless limit of the three-site model, and consider the generalization to the $N$-site case. We elucidate the Ward-Takahashi identities which underlie the gaugeless limit calculation in the three-site model, and describe how the result for the $Z\ensuremath{\rightarrow}b\overline{b}$ amplitude is obtained in unitary gauge in the full theory. We find that the phenomenological constraints on the three-site Higgsless model arising from measurements of $Z\ensuremath{\rightarrow}b\overline{b}$ are relatively mild, requiring only that the heavy Dirac fermion be heavier than 1 TeV or so, and are satisfied automatically in the range of parameters allowed by other precision electroweak data.

Weighted power counting and Lorentz violating gauge theories. I: General properties

We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, but no higher time derivatives. We show that the regularity of the gauge-field propagator privileges a particular spacetime breaking, the one into space and time. We then concentrate on the simplest class of models, study four dimensional examples and discuss a number of issues that arise in our approach, such as the low-energy recovery of Lorentz invariance.

Weighted power counting and Lorentz violating gauge theories. II: Classification

We classify the local, polynomial, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. We study the structure of such theories and prove that renormalization does not generate higher time derivatives. We work out the conditions to renormalize vertices that are usually non-renormalizable, such as the two scalar-two fermion interactions and the four fermion interactions. A number of four-dimensional examples are presented.

CLASSICAL SOLUTIONS OF GHOST CONDENSATION MODELS

Motivated by ideas obtained from both ghost condensation and gravitational Higgs mechanism, we attempt to find classical solutions in the unitary gauge in general ghost condensation models. It is shown that depending on the form of scalar fields in an action, there are three kinds of exact solutions, which are (anti-) de Sitter space–time, polynomially expanding universes and flat Minkowski space–time. We briefly comment on gravitational Higgs mechanism in these models where we have massive gravitons of five degrees of freedom and one unitary scalar field (Nambu–Goldstone boson) after spontaneous symmetry breakdown of general coordinate reparametrization invariance. The models at hand are free from the problem associated with the non-unitary propagating mode.

Stringy instantons as strong dynamics

We study the relation between stringy instantons and strong dynamics effects in type IIB toric quiver gauge theories. By exploiting the involutive property of Seiberg duality we relate the classical constraint on the moduli space of the gauge theory with the stringy instanton contribution to the superpotential. The result holds for unitary, orthogonal and symplectic gauge groups.

Spin precession due to a non-Abelian spin-orbit gauge field

We study the spatial behavior of spin precession for traversing electrons in a two-dimensional system with both the Rashba and Dresselhaus spin-orbit (SO) couplings. Treating the two SO coupling as non-Abelian SO gauges and performing the unitary gauge transformation for the Hamiltonian, the effect of SO coupling is exactly represented by a spin-rotation operator providing a convenient framework for studying the property of ballistic spin transport. We derive the analytical expression for the spin configuration and demonstrate a classical analog of spin precession. The present approach provides a powerful means (e.g., the spin-rotation axis, the precession angle, and the cone angle) allowing concrete description of the local spin orientation. In particular, the spatial features such as the specific transport path with null spin precession and the special contour with complete cycles of spin precession can be easily identified.

Supersymmetric flat direction decay: The prospect of particle production and preheating investigated in the unitary gauge

We look at the possibility of non-perturbative particle production after inflation from SUSY flat directions produced by rotating eigenstates thereby avoiding the standard adiabaticity conditions. This might lead to preheating and prevent the delay of thermalisation of the universe. We investigate the flat directions $LLE^c$ and $U^cD^cD^c$ and find no particle production. These 2 directions are very important, since they have been named as possible candidates for being the inflaton. We investigate $QLQLQLE^c$ and find particle production and therefore the possibility of preheating. We investigate the $LLE^c$ and $U^cD^cD^c$ directions appearing simultaneously, and find no production. Finally, we investigate $LLE^c$ and $QLD^c$ simultaneously - with one L-field in common. Here we do find particle production and therefore the possibility of preheating. This means that if SUSY flat directions are to delay thermalisation and thus explain the (lack of) gravitino production, it is necessary to explain why complicated directions as $QLQLQLE^c$ are not exited, and why combinations like $LLE^c$ and $QLD^c$ are not both exited.

Gaussian effective potential for the standard modelSU(2)×U(1)electroweak theory

The Gaussian effective potential is derived for the non-Abelian $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory of electroweak interactions. At variance with naive derivations, the Gaussian effective potential is proven to be a genuine variational tool in any gauge. The role of ghosts is discussed and the unitarity gauge is shown to be the only choice which allows calculability without insertion of further approximations. The full non-Abelian calculation confirms the existence of a light Higgs boson in the nonperturbative strong coupling regime of the Higgs sector.

Other meta-stable brane configuration by adding an orientifold 6-plane to Giveon–Kutasov

Giveon and Kutasov have found the type IIA intersecting nonsupersymmetric meta-stable brane configuration where the electric gauge theory superpotential has a quartic term as well as the mass term for quarks. In this Letter, by adding the orientifold 6-plane to this brane configuration, we describe the brane configuration corresponding to the meta-stable nonsupersymmetric vacua of the supersymmetric unitary gauge theory with symmetric flavor as well as fundamental flavors.

Explicit action of [formula omitted] on [formula omitted] supergravity fields

We present an explicit, exact to all orders in gravitational coupling E 7 ( 7 ) symmetry transformations of on-shell N = 8 supergravity fields in the gauge with 70 scalars in E 7 ( 7 ) SU ( 8 ) coset space, the local SU ( 8 ) symmetry being fixed. The non-linear realization of E 7 ( 7 ) includes a field-dependent SU ( 8 ) transformation preserving the unitary gauge. We find the conserved Noether–Gaillard–Zumino current of E 7 ( 7 ) symmetry, the linear part of it being a chiral SU ( 8 ) symmetry. We comment on the conformal realization of the E 7 ( 7 ) algebra which includes a dilatation operator. We hope that these results can be useful for studies of anomalies/absence of anomalies and the UV behavior of N = 8 supergravity.

M theory through the looking glass: Tachyon condensation in theE8heterotic string

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing -- connecting the two E_8 boundaries by a throat -- are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E_8 gauge group and a singlet tachyon. We then use worldsheet methods to study the tachyon condensation in the NSR formulation of this model, and show that it induces a worldsheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for worldsheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the worldsheet gravitino assimilates the goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R_\xi gauges, and note the importance of logarithmic CFT in the context of tachyon condensation.

The effective field theory of inflation

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

Brane-worlds pseudo-Goldstinos

We consider a space–time with extra dimensions containing sectors, branes and bulk, that communicate only through gravitational interactions. In each sector, if considered separately, supersymmetry could be spontaneously broken, leading to the appearance of Goldstinos. However, when taken all together, only certain combinations of the latter states turn out to be true “would-be-Goldstinos”, eaten by the gravitinos. The other (orthogonal) combinations, we call pseudo-Goldstinos, remain in the low energy spectrum. We discuss explicitly how this happen in the simplest set-up of five-dimensional space compactified on S 1 / Z 2 . Our results divide into two parts that can be considered separately. First, we build an extension of the bulk five-dimensional supergravity, by a set of new auxiliary fields, that allows coupling it to branes where supersymmetry is spontaneously broken. Second, we discuss in details the super-Higgs mechanism in the R ξ and unitary gauges, in the presence of both of a bulk Scherk–Schwarz mechanism and brane localized F-terms. This leads us to compute the gravitino mass and provide explicit formulae for the pseudo-Goldstinos spectrum.

Exact Calculations of Vertex s̄γb ands̄Zb in the Unitary Gauge

In this paper, we present the exact calculations for thevertex s̄γb and s̄Zb in the unitary gauge.We find that (a) the divergent- and μ-dependent terms are leftin the effective vertex function Γγμ(p,k) forb→sγ transition even after we sum up the contributionsfrom four related Feynman diagrams; (b) for an on-shell photon,such terms do not contribute et al.; (c) for off-shell photon, theseterms will be canceled when the contributions from both vertexs̄γb and s̄Zb are taken into account simultaneously,and therefore the finite and gauge-independent function Z0(xt) = C0(xt)+D0(xt)/4, which governs the semi-leptonic decay b→sl−l+,is derived in the unitary gauge.