The phase structure of a chirally invariant lattice Higgs-Yukawa model for small and for large values of the Yukawa coupling constant

We consider a chirally invariant lattice Higgs-Yukawa model based on the Neuberger overlap operator. As a first step towards the eventual determination of Higgs mass bounds we study the phase diagram of the model analytically in the large Nf-limit. We present an expression for the effective potential at tree-level in the regime of small Yukawa and quartic coupling constants and determine the order of the phase transitions. In the case of strong Yukawa couplings the model effectively becomes an O(4)-symmetric non-linear sigma-model for all values of the quartic coupling constant. This leads to the existence of a symmetric phase also in the regime of large values of the Yukawa coupling constant. On finite and small lattices, however, strong finite volume effects prevent the expectation value of the Higgs field from vanishing thus obscuring the existence of the symmetric phase at strong Yukawa couplings.Comment: 21 pages, 6 figures, added reference

The phase structure of a chirally invariant lattice Higgs-Yukawa model - numerical simulations

The phase diagram of a chirally invariant lattice Higgs-Yukawa model is explored by means of numerical simulations. The results revealing a rich phase structure are compared to analytical large Nf calculations which we performed earlier. The analytical and numerical results are in excellent agreement at large values of Nf. In the opposite case the large Nf computation still gives a good qualitative description of the phase diagram. In particular we find numerical evidence for the predicted ferrimagnetic phase at intermediate values of the Yukawa coupling constant and for the symmetric phase at strong Yukawa couplings. Emphasis is put on the finite size effects which can hide the existence of the latter symmetric phase.Comment: 14 pages, 11 figure

The Positivity Set of a Recurrence Sequence

We consider real sequences $(f_n)$ that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where the sequence has no positive dominating characteristic root, we establish that the density is positive. Furthermore, we determine the values that can occur as density of such a positivity set, both for the special case just mentioned and in general

Chiral Lattice Gauge Theories and The Strong Coupling Dynamics of a Yukawa-Higgs Model with Ginsparg-Wilson Fermions

The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described in hep-lat/0605003 uses exact lattice chirality to decouple the massless chiral fermions from a mirror sector, whose strong dynamics is conjectured to give cutoff-scale mass to the mirror fermions without breaking the chiral gauge symmetry. In this paper, we study the mirror sector dynamics of a two-dimensional chiral gauge theory in the limitof strong Yukawa and vanishing gauge couplings, in which case it reduces to an XY model coupled to Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass it is believed to be important that the XY model remain in its "high temperature" phase, where there is no algebraic ordering--a conjecture supported by the results of our work. We use analytic and Monte-Carlo methods with dynamical fermions to study the scalar and fermion susceptibilities, and the mirror fermion spectrum. Our results provide convincing evidence that the strong dynamics does not "break" the chiral symmetry (more precisely, that the mirror fermions do not induce algebraic ordering in two-dimensions), and that the mirror fermions decouple from the infrared physics.Comment: 44 pages, 18 figures; v2: clarification of fermion operators, discussion of recent related work

Lattice chirality and the decoupling of mirror fermions

We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into "light" and "mirror" parts, such that the "light" and "mirror" representations are chiral. The splitting of the full partition function into "light" and "mirror" is well defined only if the two sectors are separately anomaly free. We show that only then is the generating functional, and hence the spectrum, of the mirror theory a smooth function of the gauge field background. This explains how ideas to use additional non-gauge, high-scale mirror-sector dynamics to decouple the mirror fermions without breaking the gauge symmetry--for example, in symmetric phases at strong mirror Yukawa coupling--are forced to respect the anomaly-free condition when combined with the exact lattice chiral symmetry. Our results also explain a paradox posed by a recent numerical study of the mirror-fermion spectrum in a toy would-be-anomalous two-dimensional theory. In passing, we prove some general properties of the partition functions of arbitrary chiral theories on the lattice that should be of interest for further studies in this field.Comment: 29 pages, 2 figures; published version, new addendu

Topology and confinement at T \neq 0 : calorons with non-trivial holonomy

In this talk, relying on experience with various lattice filter techniques, we argue that the semiclassical structure of finite temperature gauge fields for T < T_c is dominated by calorons with non-trivial holonomy. By simulating a dilute gas of calorons with identical holonomy, superposed in the algebraic gauge, we are able to reproduce the confining properties below T_c up to distances r = O(4 fm} >> \rho (the caloron size). We compute Polyakov loop correlators as well as space-like Wilson loops for the fundamental and adjoint representation. The model parameters, including the holonomy, can be inferred from lattice results as functions of the temperature.Comment: Talk by M. M\"uller-Preussker at "Quark Confinement and Hadron Structure VII", Ponta Delgada, Azores, Portugal, September 2 - 7, 2006, 4 pages, 2 figures, to appear in the Proceeding

Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?

This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror-fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the article is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson fermions. We end by pointing out possible directions for future studies.Comment: 53 pp; 6 figs; added table of contents, references, fixed typo