Linear Sigma EFT for Nearly Conformal Gauge Theories

We construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum ($\sigma$) can be much lighter than the vector state ($\rho$) and nearly degenerate with the PNGBs ($\pi$) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality $M_{\sigma}^2 \ge 3 M_{\pi}^2$, allowing for consistency with current lattice data.Comment: 9 pages, 1 figure, published versio

Hidden Conformal Symmetry from Eight Flavors

This proceedings paper extends the scope of our conference talk, where we presented a comprehensive analysis of newly expanded and refined lattice data concerning the SU(3) gauge theory with Nf = 8 light Dirac fermions - a theory positioned near the conformal window boundary. The analysis presented here makes use of a dilaton effective field theory and we delve deeper into the intricacies of the dilaton potential. We aim to clarify the connection between parameters appearing the potential and properties of the underlying gauge theory.Comment: 10 pages, 1 figure, Lattice 2023 proceedings. Small changes made to improve clarity of discussio

Dilaton potential and lattice data

We study an effective field theory (EFT) describing the interaction of an approximate dilaton with a set of pseudo-Nambu-Goldstone bosons (pNGBs). The EFT is inspired by, and employed to analyse, recent results from lattice calculations that reveal the presence of a remarkably light singlet scalar particle. We adopt a simple form for the scalar potential for the EFT, which interpolates among earlier proposals. It describes departures from conformal symmetry, by the insertion of a single operator at leading order in the EFT. To fit the lattice results, the global internal symmetryis explicitly broken, producing a common mass for the pNGBs, as well as a further, additive deformation of the scalar potential. We discuss sub-leading corrections arising in the EFT from quantum loops. From lattice measurements of the scalar and pNGB masses and of the pNGB decay constant, we extract model parameter values, including those that characterise the scalar potential.The result includes the possibility that the conformal deformation is clearly non-marginal. The extrapolated values for the decay constants and the scalar mass would then be not far below thecurrent lattice-determined values

Hamiltonian Truncation Crafted for UV-divergent QFTs

We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of $d=1+1$ CFTs. We investigated three examples of increasing complexity: the deformed Ising, Tricritical-Ising, and non-unitary minimal model $M(3,7)$. The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The $M(3,7)$ CFT deformed by its $Z_2$-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the $M(3,5)$ CFT.Comment: Published version with corrected typos, 42 pages, 12 figure

Hamiltonian truncation crafted for UV-divergent QFTs

We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of d=1+1 CFTs. We investigated three examples of increasing complexity: The deformed Ising, Tricritical-Ising, and non-unitary minimal model M(3,7). The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The M(3,7) CFT deformed by its Z2-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the M(3,5) CFT

Computations of Viking Lander Capsule Hypersonic Aerodynamics with Comparisons to Ground and Flight Data

Comparisons are made between the LAURA Navier-Stokes code and Viking Lander Capsule hypersonic aerodynamics data from ground and flight measurements. Wind tunnel data are available for a 3.48 percent scale model at Mach 6 and a 2.75 percent scale model at Mach 10.35, both under perfect gas air conditions. Viking Lander 1 aerodynamics flight data also exist from on-board instrumentation for velocities between 2900 and 4400 m/sec (Mach 14 to 23.3). LAURA flowfield solutions are obtained for the geometry as tested or flown, including sting effects at tunnel conditions and finite-rate chemistry effects in flight. Using the flight vehicle center-of-gravity location (trim angle approx. equals -11.1 deg), the computed trim angle at tunnel conditions is within 0.31 degrees of the angle derived from Mach 6 data and 0.13 degrees from the Mach 10.35 trim angle. LAURA Mach 6 trim lift and drag force coefficients are within 2 percent of measured data, and computed trim lift-to-drag ratio is within 4 percent of the data. Computed trim lift and drag force coefficients at Mach 10.35 are within 5 percent and 3 percent, respectively, of wind tunnel data. Computed trim lift-to-drag ratio is within 2 percent of the Mach 10.35 data. Using the nominal density profile and center-of-gravity location, LAURA trim angle at flight conditions is within 0.5 degrees of the total angle measured from on-board instrumentation. LAURA trim lift and drag force coefficients at flight conditions are within 7 and 5 percent, respectively, of the flight data. Computed trim lift-to-drag ratio is within 4 percent of the data. Computed aerodynamics sensitivities to center-of-gravity location, atmospheric density, and grid refinement are generally small. The results will enable a better estimate of aerodynamics uncertainties for future Mars entry vehicles where non-zero angle-of-attack is required

Viking Afterbody Heating Computations and Comparisons to Flight Data

Computational fluid dynamics predictions of Viking Lander 1 entry vehicle afterbody heating are compared to flight data. The analysis includes a derivation of heat flux from temperature data at two base cover locations, as well as a discussion of available reconstructed entry trajectories. Based on the raw temperature-time history data, convective heat flux is derived to be 0.63-1.10 W/sq cm for the aluminum base cover at the time of thermocouple failure. Peak heat flux at the fiberglass base cover thermocouple is estimated to be 0.54-0.76 W/sq cm, occurring 16 seconds after peak stagnation point heat flux. Navier-Stokes computational solutions are obtained with two separate codes using an 8-species Mars gas model in chemical and thermal non-equilibrium. Flowfield solutions using local time-stepping did not result in converged heating at either thermocouple location. A global time-stepping approach improved the computational stability, but steady state heat flux was not reached for either base cover location. Both thermocouple locations lie within a separated flow region of the base cover that is likely unsteady. Heat flux computations averaged over the solution history are generally below the flight data and do not vary smoothly over time for both base cover locations. Possible reasons for the mismatch between flight data and flowfield solutions include underestimated conduction effects and limitations of the computational methods

Dilaton EFT framework for lattice data

We develop an effective-field-theory (EFT) framework to analyze the spectra emerging from lattice simulations of a large class of confining gauge theories. Simulations of these theories, for which the light-fermion count is not far below the critical value for transition to infrared conformal behavior, have indicated the presence of a remarkably light singlet scalar particle. We incorporate this particle by including a scalar field in the EFT along with the Nambu-Goldstone bosons (NGB's), and discuss the application of this EFT to lattice data. We highlight the feature that data on the NGB's alone can tightly restrict the form of the scalar interactions. As an example, we apply the framework to lattice data for an SU(3) gauge theory with eight fermion flavors, concluding that the EFT can describe the data well