Mon·Oct 18, 2021Monday·October 18, 2021

1. 01*

   Finite-density QCD, $\mathcal{P}\mathcal{T}$ symmetry, and exotic phases

   Moses A. Schindler🇺🇸 · Stella T. Schindler🇺🇸 · Michael C. Ogilvie🇺🇸

   We study the phase structure of effective models of finite-density QCD using analytic and lattice simulation techniques developed for the study of non-Hermitian and $\mathcal{P}\mathcal{T}$-symmetric QFTs. Finite-density QCD is symmetric under the combined operation of the charge and complex conjugation operators $\mathcal{C}\mathcal{K}$, which falls into the class of so-called generalized $\mathcal{P}\mathcal{T}$ symmetries. We show that $\mathcal{P}\mathcal{T}$-symmetric quantum field theories can support patterned ground-state field configurations in the vicinity of a critical endpoint. We apply our methods to a lattice heavy quark model at nonzero chemical potential that displays patterning behavior for a range of parameters. We derive a simple approximate criterion for the formation of these patterns, which can be used with lattice results.

   hep-lathep-phnucl-thPoS(2022)·8 citations
2. 02*

   Dilaton chiral perturbation theory and applications

   Maarten Golterman🇺🇸 · Yigal Shamir🇮🇱

   We review dilaton chiral perturbation theory (dChPT), the effective low-energy theory for the light sector of near-conformal, confining theories. dChPT provides a systematic expansion in both the fermion mass and the distance to the conformal window. It accounts for the pions and the light scalar, the approximate Nambu-Goldstone bosons for chiral and scale symmetry, respectively. A unique feature of dChPT is the existence of a large-mass regime in which the theory exhibits approximate hyperscaling, while the expansion nevertheless remains systematic. We discuss applications to lattice data, presenting successes as well as directions for future work.

   hep-lathep-phPoS(2024)·8 citations
3. 03*

   Breaking the gauge symmetry in lattice gauge-invariant models

   Claudio Bonati🇮🇹 · Andrea Pelissetto🇮🇹 · Ettore Vicari🇮🇹

   We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions. As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a U(1) gauge field. We discuss under which conditions a gauge-symmetry breaking term destabilizes the critical behavior (continuum limit) of the gauge-invariant theory. We find that the gauge symmetry is robust at transitions at which gauge fields are not critical. At charged transitions, where gauge fields are critical, gauge symmetry is lost as soon as the perturbation is added.

   hep-latcond-mat.stat-mechPoS(2022)·2 citations
4. 04*

   Hamiltonian Truncation Effective Theory

   Timothy Cohen🇺🇸 · Kara Farnsworth🇺🇸 · Rachel Houtz🇬🇧 · Markus A. Luty🇺🇸

   Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian $H_0$ with eigenvalues below some energy cutoff $E_{\text{max}}$. In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above $E_{\text{max}}$. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of $1/E_{\text{max}}$. The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of $H_0/E_{\text{max}}$. The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D $\lambda {\varphi }^4$ theory, and compute the the leading $1/E_{\text{max}}^2$ corrections to the effective Hamiltonian. We show that these corrections non-trivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order $1/E_{\text{max}}^3$, as expected by our power counting. We also present the power counting for 3D $\lambda {\varphi }^4$ theory and perform calculations that demonstrate the separation of scales in this theory.

   ↳ hep-thcond-mat.str-elhep-lathep-phSciPost Phys.(2022)·25 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.