arXiv subjects

Walter D. Goldberger

Publications and source records attributed to Walter D. Goldberger.

At least 37 records · Page 2Linked to original sources

arXiv2011

Structure Function Sum rules for Systems with Large Scattering Lengths

We use a dispersion relation in conjunction with the operator product expansion (OPE) to derive model independent sum rules for the dynamic structure functions of systems with large scattering lengths. We present an explicit sum rule for the structure functions that control the density and spin response of the many-body ground state. Our methods are general, and apply to either fermions or bosons which interact through two-body contact interactions with large scattering lengths. By employing a Borel transform of the OPE, the relevant integrals are weighted towards infrared frequencies, thus allowing for greater overlap low energy data. Similar sum rules can be derived for other response functions. The sum rules can be used to extract the contact parameter introduced by Tan, including universality violating corrections at finite scattering lengths.

hep-ph↗

arXiv2010

Gravitational radiative corrections from effective field theory

In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN ($v^6$) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

gr-qc↗

arXiv2008

AdS/CFT duality for non-relativistic field theory

We formulate a correspondence between non-relativistic conformal field theories (NRCFTs) in d-1 spatial dimensions and gravitational theories in AdS_{d+2} backgrounds with one compactified lightlike direction. The breaking of the maximal SO(2,d+1) symmetry of AdS_{d+2} to the non-relativistic conformal group arises from boundary conditions on bulk fields, without the need to introduce non-vacuum sources of energy-momentum. As a check of the proposal, we use the gravitational theory to reproduce the NRCFT state-operator correspondence between scaling dimensions of primary operators and energy eigenstates of the non-relativistic system placed in an external harmonic potential.

hep-th↗

arXiv2008

Standard Model couplings and collider signatures of a light scalar

The electroweak symmetry breaking (EWSB) sector of the Standard Model can be far richer and more interesting than the usual single scalar doublet model. We explore scenarios where the EWSB sector is nearly scale invariant and consequently gives rise to a light CP even scalar particle. The one-doublet SM is in that category, as are many other models with either weakly or strongly coupled sectors that trigger EWSB. We study the couplings of the light scalar to the SM particles that can arise from the explicit breaking of scale invariance focusing on the possible differences with the minimal SM. The couplings of the light scalar to light fermions, as well as to the massless gauge bosons, can be significantly enhanced. We find possible new discovery channels due to the decays of the conformal scalar into e^+e^- and mu^+mu^- pairs as well as new production channels via light quark annihilation.

hep-ph↗

arXiv2007

Light scalar at LHC: the Higgs or the dilaton?

It is likely that the LHC will observe a color- and charge-neutral scalar whose decays are consistent with those of the Standard Model (SM) Higgs boson. The Higgs interpretation of such a discovery is not the only possibility. For example, electroweak symmetry breaking (EWSB) could be triggered by a spontaneously broken, nearly conformal sector. The spectrum of states at the electroweak scale would then contain a narrow scalar resonance, the pseudo-Goldstone boson of conformal symmetry breaking, with Higgs-like properties. If the conformal sector is strongly coupled, this pseudo-dilaton may be the only new state accessible at high energy colliders. We discuss the prospects for distinguishing this mode from a minimal Higgs boson at the LHC and ILC. The main discriminants between the two scenarios are (1) cubic self-interactions and (2) a potential enhancement of couplings to massless SM gauge bosons. A particularly interesting situation arises when the scale f of conformal symmetry breaking is approximately the electroweak scale v~246 GeV. Although in this case the LHC may not be able to tell apart a pseudo-dilaton from the Higgs boson, the self-interactions differ in a way that depends only on the scaling dimension of certain operators in the conformal sector. This opens the possibility of using dilaton pair production at future colliders as a probe of EWSB induced by nearly conformal new physics.

hep-ph↗

arXiv2007

Les Houches Lectures on Effective Field Theories and Gravitational Radiation

These lectures give an overview of the uses of effective field theories in describing gravitational radiation sources for LIGO or LISA. The first lecture reviews some of the standard ideas of effective field theory (decoupling, matching, power counting) mostly in the context of a simple toy model. The second lecture sets up the problem of calculating gravitational wave emission from non-relativistic binary stars by constructing a tower of effective theories that separately describe each scale in the problem: the internal size of each binary constituent, the orbital separation, and the wavelength of radiated gravitons.

hep-ph↗

arXiv2006

Spin dependent masses and Sim(2) symmetry

Recently, Cohen and Glashow pointed out that all known experimental tests of relativistic kinematics are consistent with invariance of physics under the four-parameter subgroup Sim(2) of the Lorentz group. The massive one-particle irreducible representations of ISim(2), that is Sim(2) times spacetime translations, are all one-dimensional, labeled by spin along a preferred axis. Consequently particle theories based on this symmetry can accomodate lepton number conserving masses for left-handed neutrinos without the need to introduce sterile states. The same property of massive particle representations, however, also leads to the possibility that particle masses may be split within the diffferent spins of a representation of the ordinary Poincare group. In this article we investigate the low-energy structure of theories with spin dependent masses and comment on the bounds on such effects.

hep-ph↗

arXiv2006

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.

hep-th↗

arXiv2006

Asymptotics of d-dimensional Kaluza-Klein black holes: beyond the Newtonian approximation

We study the thermodynamics of small black holes in compactified spacetimes of the form R^(d-1)x S^1. This system is analyzed with the aid of an effective field theory (EFT) formalism in which the structure of the black hole is encoded in the coefficients of operators in an effective worldline Lagrangian. In this effective theory, there is a small parameter $λ$ that characterizes the corrections to the thermodynamics due to both the non-linear nature of the gravitational action as well as effects arising from the finite size of the black hole. Using the power counting of the EFT we show that the series expansion for the thermodynamic variables contains terms that are analytic in $λ$, as well as certain fractional powers that can be attributed to finite size operators. In particular our operator analysis shows that existing analytical results do not probe effects coming from horizon deformation. As an example, we work out the order $λ^2$ corrections to the thermodynamics of small black holes for arbitrary d, generalizing the results in the literature.

hep-th↗

arXiv2005

Dissipative Effects in the Worldline Approach to Black Hole Dynamics

We derive a long wavelength effective point particle description of four-dimensional Schwarzschild black holes. In this effective theory, absorptive effects are incorporated by introducing degrees of freedom localized on the worldline that mimic the interaction between the horizon and bulk fields. The correlation functions of composite operators in this worldline theory can be obtained by standard matching calculations. For example, we obtain the low frequency two-point function of multipole worldline operators by relating them to the long wavelength graviton black hole absorptive cross section. The effective theory is then used to predict the leading effects of absorption in several astrophysically motivated examples, including the dynamics of non-relativistic black hole binary inspirals and the motion of a small black hole in an arbitrary background geometry. Our results can be written compactly in terms of absorption cross sections, and can be easily applied to the dissipative dynamics of any compact object, e.g. neutron stars. The relation of our methodology to that developed in the context of the AdS/CFT correspondence is discussed.

hep-th↗

arXiv2005

An Effective Field Theory of Gravity for Extended Objects

We present an Effective Field Theory (EFT) formalism which describes the dynamics of non-relativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation of the three relevant scales: r_s, the size of the compact objects, r the orbital radius and r/v, the wavelength of the physical radiation (where the velocity v is the expansion parameter). In the EFT radiation is systematically included in the v expansion without need to separate integrals into near zones and radiation zones. We show that the renormalization of ultraviolet divergences which arise at v^6 in post-Newtonian (PN) calculations requires the presence of two non-minimal worldline gravitational couplings linear in the Ricci curvature. However, these operators can be removed by a redefinition of the metric tensor, so that the divergences at arising at v^6 have no physically observable effect. Because in the EFT finite size features are encoded in the coefficients of non-minimal couplings, this implies a simple proof of the decoupling of internal structure for spinless objects to at least order v^6. Neglecting absorptive effects, we find that the power counting rules of the EFT indicate that the next set of short distance operators, which are quadratic in the curvature and are associated with tidal deformations, do not play a role until order v^10. These operators, which encapsulate finite size properties of the sources, have coefficients that can be fixed by a matching calculation. By including the most general set of such operators, the EFT allows one to work within a point particle theory to arbitrary orders in v.

hep-th↗

arXiv2003

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.

hep-th↗

arXiv2003

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.

hep-ph↗

arXiv2003

Quantum Stabilization of Compactified AdS_5

We investigate the role of quantum fluctuations in the system composed of two branes bounding a region of AdS. It is shown that the modulus effective potential generated by quantum fluctuations of both brane and bulk fields is incapable of stabilizing the space naturally at the separation needed to generate the hierarchy. Consequently, a classical stabilization mechanism is required. We describe the proper method of regulating the loop integrals and show that, for large brane separation, the quantum effects are power suppressed and therefore have negligible affects on the bulk dynamics once a classical stabilization mechanism is in place.

hep-th↗

arXiv2003

Warped Supersymmetric Grand Unification

We construct a realistic theory of grand unification in AdS_5 truncated by branes, in which the unified gauge symmetry is broken by boundary conditions and the electroweak scale is generated by the AdS warp factor. We show that the theory preserves the successful gauge coupling unification of the 4D MSSM at leading-logarithmic level. Kaluza-Klein (KK) towers, including those of XY gauge and colored Higgs multiplets, appear at the TeV scale, while the extra dimension provides natural mechanisms for doublet-triplet splitting and proton decay suppression. In one possible scenario supersymmetry is strongly broken on the TeV brane, in which case the lightest SU(3)_C x SU(2)_L x U(1)_Y gauginos are approximately Dirac and the mass of the lightest XY gaugino is pushed well below that of the lowest gauge boson KK mode, improving the prospects for its production at the LHC. The bulk Lagrangian possesses a symmetry that we call GUT parity. If GUT parity is exact, the lightest GUT particle, most likely an XY gaugino, is stable. Once produced in a collider, the XY gaugino hadronizes to form mesons, some of which will be charged and visible as highly ionizing tracks. The lightest supersymmetric particle is the gravitino of mass \sim 10^{-3} eV, which is also stable if R parity is conserved.

hep-ph↗

arXiv2002

High Energy Field Theory in Truncated AdS Backgrounds

In this letter we show that, in five-dimensional anti-deSitter space (AdS) truncated by boundary branes, effective field theory techniques are reliable at high energy (much higher than the scale suggested by the Kaluza-Klein mass gap), provided one computes suitable observables. We argue that in the model of Randall and Sundrum for generating the weak scale from the AdS warp factor, the high energy behavior of gauge fields can be calculated in a {\em cutoff independent manner}, provided one restricts Green's functions to external points on the Planck brane. Using the AdS/CFT correspondence, we calculate the one-loop correction to the Planck brane gauge propagator due to charged bulk fields. These effects give rise to non-universal logarithmic energy dependence for a range of scales above the Kaluza-Klein gap.

hep-th↗

arXiv2001

Renormalization Group Flows for Brane Couplings

Field theories in the presence of branes encounter localized divergences that renormalize brane couplings. The sources of these brane-localized divergences are understood as arising either from broken translation invariance, or from short distance singularities as the brane thickness vanishes. While the former are generated only by quantum corrections, the latter can appear even at the classical level. Using as an example six-dimensional scalar field theory in the background of a 3-brane, we show how to interpret such classical divergences by the usual regularization and renormalization procedure of quantum field theory. In our example, the zero thickness divergences are logarithmic, and lead classically to non-trivial renormalization group flows for the brane couplings. We construct the tree level renormalization group equations for these couplings as well as the one-loop corrections to these flows from bulk-to-brane renormalization effects.

hep-th↗

arXiv1999

Phenomenology of a Stabilized Modulus

We explore the phenomenology of a stabilized modulus field in the Randall-Sundrum scenario. It is found that if the large separation between branes arises from a small bulk scalar mass then the modulus (i.e. radion) is likely to be lighter than the lowest Kaluza-Klein excitations of bulk fields, and consequently may be the first direct signature of the model. Four-dimensional general covariance completely determines the couplings of the modulus to Standard Model fields. The strength of these couplings is determined by a single parameter which is set by the TeV rather than the Planck scale.

hep-ph↗