Lack of trinification in Z_3 orbifolds of the SO(32) heterotic string

We report results relating to the trinification scenario in some explicit string constructions that contain SU(3)^3 as a gauge symmetry. These models are obtained from symmetric Z_3 orbifolds of the SO(32) heterotic string with one discrete Wilson line. We highlight the obstacles that were encountered: the absence of the usual Higgs sector that would break SU(3)^3 \to SU(3)_c \times SU(2)_L \times U(1)_Y; the presence of exotics that would generically befoul gauge coupling unification and lead to fractionally-charged states in the low energy spectrum.Comment: 1+7 pages, comments and refs adde

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U(1)_R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.Comment: 19 pages, 5 figure

Vortex Structure vs. Monopole Dominance in Abelian-Projected Gauge Theory

We find that Polyakov lines, computed in abelian-projected SU(2) lattice gauge theory in the confined phase, have finite expectation values for lines corresponding to two units of the abelian electric charge. This means that the abelian-projected lattice has at most Z(2), rather than U(1), global symmetry. We also find a severe breakdown of the monopole dominance approximation, as well as positivity, in this charge-2 case. These results imply that the abelian-projected lattice is not adequately represented by a monopole Coulomb gas; the data is, however, consistent with a center vortex structure. Further evidence is provided, in lattice Monte Carlo simulations, for collimation of confining color-magnetic flux into vortices.Comment: 37 pages, including 23 eps figures, Latex2

Warped Domain Wall Fermions

We consider Kaplan's domain wall fermions in the presence of an Anti-de Sitter (AdS) background in the extra dimension. Just as in the flat space case, in a completely vector-like gauge theory defined after discretizing this extra dimension, the spectrum contains a very light charged fermion whose chiral components are localized at the ends of the extra dimensional interval. The component on the IR boundary of the AdS space can be given a large mass by coupling it to a neutral fermion via the Higgs mechanism. In this theory, gauge invariance can be restored either by taking the limit of infinite proper length of the extra dimension or by reducing the AdS curvature radius towards zero. In the latter case, the Kaluza-Klein modes stay heavy and the resulting classical theory approaches a chiral gauge theory, as we verify numerically. Potential difficulties for this approach could arise from the coupling of the longitudinal mode of the light gauge boson, which has to be treated non-perturbatively

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

RG inspired Machine Learning for lattice field theory

Machine learning has been a fast growing field of research in several areas dealing with large datasets. We report recent attempts to use Renormalization Group (RG) ideas in the context of machine learning. We examine coarse graining procedures for perceptron models designed to identify the digits of the MNIST data. We discuss the correspondence between principal components analysis (PCA) and RG flows across the transition for worm configurations of the 2D Ising model. Preliminary results regarding the logarithmic divergence of the leading PCA eigenvalue were presented at the conference and have been improved after. More generally, we discuss the relationship between PCA and observables in Monte Carlo simulations and the possibility of reduction of the number of learning parameters in supervised learning based on RG inspired hierarchical ansatzes.Comment: Talk given by Yannick Meurice at the conference Lattice 2017, Granada, Spai

"Light from chaos" in two dimensions

We perform a Monte-Carlo study of the lattice two-dimensional gauged XY-model. Our results confirm the strong-coupling expansion arguments that for sufficiently small values of the spin-spin coupling the ``gauge symmetry breaking" terms decouple and the long-distance physics is that of the unbroken pure gauge theory. We find no evidence for the existence, conjectured earlier, of massless states near a critical value of the spin-spin coupling. We comment on recent remarks in the literature on the use of gauged XY-models in proposed constructions of chiral lattice gauge theories.Comment: 6 pages, 7 figure

Deconstruction and other approaches to supersymmetric lattice field theories

This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.Comment: 70 page

Bulk fields in AdS_5 from probe D7 branes

We relate bulk fields in Randall-Sundrum AdS_5 phenomenological models to the world-volume fields of probe D7 branes in the Klebanov-Witten background of type IIB string theory. The string constructions are described by AdS_5 X T^{1,1} in their near-horizon geometry, with T^{1,1} a 5d compact internal manifold that yields N=1 supersymmetry in the dual 4d gauge theory. The effective 5d Lagrangian description derived from the explicit string construction leads to additional features that are not usually encountered in phenomenological model building.Comment: 23 pages, 4 figures; v2: references added; v3: equations simplified, typos correcte