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

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

Dilaton forbidden dark matter

Dilaton effective field theory (dEFT) describes the long distance behavior of certain confining, nearconformal gauge theories that have been studied via lattice computation. Pseudo-Nambu- Goldstone bosons (pNGBs), emerging from the breaking of approximate, continuous, internal symmetries, are coupled to an additional scalar particle, the dilaton, arising from the spontaneous breaking of approximate scale invariance. This effective theory has been employed to study possible extensions of the standard model. In this paper, we propose a complementary role for dEFT, as a description of the dark matter of the Universe, with the pNGBs identified as the dark matter particles. We show that this theory provides a natural implementation of the “forbidden” dark matter mechanism, and we identify regions of parameter space for which the thermal history of dEFT yields the measured dark matter relic density

Analysis of a dilaton EFT for lattice data

In a recent paper, we developed and applied a dilaton-based effective field theory (EFT) to the analysis of lattice-simulation data for a class of confining gauge theories with near-conformal infrared behavior. It was employed there at the classical level to the SU(3) gauge theory with eight Dirac fermions in the fundamental representation. Here, we explore the structure of the EFT further. We examine its application to lattice data (newly updated) for the SU(3) theory with eight Dirac fermions in the fundamental representation, and the SU(3) theory with two Dirac fermions in the sextet representation. In each case, we determine additional fit parameters and discuss uncertainties associated with extrapolation to zero fermion mass. We highlight universal features, study the EFT at the quantum loop level and discuss the importance of future lattice simulations

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