Spectrum of Trace Deformed Yang-Mills Theories

Abstract

In this paper we study, by means of numerical simulations, the behaviour of the scalar glueball mass and the ground state of the torelon for trace deformed Yang-Mills theory defined on ${\mathbb{R}}^3\times S^1$, in which center symmetry is recovered even at small compactification radii. We find, by investigating both $SU(3)$ and $SU(4)$ pure gauge theories, that the glueball mass computed in the deformed theory, when center symmetry is recovered, is compatible with its value at zero temperature and does not show any significant dependence on the compactification radius; moreover, we establish a connection between the deformation parameter and an effective compactification size, which works well at least for small deformations. In addition, we observe that the ground state of the torelon which winds around the small traced deformed circle with size $l$ acquires a pleateau for large values of the strength $h$, with values which are compatible with a $1/l$ behavior but, on the other hand, are still not in complete agreement with the asymptotic semiclassical large-$N$ predictions.

arXiv comment12 pages, 11 figures. In v2, in addition to SU(3) we also provide results for SU(4) at one lattice spacing. Furthermore, we provide a connection between the deformation parameter h and an effective compactification size l_eff. Major revision to the text

References in corpus (34)

• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Glueballs and k-strings in SU(N) gauge theories : calculations with improved operators
• The high temperature phase transition in SU(N) gauge theories
• Volume independence in large Nc QCD-like gauge theories
• The Effective Theory of Long Strings
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups
• The glueball spectrum of SU(3) gauge theory in 3+1 dimension
• Finite size phase transitions in QCD with adjoint fermions
• Modified instanton sum in QCD and higher-groups
• New Phases of SU(3) and SU(4) at Finite Temperature
• Closed flux tubes and their string description in D=3+1 SU(N) gauge theories
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Flux Tube Spectra from Approximate Integrability at Low Energies
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Large-N volume independence in conformal and confining gauge theories
• QCD on a small circle
• Glueball-Like Screening Masses in Pure SU(3) at Finite Temperatures
• $\theta$ dependence in trace deformed $SU(3)$ Yang-Mills theory: a lattice study
• String Tension Scaling in High-Temperature Confined SU(N) Gauge Theories
• Metastable vacuum decay and $\theta$ dependence in gauge theory. Deformed QCD as a toy model
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• $\theta$-dependence and center symmetry in Yang-Mills theories
• Oblique Confinement at $\theta \ne 0$ in weakly coupled gauge theories with deformations
• Casimir scaling in gauge theories with a gap. Deformed QCD as a toy model
• Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
• Exponential reduction of finite volume effects with twisted boundary conditions
• Long range order in gauge theories. Deformed QCD as a toy model
• Screening masses in the SU(3) pure gauge theory and universality
• Screening masses in the SU(3) pure gauge theory and universality

Cited by in corpus (2)

• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD