arXiv subjects

Ira Z. Rothstein

Publications and source records attributed to Ira Z. Rothstein.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Treatment of the Self-Force Problem

This paper introduces formalism, based on worldline effective field theory, which allows one to systematically calculate the gravitational self-force on a compact object immersed in an environment with non-vanishing stress energy. Using the closed time path integral we present a universal effective action that can be used to calculate the equations of motion of a compact object due to its interaction with the environment to any order in the relevant expansion parameters, the relative importance of which depends upon the choice of environment. We show that the leading order equations of motion can be universally written in terms of the retarded two-point function of the stress-energy tensor for the environment. The resulting action can be used to calculate both dissipative (dynamical friction) and conservative forces in a completely relativistic fashion. We demonstrate the utility of the result by calculating the dissipative force due to dust, an inviscid fluid, and a coherent field. Our results agree with those previously derived in the literature. We furthermore show that the famous ``Coulomb Log" found by Chandrasekhar should be interpreted as a renormalization group log due to a UV divergence that renormalizes the dissipative part of the in-in action. We then prove that this log is universal in the Newtonian limit in that its value is universal, for a generic class of environments and trajectories. This log is the leading log in an RG flow in the dissipative action that has yet to be explored.

gr-qc↗

arXiv2026

Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms

We investigate the high-energy, small-angle limit of two-body gravitational scattering. Using power counting arguments and dispersion relations in an effective field theory for the Regge regime, we derive the general loop expansion that determines how the leading Regge logarithms and their complex structure arise as a power series in $t/s$. Focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior, we compute the leading double logarithm at four loops (5PM) using both effective field theory methods and the multi-Regge expansion, finding complete agreement. Finally, using the aforementioned dispersion relations, we extract the single logarithmic contribution to the imaginary part of the eikonal phase at 5PM in the Regge limit.

hep-th↗

arXiv2026

A Systematic Lagrangian Formulation for Quantum and Classical Gravity at High Energies

We derive a systematic Lagrangian approach for quantum gravity in the super-Planckian limit where $s\gg M_{pl}^2\gg t$. The action can be used to calculate to arbitrary accuracy in the quantum and classical expansion parameters $α_Q= \frac{t}{M_{pl}^2}$ and $α_C= \frac{st}{M_{pl}^4}$, respectively, for the scattering of massless particles. The perturbative series contains powers of $\log(s/t)$ which can be resummed using a rapidity renormalization group equation (RRGE) that follows from a factorization theorem which allows us to write the amplitude as a convolution of a soft and collinear jet functions. We prove that the soft function is composed of an infinite tower of operators which do not mix under rapidity renormalization. The running of the leading order (in $G$) operator leads to the graviton Regge trajectory while the next to leading operator running corresponds to the gravitational BFKL equation. For the former, we find agreement with one of the two results previously presented in the literature, while for the ladder our result agrees (up to regulator dependent pieces) with those of Lipatov. We find that the convolutive piece of the gravitational BFKL kernel is the square of that of QCD. The power counting simplifies considerably in the classical limit where we can use our formalism to extract logs at any order in the PM expansion. The leading log at any order in the PM expansion can be calculated without going beyond one loop. The log at $(2N+1)$ order in the Post-Minkowskian expansion follows from calculating the one loop anomalous dimension for the $N+1$th order piece of the soft function and perturbatively solving the RRGE $N-1$ times. The factorization theorem implies that the classical logs which arise alternate between being real and imaginary in nature as $N$ increases.

hep-th↗

arXiv2025

Fermi Liquid Fixed Point Deformations due to Codimension Two Defects

We show that codimension-two defects in Fermi liquids deform the renormalization group flow via a marginally relevant coupling. The mechanism for generating the flow is distinct from the case of the Kondo problem (codimension-three defects) in that the effective particle-hole asymmetry that leads to the log running is due to the spatial anisotropy generated by the defect. The mechanism for the log generation has a simple geometric explanation which shows that hole fluctuations are suppressed as the incoming momentum is taken to be along the direction of the defect. The RG flow time is shown to scale with the length of the defect. We also show that the dislon, the Goldstone mode localized to the defect, couples in a non-derivative fashion to the bulk fermions and becomes relevant above the dislons' Debye frequency which depends upon the defect tension.

cond-mat.str-el↗

arXiv2025

Dispersion Relations for Dislocation Modes and their Sensitivity to the Lattice Structure

In this letter we show that the dispersion relation for the dynamical modes of dislocations ("dislons") in solids is sensitive to the lattice symmetries. In particular, we show that in the IR, the dislon dispersion relation develops a logarithmic dependence on momenta for approximately isotropic lattices whereas for non-isotropic lattices, the linear term dominates. The renormalization group flows for dislocation tension are shown to be distinct for isotropic and anisotropic lattices.

hep-th↗

arXiv2024

On the Motion of Compact Objects in Relativistic Viscous Fluids

We present a world-line effective field theory of compact objects moving relativistically through a viscous fluid. The theory is valid when velocity gradients are small compared to the inverse size of the object. Working within the EFT eliminates the need to solve a boundary value problem by turning all interactions between the fluid and the object into a source term in the action. We use the EFT to derive the relativistic equations of motion for a compact object immersed in a viscous fluid in a curved background.

gr-qc↗

arXiv2024

New Physics Hiding at the Ends

Is field space infinite? If not, it either loops back on itself or ends altogether. Periodic boundary conditions are of course familiar, but field space endpoints--which appear in real-world systems--are far less explored. In this paper we argue that boundaries in field space are generic, radiatively stable structures that allow for new physics at very low scales not ruled out by experiment. Such boundaries are delocalized in field space from the vacuum, so they can only be accessed by coherent fields or high multiplicity processes, both of which are weakly constrained observationally. Low multiplicity interactions do not detect the boundary and instead perceive a "mirage cutoff" that is parametrically higher than the true cutoff of the theory. Hence, field space boundaries are deformations of the standard model that are Lorentz invariant, local, unitary at low energies, and experimentally unconstrained. We comment on the possibility of field space boundaries on the long-range force carriers and the Higgs, as well as possible implications for the hierarchy problem.

hep-ph↗

arXiv2024

Relations Between Anomalous Dimensions in the Regge Limit

We extend the recent formalism developed for computing rapidity anomalous dimension of form factors using unitarity to the problem of high-energy near forward scattering. By combining the factorization of $2\rightarrow 2$ scattering in the effective field theory (EFT) for Glauber operators with definite signature amplitudes, we derive an expression that relates anomalous dimensions (including Regge trajectories) to cut amplitudes, leading to significant computational simplifications. We demonstrate this explicitly by computing the one and two-loop Regge trajectories. Our formalism can also be used to bootstrap anomalous dimensions of operators not related by symmetries. As an example, we show that the full anomalous dimensions (including both the Regge pole and cut pieces) of the two Glauber operator anti-symmetric octet operator, can be determined from the anomalous dimension of the single Glauber exchange operator. Many other such relations exist between other color channels at each order in $α$.

hep-ph↗

arXiv2024

Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory

We explore a recently proposed effective field theory describing electromagnetically or gravitationally interacting massive particles in an expansion about their mass ratio, also known as the self-force (SF) expansion. By integrating out the deviation of the heavy particle about its inertial trajectory, we obtain an effective action whose only degrees of freedom are the lighter particle together with the photon or graviton, all propagating in a Coulomb or Schwarzschild background. The 0SF dynamics are described by the usual background field method, which at 1SF is supplemented by a "recoil operator" that encodes the wobble of the heavy particle, and similarly computable corrections appearing at 2SF and higher. Our formalism exploits the fact that the analytic expressions for classical backgrounds and particle trajectories encode dynamical information to all orders in the couplings, and from them we extract multiloop integrands for perturbative scattering. As a check, we study the two-loop classical scattering of scalar particles in electromagnetism and gravity, verifying known results. We then present new calculations for the two-loop classical scattering of dyons, and of particles interacting with an additional scalar or vector field coupling directly to the lighter particle but only gravitationally to the heavier particle.

hep-th↗

arXiv2024

First Principle Predictions for Cold Fermionic Gases Near Criticality via Critical Boson Dominance and Anomaly Matching

Recently the authors have developed an effective field theory formalism to systematically describe cold fermionic gases near the unitary limit. The theory has enhanced predictive power due to the fact that interactions are dominated by the exchange of a gapped critical boson whose couplings and mass are fixed by matching the dilatation anomaly between the UV and IR theories. We utilize this theory to give analytic predictions for the compressibility and magnetic susceptibility for fermions near unitarity with attractive interactions above the critical temperature $T_c$, with a well defined theoretical error. The inputs to the predictions are: the scattering length $a$, the effective mass $m^\star$ and contact parameter $\tilde C(a)$. We then compare our predictions to numerical simulations and find excellent agreement within the window of scattering lengths where the EFT is valid ($10\geq \mid \! k_F a \! \mid\geq 1$). Experimental corroboration of this theory supports critical point that can be describe by the inclusion of a scalar dilaton mode, whose action is fixed by symmetries.

cond-mat.quant-gas↗

arXiv2024

Extracting the Asymptotic Behavior of S-matrix Elements from their Phases

The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called "rapidity logs". It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a complex boost. The methodology introduced here also allows one to calculate without the need for a rapidity regulator. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor, the two parton soft function and the Regge trajectory in QCD.

hep-th↗

arXiv2024

Effective Field Theory for Extreme Mass Ratios

We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton's constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration -- that is, the geodesic deviation of the light body and the fluctuation graviton -- but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.

hep-th↗

arXiv2023

First Principles Prediction of the Landau Parameter for Fermi Liquids near the Unitarity Limit

This paper explores the behavior of systems of cold fermions as they approach unitarity above the critical temperature. As we move away from unitarity, by decreasing the scattering length, the dilaton, the Goldstone boson resulting from the spontaneous breaking of Schrodinger symmetry by the Fermi sea, becomes gapped. At energies below this gap, the interaction between quasi-particles will be dominated by local interactions generated by off-shell dilaton exchange. The dilaton mass can, in turn, be related via anomaly matching, to the scattering length and contact parameter within the confines of a systematic expansion. We use this relation to predict the s-wave Landau parameter to be $f=\frac{4πa (2ε(p_F)-p_F^2/m_\star)^2 m}{3p_F^4 \tilde{C}(a)}$ where $a$ is the scattering length, $m$ the atomic mass, $m_\star$, the effective mass which can be extracted from heat capacity, and $\tilde {C}(a)$ is the dimensionless contact parameter. The range of validity of this prediction (given in eq.(21)) is determined by the value of contact parameter and Fermi velocity, which depend upon the scattering length. It is expected to be valid in a range above $k_F a \sim 1$, but the actual window will depend upon the values of aforementioned parameters. Given this result for $f$, we predict the compressibility, spin susceptibility and the quasi-particle life-time.

cond-mat.quant-gas↗

arXiv2022

Apparent Fine Tunings for Field Theories with Broken Space-Time Symmetries

We exhibit a class of effective field theories that have hierarchically small Wilson coefficients for operators that are not protected by symmetries but are not finely tuned. These theories possess bounded target spaces and vacua that break space-time symmetries. We give a physical interpretation of these theories as generalized solids with open boundary conditions. We show that these theories realize unusual RG flows where higher dimensional (seemingly irrelevant) operators become relevant even at weak coupling. Finally, we present an example of a field theory whose vacuum energy relaxes to a hierarchically small value compared to the UV cut-off.

hep-th↗

arXiv2022

An Effective Field Theory of Magneto-Elasticity

We utilize the coset construction to derive the effective field theory of magnon-phonon interactions in (anti)-ferromagnetic and ferrimagnetic insulating materials. The action is used to calculate the equations of motion which generalize the Landau-Lifshitz and stress equations to allow for magneto-acoustic couplings to all orders in the fields at lowest order in the derivative expansion. We also include the symmetry breaking effects due to Zeeman, and Dzyaloshinsky-Moriya interactions. This effective theory is a toolbox for the study of magneto-elastic phenomena from first principles. As an example we use this theory to calculate the leading order contribution to the magnon decay width due to its the decay into phonons.

hep-th↗

arXiv2021

An Effective Field Theory for Forward Scattering and Factorization Violation

Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, where $|t| \ll s$. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs with soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with $\ge 2$ soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to SCET. The rapidity RGE yields gluon Reggeization at the amplitude level, and gives the BFKL equation for the soft and collinear functions in the forward scattering cross section. We derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. We also discuss criteria for factorization violation.

hep-ph↗

arXiv2020

Non-conservative effects on Spinning Black Holes from World-Line Effective Field Theory

We generalize the worldline EFT formalism developed in [4-9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin. We present results for the rate of change of mass and angular momentum in a background field and find agreement with previous calculations obtained by different techniques. We also present new results for both the non-conservative equations of motion and power loss/gain for a binary inspiral, which start at 5PN and 2.5PN order respectively and manifest the Penrose process.

hep-th↗

arXiv2020

Horizon radiation reaction forces

Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton's constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

hep-th↗