The Delocalized Effective Degrees of Freedom of a Black Hole at Low Frequencies

Identifying the fundamental degrees of freedom of a black hole poses a long-standing puzzle. In hep-th/0511133 Goldberger and Rothstein forwarded a theory of the low frequency degrees of freedom within the effective field theory approach, where they are relevancy-ordered but of unclear physical origin. Here these degrees of freedom are identified with near-horizon but non-compact gravitational perturbations which are decomposed into delocalized multipoles. Their world-line (kinetic) action is determined within the classical effective field theory (CLEFT) approach and their interactions are discussed. The case of the long-wavelength scattering of a scalar wave off a Schwarzschild black hole is treated in some detail, interpreting within the CLEFT approach the equality of the leading absorption cross section with the horizon area.Comment: 8 pages. Awarded fifth prize in the 2008 Gravity Research Foundation essay contest. v2: minor change

Effective Field Theory and Unification in AdS Backgrounds

This work is an extension of our previous work, hep-th/0204160, which showed how to systematically calculate the high energy evolution of gauge couplings in compact AdS_5 backgrounds. We first directly compute the one-loop effects of massive charged scalar fields on the low energy couplings of a gauge theory propagating in the AdS background. It is found that scalar bulk mass scales (which generically are of order the Planck scale) enter only logarithmically in the corrections to the tree-level gauge couplings. As we pointed out previously, we show that the large logarithms that appear in the AdS one-loop calculation can be obtained within the confines of an effective field theory, by running the Planck brane correlator from a high UV matching scale down to the TeV scale. This result exactly reproduces our previous calculation, which was based on AdS/CFT duality. We also calculate the effects of scalar fields satisfying non-trivial boundary conditions (relevant for orbifold breaking of bulk symmetries) on the running of gauge couplings.Comment: LaTeX, 27 pages; minor typos fixed, comments adde

Towers of Gravitational Theories

In this essay we introduce a theoretical framework designed to describe black hole dynamics. The difficulties in understanding such dynamics stems from the proliferation of scales involved when one attempts to simultaneously describe all of the relevant dynamical degrees of freedom. These range from the modes that describe the black hole horizon, which are responsible for dissipative effects, to the long wavelength gravitational radiation that drains mechanical energy from macroscopic black hole bound states. We approach the problem from a Wilsonian point of view, by building a tower of theories of gravity each of which is valid at different scales. The methodology leads to multiple new results in diverse topics including phase transitions of Kaluza-Klein black holes and the interactions of spinning black hole in non-relativistic orbits. Moreover, our methods tie together speculative ideas regarding dualities for black hole horizons to real physical measurements in gravitational wave detectors.Comment: Awarded second prize for 2006 Gravity Research Foundation essay contes

Systematics of Coupling Flows in AdS Backgrounds

We give an effective field theory derivation, based on the running of Planck brane gauge correlators, of the large logarithms that arise in the predictions for low energy gauge couplings in compactified AdS}_5 backgrounds, including the one-loop effects of bulk scalars, fermions, and gauge bosons. In contrast to the case of charged scalars coupled to Abelian gauge fields that has been considered previously in the literature, the one-loop corrections are not dominated by a single 4D Kaluza-Klein mode. Nevertheless, in the case of gauge field loops, the amplitudes can be reorganized into a leading logarithmic contribution that is identical to the running in 4D non-Abelian gauge theory, and a term which is not logarithmically enhanced and is analogous to a two-loop effect in 4D. In a warped GUT model broken by the Higgs mechanism in the bulk,we show that the matching scale that appears in the large logarithms induced by the non-Abelian gauge fields is m_{XY}^2/k where m_{XY} is the bulk mass of the XY bosons and k is the AdS curvature. This is in contrast to the UV scale in the logarithmic contributions of scalars, which is simply the bulk mass m. Our results are summarized in a set of simple rules that can be applied to compute the leading logarithmic predictions for coupling constant relations within a given warped GUT model. We present results for both bulk Higgs and boundary breaking of the GUT gauge group.Comment: 22 pages, LaTeX, 3 figures. Comments and references adde

Stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum brane model

We calculate the vacuum expectation value of the stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum model, and discuss the consequences of its local behaviour for the self-consistency of the model. We find that, in general, the stress-energy tensor diverges in the vicinity of the branes. Our main conclusion is that the stress-energy tensor is sufficiently complicated that it has implications for the effective potential, or radion stabilisation, methods that have so far been used.Comment: 16 pages, 3 figures. Minor changes made and references added. To appear in Phys. Rev.

Spectrum of TeV Particles in Warped Supersymmetric Grand Unification

In warped supersymmetric grand unification, XY gauge particles appear near the TeV scale along with Kaluza-Klein towers of the standard model gauge fields. In spite of this exotic low-energy physics, MSSM gauge coupling unification is preserved and proton decay is naturally suppressed. In this paper we study in detail the low-lying mass spectrum of superparticles and GUT particles in this theory, taking supersymmetry breaking to be localized to the TeV brane. The masses of the MSSM particles, Kaluza-Klein modes, and XY states are all determined by two parameters, one which fixes the strength of the supersymmetry breaking and the other which sets the scale of the infrared brane. A particularly interesting result is that for relatively strong supersymmetry breaking, the XY gauginos and the lowest Kaluza-Klein excitations of the MSSM gauginos may both lie within reach of the LHC, providing the possibility that the underlying unified gauge symmetry and the enhanced N=2 supersymmetry of the theory will both be revealed.Comment: 29 pages, 5 figure

Bulk Gauge Fields in Warped Space and Localized Supersymmetry Breaking

We consider five dimensional supersymmetric warped scenarios in which the Standard Model quark and lepton fields are localized on the ultraviolet brane, while the Standard Model gauge fields propagate in the bulk. Supersymmetry is assumed to be broken on the infrared brane. The relative sizes of supersymmetry breaking effects are found to depend on the hierarchy between the infrared scale and the weak scale. If the infrared scale is much larger than the weak scale the leading supersymmetry breaking effect on the visible brane is given by gaugino mediation. The gaugino masses at the weak scale are proportional to the square of the corresponding gauge coupling, while the dominant contribution to the scalar masses arises from logarithmically enhanced radiative effects involving the gaugino mass that are cutoff at the infrared scale. While the LSP is the gravitino, the NLSP which is the stau is stable on collider time scales. If however the infrared scale is close to the weak scale then the effects of hard supersymmetry breaking operators on the scalar masses can become comparable to those from gaugino mediation. These operators alter the relative strengths of the couplings of gauge bosons and gauginos to matter, and give loop contributions to the scalar masses that are also cutoff at the infrared scale. The gaugino masses, while exhibiting a more complicated dependence on the corresponding gauge coupling, remain hierarchical and become proportional to the corresponding gauge coupling in the limit of strong supersymmetry breaking. The scalar masses are finite and a loop factor smaller than the gaugino masses. The LSP remains the gravitino.Comment: 36 pages, 2 figure

Z boson pair production at LHC in a stabilized Randall-Sundrum scenario

We study the Z boson pair production at LHC in the Randall-Sundrum scenario with the Goldberger-Wise stabilization mechanism. It is shown that comprehensive account of the Kaluza-Klein graviton and radion effects is crucial to probe the model: The KK graviton effects enhance the cross section of $g g \to Z Z$ on the whole so that the resonance peak of the radion becomes easy to detect, whereas the RS effects on the $q\bar{q} \to Z Z$ process are rather insignificant. The $p_T$ and invariant-mass distributions are presented to study the dependence of the RS model parameters. The production of longitudinally polarized Z bosons, to which the SM contributions are suppressed, is mainly due to KK gravitons and the radion, providing one of the most robust methods to signal the RS effects. The $1 \sigma$ sensitivity bounds on $(\Lambda_\pi, m_\phi)$ with $k/M_{\rm Pl} =0.1$ are also obtained such that the effective weak scale $\Lambda_\pi$ of order 5 TeV can be experimentally probed.Comment: 28 pages, LaTex file, 18 eps figure

Higgsless Theory of Electroweak Symmetry Breaking from Warped Space

We study a theory of electroweak symmetry breaking without a Higgs boson, recently suggested by Csaki et al. The theory is formulated in 5D warped space with the gauge bosons and matter fields propagating in the bulk. In the 4D dual picture, the theory appears as the standard model without a Higgs field, but with an extra gauge group G which becomes strong at the TeV scale. The strong dynamics of G breaks the electroweak symmetry, giving the masses for the W and Z bosons and the quarks and leptons. We study corrections in 5D which are logarithmically enhanced by the large mass ratio between the Planck and weak scales, and show that they do not destroy the structure of the electroweak gauge sector at the leading order. We introduce a new parameter, the ratio between the two bulk gauge couplings, into the theory and find that it allows us to control the scale of new physics. We also present a potentially realistic theory accommodating quarks and leptons and discuss its implications, including the violation of universality in the W and Z boson couplings to matter and the spectrum of the Kaluza-Klein excitations of the gauge bosons. The theory reproduces many successful features of the standard model, although some cancellations may still be needed to satisfy constraints from the precision electroweak data.Comment: 17 pages, Latex; important correction in discussions on effects from brane terms, reference adde

Brane Localized Curvature for Warped Gravitons

We study the effects of including brane localized curvature terms in the Randall-Sundrum (RS) model of the hierarchy. This leads to the existence of brane localized kinetic terms for the graviton. Such terms can be induced by brane and bulk quantum effects as well as Higgs-curvature mixing on the brane. We derive the modified spectrum of Kaluza-Klein (KK) gravitons and their couplings to 4-dimensional fields in the presence of these terms. We find that the masses and couplings of the KK gravitons have considerable dependence on the size of the brane localized terms; the weak-scale phenomenology of the model is consequently modified . In particular, the weak-scale spin-2 graviton resonances which generically appear in the RS model may be significantly lighter than previously assumed. However, they may avoid detection as their widths may be too narrow to be observable at colliders. In the contact interaction limit, for a certain range of parameters, the experimental reach for the scale of the theory is independent of the size of the boundary terms.Comment: 20 pages, 11 figures, LaTex, minor revision