scholarly journals Higgs compositeness in Sp(2N) gauge theories — Resymplecticisation, scale setting and topology

2018 ◽  
Vol 175 ◽  
pp. 08012 ◽  
Author(s):  
Ed Bennett ◽  
Deog Ki Hong ◽  
Jong-Wan Lee ◽  
C.-J. David Lin ◽  
Biagio Lucini ◽  
...  
Keyword(s):  
Topological Charge ◽  
Gauge Theories ◽  
Gradient Flow ◽  
Dirac Fermion ◽  
Fundamental Representation ◽  
Technical Aspects ◽  
Composite Higgs ◽  
And Topology ◽  
Pure Gauge Theory ◽  
Ongoing Programme

As part of an ongoing programme to study Sp(2N) gauge theories as potential realisations of composite Higgs models, we consider the case of Sp(4) on the lattice, both as a pure gauge theory, and with two Dirac fermion flavors in the fundamental representation. In order to compare results between these two cases and maintain control of lattice artefacts, we make use of the gradient flow to set the scale of the simulations. We present some technical aspects of the simulations, including preliminary results for the scale setting in the two cases and results for the topological charge history.

scholarly journals Memory efficient finite volume schemes with twisted boundary conditions

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Eduardo I. Bribián ◽  
Jorge Dasilva Golán ◽  
Margarita García Pérez ◽  
Alberto Ramos
Keyword(s):  
Boundary Conditions ◽  
Finite Volume ◽  
Gauge Theories ◽  
Gradient Flow ◽  
Finite Volume Schemes ◽  
Translational Invariance ◽  
Pure Gauge Theory ◽  
Gpu Clusters ◽  
Twisted Boundary Conditions

AbstractIn this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size $$l^2 \times (Nl)^2$$ l 2 × ( N l ) 2 , a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $$\Lambda $$ Λ parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $$\Lambda _{\overline{\mathrm{MS}}}\sqrt{8 t_0} =0.603(17)$$ Λ MS ¯ 8 t 0 = 0.603 ( 17 ) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

scholarly journals Thermodynamics for SU(2) pure gauge theory using gradient flow

2019 ◽  
Author(s):  
Takehiro Hirakida ◽  
Etsuko Itou ◽  
Hiroaki Kouno
Keyword(s):  
Gauge Theory ◽  
Gradient Flow ◽  
Pure Gauge ◽  
Pure Gauge Theory

scholarly journals Higgs compositeness in Sp(2N) gauge theories – Determining the low-energy constants with lattice calculations

2018 ◽  
Vol 175 ◽  
pp. 08011 ◽  
Author(s):  
Ed Bennett ◽  
Deog Ki Hong ◽  
Jong-Wan Lee ◽  
C.-J. David Lin ◽  
Biagio Lucini ◽  
...  
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Higgs Model ◽  
Low Energy ◽  
Dirac Fermion ◽  
Global Symmetry ◽  
Composite Higgs ◽  
Lattice Calculations ◽  
Energy Constants

As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) → Sp(4) global symmetry breaking pattern. We then consider an Sp(4) gauge theory with two Dirac fermion flavours in the fundamental representation on a lattice, which provides a concrete example of the microscopic realisation of the SU(4)/Sp(4) composite Higgs model. For this system, we outline a programme of numerical simulations aiming at the determination of the low-energy constants of the effective field theory and we test the method on the quenched theory. We also report early results from dynamical simulations, focussing on the phase structure of the lattice theory and a calculation of the lowest-lying meson spectrum at coarse lattice spacing.

scholarly journals M and F Theory Instantons, N = 1 Supersymmetry and Fractional Topological Charge

1997 ◽  
Vol 12 (28) ◽  
pp. 5141-5149 ◽  
Author(s):  
César Gómez ◽  
Rafael Hernández
Keyword(s):  
Topological Charge ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Singular Points ◽  
Coulomb Branch ◽  
Supersymmetric Gauge Theories ◽  
Dimensional Theory ◽  
Pure Gauge ◽  
Supersymmetric Gauge

We analyze instanton generated superpotentials for three-dimensional N = 2 supersymmetric gauge theories obtained by compactifying on S1 N = 1 four-dimensional theories. For SU(2) with Nf = 1, we find that the vacua in the decompactification limit is given by the singular points of the Coulomb branch of the N = 2 four-dimensional theory (we also consider the massive case). The decompactification limit of the superpotential for pure gauge theories without chiral matter is interpreted in terms of 't Hooft's fractional instanton amplitudes.

scholarly journals Anomalies in the space of coupling constants and their dynamical applications II

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Clay Cordova ◽  
Daniel Freed ◽  
Ho Tat Lam ◽  
Nathan Seiberg
Keyword(s):  
Phase Transitions ◽  
Time Reversal ◽  
Discrete Symmetries ◽  
Gauge Theories ◽  
Coupling Constants ◽  
Global Symmetry ◽  
Flavor Symmetry ◽  
Fundamental Representation ◽  
Yang Mills ◽  
Simply Connected

We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form global symmetry (associated with the center) and the periodicity of the \thetaθ-parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as time-reversal). We also study SU(N)SU(N) and Sp(N)Sp(N) gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the \thetaθ-periodicity. Again, this anomaly unifies distinct recently-discovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.

scholarly journals Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learning

2020 ◽  
Author(s):  
Takuya Matsumoto ◽  
Masakiyo Kitazawa ◽  
Yasuhiro Kohno
Keyword(s):  
Machine Learning ◽  
Charge Density ◽  
Topological Charge ◽  
Dimensional Space ◽  
Gradient Flow ◽  
Fully Integrated ◽  
Yang Mills ◽  
Physical Volume ◽  
Spatial Coordinates ◽  
Small Flow

Abstract We apply a machine learning technique for identifying the topological charge of quantum gauge configurations in four-dimensional SU(3) Yang-Mills theory. The topological charge density measured on the original and smoothed gauge configurations with and without dimensional reduction is used for inputs of the neural networks (NN) with and without convolutional layers. The gradient flow is used for the smoothing of the gauge field. We find that the topological charge determined at a large flow time can be predicted with high accuracy from the data at small flow times by the trained NN; for example, the accuracy exceeds 99% with the data at t/a2 ≤ 0.3. High robustness against the change of simulation parameters is also confirmed with a fixed physical volume. We find that the best performance is obtained when the spatial coordinates of the topological charge density are fully integrated out as a preprocessing, which implies that our convolutional NN does not find characteristic structures in multi-dimensional space relevant for the determination of the topological charge.

scholarly journals Confinement transition of ℤ2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

2018 ◽  
Vol 115 (30) ◽  
pp. E6987-E6995 ◽  
Author(s):  
Snir Gazit ◽  
Fakher F. Assaad ◽  
Subir Sachdev ◽  
Ashvin Vishwanath ◽  
Chong Wang
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Symmetry Breaking ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Gauge Theories ◽  
Square Lattice ◽  
Dirac Fermion ◽  
Topological Order ◽  
Continuous Transition

We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory that was recently shown in Monte Carlo simulations to exhibit Z2 topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with coincident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well-understood in terms of condensing magnetic flux excitations, the same transition in the presence of gapless fermions is a challenging problem owing to the statistical interactions between fermions and the condensing flux excitations. The conventional scenario then proceeds via a two-step transition, involving a symmetry-breaking transition leading to gapped fermions followed by confinement. In contrast, here, using quantum Monte Carlo simulations, we provide further evidence for a direct, continuous transition and also find numerical evidence for an enlarged SO(5) symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality. Guided by our numerical finding, we develop a field theory description of the direct transition involving an emergent nonabelian [SU(2)] gauge theory and a matrix Higgs field. We contrast our results with the conventional Gross–Neveu–Yukawa transition.

Sign in / Sign up

Export Citation Format

Share Document